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  Software design

  Software design is the process of conceptualizing how a software system will work before it is implemented or modified. Software design also refers to the direct result of the design process – the concepts of how the software will work which may be formally documented or may be maintained less formally, including via oral tradition. The design process enables a designer to model aspects of a software system before it exists with the intent of making the effort of writing the code more efficiently. Creativity, past experience, a sense of what makes "good" software, and a commitment to quality are success factors for a competent design. A software design can be compared to an architected plan for a house. High-level plans represent the totality of the house (e.g., a three-dimensional rendering of the house). Lower-level plans provide guidance for constructing each detail (e.g., the plumbing lay). Similarly, the software design model provides a variety of views of the proposed software solution. == Part of the overall process == In terms of the waterfall development process, software design is the activity that occurs after requirements analysis and before coding. Requirements analysis determines what the system needs to do without determining how it will do it, and thus, multiple designs can be imagined that satisfy the requirements. The design can be created while coding, without a plan or requirements analysis, but for more complex projects this is less feasible. Completing a design prior to coding allows for multidisciplinary designers and subject-matter experts to collaborate with programmers to produce software that is useful and technically sound. Sometimes, a simulation or prototype is created to model the system in an effort to determine a valid and good design. == Code as design == A common point of confusion with the term design in software is that the process applies at multiple levels of abstraction such as a high-level software architecture and lower-level components, functions and algorithms. A relatively formal process may occur at high levels of abstraction but at lower levels, the design process is almost always less formal where the only artifact of design may be the code itself. To the extent that this is true, software design refers to the design of the design. Edsger W. Dijkstra referred to this layering of semantic levels as the "radical novelty" of computer programming, and Donald Knuth used his experience writing TeX to describe the futility of attempting to design a program prior to implementing it: TEX would have been a complete failure if I had merely specified it and not participated fully in its initial implementation. The process of implementation constantly led me to unanticipated questions and to new insights about how the original specifications could be improved. == Artifacts == A design process may include the production of art Software design documentation such as flow chart, use case, Pseudocode, Unified Modeling Language model and other Fundamental modeling concepts. For user centered software, design may involve user experience design yielding a storyboard to help determine those specifications. Documentation may be reviewed to allow constraints, specifications and even requirements to be adjusted prior to coding. == Iterative design == Software systems inherently deal with uncertainties, and the size of software components can significantly influence a system's outcomes, both positively and negatively. Neal Ford and Mark Richards propose an iterative approach to address the challenge of identifying and right-sizing components. This method emphasizes continuous refinement as teams develop a more nuanced understanding of system behavior and requirements. The approach typically involves a cycle with several stages: A high-level partitioning strategy is established, often categorized as technical or domain-based. Guidelines for the smallest meaningful deployable unit, referred to as "quanta," are defined. While these foundational decisions are made early, they may be revisited later in the cycle if necessary. Initial components are identified based on the established strategy. Requirements are assigned to the identified components. The roles and responsibilities of each component are analyzed to ensure clarity and minimize overlap. Architectural characteristics, such as scalability, fault tolerance, and maintainability, are evaluated. Components may be restructured based on feedback from development teams. This cycle serves as a general framework and can be adapted to different domains. == Design principles == Design principles enable a software engineer to navigate the design process. Davis suggested principles which have been refined over time as: The design process should not suffer from "tunnel vision" A good designer should consider alternative approaches, judging each based on the requirements of the problem, the resources available to do the job. The design should be traceable to the analysis model Because a single element of the design model can often be traced back to multiple requirements, it is necessary to have a means for tracking how requirements have been satisfied by the design model. The design should not reinvent the wheel Systems are constructed using a set of design patterns, many of which have likely been encountered before. These patterns should always be chosen as an alternative to reinvention. Time is short and resources are limited; design time should be invested in representing (truly new) ideas by integrating patterns that already exist (when applicable). The design should "minimize the intellectual distance" between the software and the problem as it exists in the real world That is, the structure of the software design should, whenever possible, mimic the structure of the problem domain. The design should exhibit uniformity and integration A design is uniform if it appears fully coherent. In order to achieve this outcome, rules of style and format should be defined for a design team before design work begins. A design is integrated if care is taken in defining interfaces between design components. The design should be structured to accommodate change The design concepts discussed in the next section enable a design to achieve this principle. The design should be structured to degrade gently, even when aberrant data, events, or operating conditions are encountered Well-designed software should never "bomb"; it should be designed to accommodate unusual circumstances, and if it must terminate processing, it should do so in a graceful manner. Design is not coding, coding is not design Even when detailed procedural designs are created for program components, the level of abstraction of the design model is higher than the source code. The only design decisions made at the coding level should address the small implementation details that enable the procedural design to be coded. The design should be assessed for quality as it is being created, not after the fact A variety of design concepts and design measures are available to assist the designer in assessing quality throughout the development process. The design should be reviewed to minimize conceptual (semantic) errors There is sometimes a tendency to focus on minutiae when the design is reviewed, missing the forest for the trees. A design team should ensure that major conceptual elements of the design (omissions, ambiguity, inconsistency) have been addressed before worrying about the syntax of the design model. == Design concepts == Design concepts provide a designer with a foundation from which more sophisticated methods can be applied. Design concepts include: Abstraction Reducing the information content of a concept or an observable phenomenon, typically to retain only information that is relevant for a particular purpose. It is an act of Representing essential features without including the background details or explanations. Architecture The overall structure of the software and the ways in which that structure provides conceptual integrity for a system. Good software architecture will yield a good return on investment with respect to the desired outcome of the project, e.g. in terms of performance, quality, schedule and cost. Control hierarchy A program structure that represents the organization of a program component and implies a hierarchy of control. Data structure Representing the logical relationship between elements of data. Design pattern A designer may identify a design aspect of the system that has solved in the past. The reuse of such patterns can increase software development velocity. Information hiding Modules should be specified and designed so that information contained within a module is inaccessible to other modules that have no need for such information. Modularity Dividing the solution into parts (modules). Refinement The process of elaboration. A hierarchy is developed by decomposing a macrosco

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  Thompson sampling

  Thompson sampling, named after William R. Thompson, is a heuristic for choosing actions that address the exploration–exploitation dilemma in the multi-armed bandit problem. It consists of choosing the action that maximizes the expected reward with respect to a randomly drawn belief. == Description == Consider a set of contexts X {\displaystyle {\mathcal {X}}} , a set of actions A {\displaystyle {\mathcal {A}}} , and rewards in R {\displaystyle \mathbb {R} } . The aim of the player is to play actions under the various contexts, such as to maximize the cumulative rewards. Specifically, in each round, the player obtains a context x ∈ X {\displaystyle x\in {\mathcal {X}}} , plays an action a ∈ A {\displaystyle a\in {\mathcal {A}}} and receives a reward r ∈ R {\displaystyle r\in \mathbb {R} } following a distribution that depends on the context and the issued action. The elements of Thompson sampling are as follows: a likelihood function P ( r | θ , a , x ) {\displaystyle P(r|\theta ,a,x)} ; a set Θ {\displaystyle \Theta } of parameters θ {\displaystyle \theta } of the distribution of r {\displaystyle r} ; a prior distribution P ( θ ) {\displaystyle P(\theta )} on these parameters; past observations triplets D = { ( x ; a ; r ) } {\displaystyle {\mathcal {D}}=\{(x;a;r)\}} ; a posterior distribution P ( θ | D ) ∝ P ( D | θ ) P ( θ ) {\displaystyle P(\theta |{\mathcal {D}})\propto P({\mathcal {D}}|\theta )P(\theta )} , where P ( D | θ ) {\displaystyle P({\mathcal {D}}|\theta )} is the likelihood function. Thompson sampling consists of playing the action a ∗ ∈ A {\displaystyle a^{\ast }\in {\mathcal {A}}} according to the probability that it maximizes the expected reward; action a ∗ {\displaystyle a^{\ast }} is chosen with probability ∫ I [ E ( r | a ∗ , x , θ ) = max a ′ E ( r | a ′ , x , θ ) ] P ( θ | D ) d θ , {\displaystyle \int \mathbb {I} \left[\mathbb {E} (r|a^{\ast },x,\theta )=\max _{a'}\mathbb {E} (r|a',x,\theta )\right]P(\theta |{\mathcal {D}})d\theta ,} where I {\displaystyle \mathbb {I} } is the indicator function. In practice, the rule is implemented by sampling. In each round, parameters θ ∗ {\displaystyle \theta ^{\ast }} are sampled from the posterior P ( θ | D ) {\displaystyle P(\theta |{\mathcal {D}})} , and an action a ∗ {\displaystyle a^{\ast }} chosen that maximizes E [ r | θ ∗ , a ∗ , x ] {\displaystyle \mathbb {E} [r|\theta ^{\ast },a^{\ast },x]} , i.e. the expected reward given the sampled parameters, the action, and the current context. Conceptually, this means that the player instantiates their beliefs randomly in each round according to the posterior distribution, and then acts optimally according to them. In most practical applications, it is computationally onerous to maintain and sample from a posterior distribution over models. As such, Thompson sampling is often used in conjunction with approximate sampling techniques. == History == Thompson sampling was originally described by Thompson in 1933. It was subsequently rediscovered numerous times independently in the context of multi-armed bandit problems. A first proof of convergence for the bandit case has been shown in 1997. The first application to Markov decision processes was in 2000. A related approach (see Bayesian control rule) was published in 2010. In 2010 it was also shown that Thompson sampling is instantaneously self-correcting. Asymptotic convergence results for contextual bandits were published in 2011. Thompson Sampling has been widely used in many online learning problems including A/B testing in website design and online advertising, and accelerated learning in decentralized decision making. A Double Thompson Sampling (D-TS) algorithm has been proposed for dueling bandits, a variant of traditional MAB, where feedback comes in the form of pairwise comparison. == Relationship to other approaches == === Probability matching === Probability matching is a decision strategy in which predictions of class membership are proportional to the class base rates. Thus, if in the training set positive examples are observed 60% of the time, and negative examples are observed 40% of the time, the observer using a probability-matching strategy will predict (for unlabeled examples) a class label of "positive" on 60% of instances, and a class label of "negative" on 40% of instances. === Bayesian control rule === A generalization of Thompson sampling to arbitrary dynamical environments and causal structures, known as Bayesian control rule, has been shown to be the optimal solution to the adaptive coding problem with actions and observations. In this formulation, an agent is conceptualized as a mixture over a set of behaviours. As the agent interacts with its environment, it learns the causal properties and adopts the behaviour that minimizes the relative entropy to the behaviour with the best prediction of the environment's behaviour. If these behaviours have been chosen according to the maximum expected utility principle, then the asymptotic behaviour of the Bayesian control rule matches the asymptotic behaviour of the perfectly rational agent. The setup is as follows. Let a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} be the actions issued by an agent up to time T {\displaystyle T} , and let o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} be the observations gathered by the agent up to time T {\displaystyle T} . Then, the agent issues the action a T + 1 {\displaystyle a_{T+1}} with probability: P ( a T + 1 | a ^ 1 : T , o 1 : T ) , {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T}),} where the "hat"-notation a ^ t {\displaystyle {\hat {a}}_{t}} denotes the fact that a t {\displaystyle a_{t}} is a causal intervention (see Causality), and not an ordinary observation. If the agent holds beliefs θ ∈ Θ {\displaystyle \theta \in \Theta } over its behaviors, then the Bayesian control rule becomes P ( a T + 1 | a ^ 1 : T , o 1 : T ) = ∫ Θ P ( a T + 1 | θ , a ^ 1 : T , o 1 : T ) P ( θ | a ^ 1 : T , o 1 : T ) d θ {\displaystyle P(a_{T+1}|{\hat {a}}_{1:T},o_{1:T})=\int _{\Theta }P(a_{T+1}|\theta ,{\hat {a}}_{1:T},o_{1:T})P(\theta |{\hat {a}}_{1:T},o_{1:T})\,d\theta } , where P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} is the posterior distribution over the parameter θ {\displaystyle \theta } given actions a 1 : T {\displaystyle a_{1:T}} and observations o 1 : T {\displaystyle o_{1:T}} . In practice, the Bayesian control amounts to sampling, at each time step, a parameter θ ∗ {\displaystyle \theta ^{\ast }} from the posterior distribution P ( θ | a ^ 1 : T , o 1 : T ) {\displaystyle P(\theta |{\hat {a}}_{1:T},o_{1:T})} , where the posterior distribution is computed using Bayes' rule by only considering the (causal) likelihoods of the observations o 1 , o 2 , … , o T {\displaystyle o_{1},o_{2},\ldots ,o_{T}} and ignoring the (causal) likelihoods of the actions a 1 , a 2 , … , a T {\displaystyle a_{1},a_{2},\ldots ,a_{T}} , and then by sampling the action a T + 1 ∗ {\displaystyle a_{T+1}^{\ast }} from the action distribution P ( a T + 1 | θ ∗ , a ^ 1 : T , o 1 : T ) {\displaystyle P(a_{T+1}|\theta ^{\ast },{\hat {a}}_{1:T},o_{1:T})} . === Upper-confidence-bound (UCB) algorithms === Thompson sampling and upper-confidence bound algorithms share a fundamental property that underlies many of their theoretical guarantees. Roughly speaking, both algorithms allocate exploratory effort to actions that might be optimal and are in this sense "optimistic". Leveraging this property, one can translate regret bounds established for UCB algorithms to Bayesian regret bounds for Thompson sampling or unify regret analysis across both these algorithms and many classes of problems.

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  Random-fuzzy variable

  In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. Statistical methods can be used to calculate the total uncertainty from both systematic and random contributions in a measurement. However, the computational complexity is very high, and hence not desirable. L.A.Zadeh introduced the concepts of fuzzy variables and fuzzy sets. Fuzzy variables are based on the theory of possibility and hence are possibility distributions. This makes them suitable to handle any type of uncertainty, i.e., both systematic and random contributions to the total uncertainty. Random-fuzzy variable (RFV) is a type 2 fuzzy variable, defined using the mathematical possibility theory, used to represent the entire information associated to a measurement result. It has an internal possibility distribution and an external possibility distribution called membership functions. The internal distribution is the uncertainty contributions due to the systematic uncertainty and the bounds of the RFV are because of the random contributions. The external distribution gives the uncertainty bounds from all contributions. == Definition == A random-fuzzy Variable (RFV) is defined as a type 2 fuzzy variable which satisfies the following conditions: Both the internal and the external functions of the RFV can be identified. Both the internal and the external functions are modeled as possibility distributions (PD). Both the internal and external functions have a unitary value for possibility to the same interval of values. An RFV can be seen in the figure. The external membership function is the distribution in blue and the internal membership function is the distribution in red. Both the membership functions are possibility distributions. Both the internal and external membership functions have a unitary value of possibility only in the rectangular part of the RFV. Therefore, all three conditions have been satisfied. If there are only systematic errors in the measurement, then the RFV simply becomes a fuzzy variable which consists of just the internal membership function. Similarly, if there is no systematic error, then the RFV becomes a fuzzy variable with just the random contributions and therefore, is just the possibility distribution of the random contributions. == Construction == A random-fuzzy variable can be constructed using an internal possibility distribution (rinternal) and a random possibility distribution (rrandom). === The random distribution (rrandom) === rrandom is the possibility distribution of the random contributions to the uncertainty. Any measurement instrument or process suffers from random error contributions due to intrinsic noise or other effects. This is completely random in nature and is a normal probability distribution when several random contributions are combined according to the central limit theorem. However, there can also be random contributions from other probability distributions, such as a uniform distribution, gamma distribution and so on. The probability distribution can be modeled from the measurement data. Then, the probability distribution can be used to model an equivalent possibility distribution using the maximally specific probability-possibility transformation. Some common probability distributions and the corresponding possibility distributions can be seen in the figures. === The internal distribution (rinternal) === rinternal is the internal distribution in the RFV which is the possibility distribution of the systematic contribution to the total uncertainty. This distribution can be built based on the information that is available about the measuring instrument and the process. The largest possible distribution is the uniform or rectangular possibility distribution. This means that every value in the specified interval is equally possible. This actually represents the state of total ignorance according to the theory of evidence which means it represents a scenario in which there is maximum lack of information. This distribution is used for the systematic error when we have absolutely no idea about the systematic error except that it belongs to a particular interval of values. This is quite common in measurements. However, in certain cases, it may be known that certain values have a higher or lower degrees of belief than certain other values. In this case, depending on the degrees of belief for the values, an appropriate possibility distribution could be constructed. === The construction of the external distribution (rexternal) and the RFV === After modeling the random and internal possibility distribution, the external membership function, rexternal, of the RFV can be constructed by using the following equation: where x ∗ {\displaystyle x^{}} is the mode of r random {\displaystyle r_{\textit {random}}} , which is the peak in the membership function of r r a n d o m {\displaystyle r_{random}} and Tmin is the minimum triangular norm. RFV can also be built from the internal and random distributions by considering the α-cuts of the two possibility distributions (PDs). An α-cut of a fuzzy variable F can be defined as Therefore, essentially an α-cut is the set of values for which the value of the membership function μ F ( a ) {\displaystyle \mu _{\rm {F}}(a)} of the fuzzy variable is greater than α. This gives the upper and lower bounds of the fuzzy variable F for each α-cut. The α-cut of an RFV, however, has 4 specific bounds and is given by R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} . X a α {\displaystyle X_{a}^{\alpha }} and X d α {\displaystyle X_{d}^{\alpha }} are the lower and upper bounds respectively of the external membership function (rexternal) which is a fuzzy variable on its own. X b α {\displaystyle X_{b}^{\alpha }} and X c α {\displaystyle X_{c}^{\alpha }} are the lower and upper bounds respectively of the internal membership function (rinternal) which is a fuzzy variable on its own. To build the RFV, let us consider the α-cuts of the two PDs i.e., rrandom and rinternal for the same value of α. This gives the lower and upper bounds for the two α-cuts. Let them be [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} and [ X L I α , X U I α ] {\displaystyle [X_{LI}^{\alpha },X_{UI}^{\alpha }]} for the random and internal distributions respectively. [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} can be again divided into two sub-intervals [ X L R α , x ∗ ] {\displaystyle [X_{LR}^{\alpha },x^{}]} and [ x ∗ , X U R α ] {\displaystyle [x^{},X_{UR}^{\alpha }]} where x ∗ {\displaystyle x^{}} is the mode of the fuzzy variable. Then, the α-cut for the RFV for the same value of α, R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} can be defined by Using the above equations, the α-cuts are calculated for every value of α which gives us the final plot of the RFV. A random-fuzzy variable is capable of giving a complete picture of the random and systematic contributions to the total uncertainty from the α-cuts for any confidence level as the confidence level is nothing but 1-α. An example for the construction of the corresponding external membership function (rexternal) and the RFV from a random PD and an internal PD can be seen in the following figure.

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  Random-fuzzy variable

  In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. Statistical methods can be used to calculate the total uncertainty from both systematic and random contributions in a measurement. However, the computational complexity is very high, and hence not desirable. L.A.Zadeh introduced the concepts of fuzzy variables and fuzzy sets. Fuzzy variables are based on the theory of possibility and hence are possibility distributions. This makes them suitable to handle any type of uncertainty, i.e., both systematic and random contributions to the total uncertainty. Random-fuzzy variable (RFV) is a type 2 fuzzy variable, defined using the mathematical possibility theory, used to represent the entire information associated to a measurement result. It has an internal possibility distribution and an external possibility distribution called membership functions. The internal distribution is the uncertainty contributions due to the systematic uncertainty and the bounds of the RFV are because of the random contributions. The external distribution gives the uncertainty bounds from all contributions. == Definition == A random-fuzzy Variable (RFV) is defined as a type 2 fuzzy variable which satisfies the following conditions: Both the internal and the external functions of the RFV can be identified. Both the internal and the external functions are modeled as possibility distributions (PD). Both the internal and external functions have a unitary value for possibility to the same interval of values. An RFV can be seen in the figure. The external membership function is the distribution in blue and the internal membership function is the distribution in red. Both the membership functions are possibility distributions. Both the internal and external membership functions have a unitary value of possibility only in the rectangular part of the RFV. Therefore, all three conditions have been satisfied. If there are only systematic errors in the measurement, then the RFV simply becomes a fuzzy variable which consists of just the internal membership function. Similarly, if there is no systematic error, then the RFV becomes a fuzzy variable with just the random contributions and therefore, is just the possibility distribution of the random contributions. == Construction == A random-fuzzy variable can be constructed using an internal possibility distribution (rinternal) and a random possibility distribution (rrandom). === The random distribution (rrandom) === rrandom is the possibility distribution of the random contributions to the uncertainty. Any measurement instrument or process suffers from random error contributions due to intrinsic noise or other effects. This is completely random in nature and is a normal probability distribution when several random contributions are combined according to the central limit theorem. However, there can also be random contributions from other probability distributions, such as a uniform distribution, gamma distribution and so on. The probability distribution can be modeled from the measurement data. Then, the probability distribution can be used to model an equivalent possibility distribution using the maximally specific probability-possibility transformation. Some common probability distributions and the corresponding possibility distributions can be seen in the figures. === The internal distribution (rinternal) === rinternal is the internal distribution in the RFV which is the possibility distribution of the systematic contribution to the total uncertainty. This distribution can be built based on the information that is available about the measuring instrument and the process. The largest possible distribution is the uniform or rectangular possibility distribution. This means that every value in the specified interval is equally possible. This actually represents the state of total ignorance according to the theory of evidence which means it represents a scenario in which there is maximum lack of information. This distribution is used for the systematic error when we have absolutely no idea about the systematic error except that it belongs to a particular interval of values. This is quite common in measurements. However, in certain cases, it may be known that certain values have a higher or lower degrees of belief than certain other values. In this case, depending on the degrees of belief for the values, an appropriate possibility distribution could be constructed. === The construction of the external distribution (rexternal) and the RFV === After modeling the random and internal possibility distribution, the external membership function, rexternal, of the RFV can be constructed by using the following equation: where x ∗ {\displaystyle x^{}} is the mode of r random {\displaystyle r_{\textit {random}}} , which is the peak in the membership function of r r a n d o m {\displaystyle r_{random}} and Tmin is the minimum triangular norm. RFV can also be built from the internal and random distributions by considering the α-cuts of the two possibility distributions (PDs). An α-cut of a fuzzy variable F can be defined as Therefore, essentially an α-cut is the set of values for which the value of the membership function μ F ( a ) {\displaystyle \mu _{\rm {F}}(a)} of the fuzzy variable is greater than α. This gives the upper and lower bounds of the fuzzy variable F for each α-cut. The α-cut of an RFV, however, has 4 specific bounds and is given by R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} . X a α {\displaystyle X_{a}^{\alpha }} and X d α {\displaystyle X_{d}^{\alpha }} are the lower and upper bounds respectively of the external membership function (rexternal) which is a fuzzy variable on its own. X b α {\displaystyle X_{b}^{\alpha }} and X c α {\displaystyle X_{c}^{\alpha }} are the lower and upper bounds respectively of the internal membership function (rinternal) which is a fuzzy variable on its own. To build the RFV, let us consider the α-cuts of the two PDs i.e., rrandom and rinternal for the same value of α. This gives the lower and upper bounds for the two α-cuts. Let them be [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} and [ X L I α , X U I α ] {\displaystyle [X_{LI}^{\alpha },X_{UI}^{\alpha }]} for the random and internal distributions respectively. [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} can be again divided into two sub-intervals [ X L R α , x ∗ ] {\displaystyle [X_{LR}^{\alpha },x^{}]} and [ x ∗ , X U R α ] {\displaystyle [x^{},X_{UR}^{\alpha }]} where x ∗ {\displaystyle x^{}} is the mode of the fuzzy variable. Then, the α-cut for the RFV for the same value of α, R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} can be defined by Using the above equations, the α-cuts are calculated for every value of α which gives us the final plot of the RFV. A random-fuzzy variable is capable of giving a complete picture of the random and systematic contributions to the total uncertainty from the α-cuts for any confidence level as the confidence level is nothing but 1-α. An example for the construction of the corresponding external membership function (rexternal) and the RFV from a random PD and an internal PD can be seen in the following figure.

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  Coherent extrapolated volition

  Coherent extrapolated volition (CEV) is a theoretical framework in the field of AI alignment describing an approach by which an artificial superintelligence (ASI) would act on a benevolent supposition of what humans would want if they were more knowledgeable, more rational, had more time to think, and had matured together as a society, as opposed to humanity's current individual or collective preferences. It was proposed by Eliezer Yudkowsky in 2004 as part of his work on friendly AI. == Concept == CEV proposes that an advanced AI system should derive its goals by extrapolating the idealized volition of humanity. This means aggregating and projecting human preferences into a coherent utility function that reflects what people would desire under ideal epistemic and moral conditions. The aim is to ensure that AI systems are aligned with humanity's true interests, rather than with transient or poorly informed preferences. In poetic terms, our coherent extrapolated volition is our wish if we knew more, thought faster, were more the people we wished we were, had grown up farther together; where the extrapolation converges rather than diverges, where our wishes cohere rather than interfere; extrapolated as we wish that extrapolated, interpreted as we wish that interpreted. == Debate == Yudkowsky and Nick Bostrom note that CEV has several interesting properties. It is designed to be humane and self-correcting, by capturing the source of human values instead of trying to list them. It avoids the difficulty of laying down an explicit, fixed list of rules. It encapsulates moral growth, preventing flawed current moral beliefs from getting locked in. It limits the influence that a small group of programmers can have on what the ASI would value, thus also reducing the incentives to build ASI first. And it keeps humanity in charge of its destiny. CEV also faces significant theoretical and practical challenges. Bostrom notes that CEV has "a number of free parameters that could be specified in various ways, yielding different versions of the proposal." One such parameter is the extrapolation base (whose extrapolated volition is taken into account). For example, whether it should include people with severe dementia, patients in a vegetative state, foetuses, or embryos. He also notes that if CEV's extrapolation base only includes humans, there is a risk that the result would be ungenerous toward other animals and digital minds. One possible solution would be to include a mechanism to expand CEV's extrapolation base. == Variants and alternatives == A proposed theoretical alternative to CEV is to rely on an artificial superintelligence's superior cognitive capabilities to figure out what is morally right, and let it act accordingly. It is also possible to combine both techniques, for instance with the ASI following CEV except when it is morally impermissible. In another review, a philosophical analysis explores CEV through the lens of social trust in autonomous systems. Drawing on Anthony Giddens' concept of "active trust", the author proposes an evolution of CEV into "Coherent, Extrapolated and Clustered Volition" (CECV). This formulation aims to better reflect the moral preferences of diverse cultural groups, thus offering a more pragmatic ethical framework for designing AI systems that earn public trust while accommodating societal diversity.

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  Content-based image retrieval

  Content-based image retrieval, also known as query by image content (QBIC) and content-based visual information retrieval (CBVIR), is the application of computer vision techniques to the image retrieval problem, that is, the problem of searching for digital images in large databases (see this survey for a scientific overview of the CBIR field). Content-based image retrieval is opposed to traditional concept-based approaches (see Concept-based image indexing). "Content-based" means that the search analyzes the contents of the image rather than the metadata such as keywords, tags, or descriptions associated with the image. The term "content" in this context might refer to colors, shapes, textures, or any other information that can be derived from the image itself. CBIR is desirable because searches that rely purely on metadata are dependent on annotation quality and completeness. == Comparison with metadata searching == An image meta search requires humans to have manually annotated images by entering keywords or metadata in a large database, which can be time-consuming and may not capture the keywords desired to describe the image. The evaluation of the effectiveness of keyword image search is subjective and has not been well-defined. In the same regard, CBIR systems have similar challenges in defining success. "Keywords also limit the scope of queries to the set of predetermined criteria." and, "having been set up" are less reliable than using the content itself. == History == The term "content-based image retrieval" seems to have originated in 1992 when it was used by Japanese Electrotechnical Laboratory engineer Toshikazu Kato to describe experiments into automatic retrieval of images from a database, based on the colors and shapes present. Since then, the term has been used to describe the process of retrieving desired images from a large collection on the basis of syntactical image features. The techniques, tools, and algorithms that are used originate from fields such as statistics, pattern recognition, signal processing, and computer vision. === QBIC - Query By Image Content === The earliest commercial CBIR system was developed by IBM and was called QBIC (Query By Image Content). Recent network- and graph-based approaches have presented a simple and attractive alternative to existing methods. While the storing of multiple images as part of a single entity preceded the term BLOB (Binary Large OBject), the ability to fully search by content, rather than by description, had to await IBM's QBIC. === VisualRank === == Technical progress == The interest in CBIR has grown because of the limitations inherent in metadata-based systems, as well as the large range of possible uses for efficient image retrieval. Textual information about images can be easily searched using existing technology, but this requires humans to manually describe each image in the database. This can be impractical for very large databases or for images that are generated automatically, e.g. those from surveillance cameras. It is also possible to miss images that use different synonyms in their descriptions. Systems based on categorizing images in semantic classes like "cat" as a subclass of "animal" can avoid the miscategorization problem, but will require more effort by a user to find images that might be "cats", but are only classified as an "animal". Many standards have been developed to categorize images, but all still face scaling and miscategorization issues. Initial CBIR systems were developed to search databases based on image color, texture, and shape properties. After these systems were developed, the need for user-friendly interfaces became apparent. Therefore, efforts in the CBIR field started to include human-centered design that tried to meet the needs of the user performing the search. This typically means inclusion of: query methods that may allow descriptive semantics, queries that may involve user feedback, systems that may include machine learning, and systems that may understand user satisfaction levels. == Techniques == Many CBIR systems have been developed, but as of 2006, the problem of retrieving images on the basis of their pixel content remains largely unsolved. Different query techniques and implementations of CBIR make use of different types of user queries. === Query By Example === QBE (Query By Example) is a query technique that involves providing the CBIR system with an example image that it will then base its search upon. The underlying search algorithms may vary depending on the application, but result images should all share common elements with the provided example. Options for providing example images to the system include: A preexisting image may be supplied by the user or chosen from a random set. The user draws a rough approximation of the image they are looking for, for example with blobs of color or general shapes. This query technique removes the difficulties that can arise when trying to describe images with words. === Semantic retrieval === Semantic retrieval starts with a user making a request like "find pictures of Abraham Lincoln". This type of open-ended task is very difficult for computers to perform - Lincoln may not always be facing the camera or in the same pose. Many CBIR systems therefore generally make use of lower-level features like texture, color, and shape. These features are either used in combination with interfaces that allow easier input of the criteria or with databases that have already been trained to match features (such as faces, fingerprints, or shape matching). However, in general, image retrieval requires human feedback in order to identify higher-level concepts. === Relevance feedback (human interaction) === Combining CBIR search techniques available with the wide range of potential users and their intent can be a difficult task. An aspect of making CBIR successful relies entirely on the ability to understand the user intent. CBIR systems can make use of relevance feedback, where the user progressively refines the search results by marking images in the results as "relevant", "not relevant", or "neutral" to the search query, then repeating the search with the new information. Examples of this type of interface have been developed. === Iterative/machine learning === Machine learning and application of iterative techniques are becoming more common in CBIR. === Other query methods === Other query methods include browsing for example images, navigating customized/hierarchical categories, querying by image region (rather than the entire image), querying by multiple example images, querying by visual sketch, querying by direct specification of image features, and multimodal queries (e.g. combining touch, voice, etc.) == Content comparison using image distance measures == The most common method for comparing two images in content-based image retrieval (typically an example image and an image from the database) is using an image distance measure. An image distance measure compares the similarity of two images in various dimensions such as color, texture, shape, and others. For example, a distance of 0 signifies an exact match with the query, with respect to the dimensions that were considered. As one may intuitively gather, a value greater than 0 indicates various degrees of similarities between the images. Search results then can be sorted based on their distance to the queried image. Many measures of image distance (Similarity Models) have been developed. === Color === Computing distance measures based on color similarity is achieved by computing a color histogram for each image that identifies the proportion of pixels within an image holding specific values. Examining images based on the colors they contain is one of the most widely used techniques because it can be completed without regard to image size or orientation. However, research has also attempted to segment color proportion by region and by spatial relationship among several color regions. === Texture === Texture measures look for visual patterns in images and how they are spatially defined. Textures are represented by texels which are then placed into a number of sets, depending on how many textures are detected in the image. These sets not only define the texture, but also where in the image the texture is located. Texture is a difficult concept to represent. The identification of specific textures in an image is achieved primarily by modeling texture as a two-dimensional gray level variation. The relative brightness of pairs of pixels is computed such that degree of contrast, regularity, coarseness and directionality may be estimated. The problem is in identifying patterns of co-pixel variation and associating them with particular classes of textures such as silky, or rough. Other methods of classifying textures include: Co-occurrence matrix Laws texture energy Wavelet transform Orthogonal transforms (discrete Chebyshev moments) =

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  Gundam Build Metaverse

  Gundam Build Metaverse (Japanese: ガンダムビルドメタバース, Hepburn: Gandamu Birudo Metabāzu) is a Japanese original net animation anime mini-series produced by Sunrise Beyond, and the fifth series within the Gundam Build Series sub-series. The series celebrates the 10th anniversary of the Gundam Build franchise, including characters from the previous installments. == Plot == The story is set in the same universe of the Gundam Build series in an online metaverse space where users can use avatars to move around and interact with other users, including conducting Gunpla (Gundam plastic model) battles with them. The story centers on Rio Hōjō, a boy who lives in Hawaii, and who learns how to build Gunpla from a local hobbyist named Seria Urutsuki. In the metaverse, a figure known as Mask Lady teaches him the art of Gunpla battling, and he strives to get better at it every day. With his custom Lah Gundam, he seeks out ever stronger opponents. == Characters == === Main characters === Rio Hojo (ホウジョウ・リオ, Hōjō Rio) Voiced by: Chika Anzai A young boy from Hawaii who is an enthusiast of Gunpla Battle and is an apprentice of the mysterious Diver "Mask Lady". Rio's Gunpla is the Lah Gundam, modeled after an entry-grade RX-78-2 Gundam, from the original Mobile Suit Gundam anime series. Seria Urutsuki (ウルツキ・セリア, Urutsuki Seria) / Mask Lady (マスクレディー, Masuku Reidi) Voiced by: Rio Tsuchiya A clerk at a local hobby shop and the instructor at their Gunpla class, Seria becomes Rio's Gunpla mentor using the alias "Mask Lady". Seria's Gunpla is the ZGMF-X20A-PF Gundam Perfect Strike Freedom Rouge, based on both the MBF-02 Strike Rouge and the GAT-X105+AQM/E-YM1 Perfect Strike Gundam from Mobile Suit Gundam Seed and the ZGMF-X20A Strike Freedom Gundam from Mobile Suit Gundam Seed Destiny. === Returning characters === Fumina Hoshino (ホシノ・フミナ, Hoshino Fumina) Voiced by: Yui Makino A veteran Gunpla Battler from the early days of the sport and the Leader of "Team Try Fighters", she works as an advertiser and announcer within the Metaverse realm. Tatsuya Yuuki (ユウキ・タツヤ, Yūki Tatsuya) / Meijin Kawaguchi III (三代目メイジン・カワグチ, Sandaime Meijin Kawaguchi) Voiced by: Takuya Satō A builder and three-times Gunpla Battle world champion who inherited the name of the legendary Meijin Kawaguchi, known as "Meijin Kawaguchi III", and still the current title holder. His newest Gunpla is the Gundam Amazing Barbatos Lupus based on the ASW-G-08 Gundam Barbatos Lupus from Mobile Suit Gundam: Iron-Blooded Orphans. Riku Mikami (ミカミ・リク, Mikami Riku) / Riku (リク) Voiced by: Yūsuke Kobayashi The Founder and former leader of the legendary force, "Build Divers". His Gunpla is the Gundam 00 Diver Arc, the latest version of the original GN-0000DVR Gundam 00 Diver from Gundam Build Divers, incorporating elements from the 00 Gundam from Mobile Suit Gundam 00 and the Gundam AGE-FX from Mobile Suit Gundam AGE. Sarah (サラ, Sara) Voiced by: Haruka Terui An EL-Diver and member of the Build Divers. Momoka Yashiro (ヤシロ・モモカ, Yashiro Momoka) / Momo (モモ) Voiced by: Nene Hieda Member of Build Divers. Her gunpla is the MOMOKAPOOL (R×R), an upgraded version of her PEN-01M Momokapool from Gundam Build Divers Aya Fujisawa (フジサワ・アヤ, Fujisawa Aya) / Ayame (アヤメ) Voiced by: Manami Numakura Member of Build Divers. Her Gunpla is the F-Kunoichi Kai, an SD Gunpla based on the F91 Gundam F91 from Mobile Suit Gundam F91. Sei Iori (イオリ・セイ, Iori Sei) Voiced by: Mikako Komatsu A builder and one time Gunpla Battle World Champion. His current Gunpla is the GAT-X105B/EG Build Strike Exceed Galaxy, the latest version of the original GAT-X105B Build Strike Gundam from Gundam Build Fighters. Aria von Reiji Asuna (アリーア・フォン・レイジ・アスナ, Arīa fon Reiji Asuna) Voiced by: Sachi Kokuryu A prince from the country called Arian that exists within a space colony in another dimension, who became friends with Sei Iori and together won the Gunpla Battle World Championship. He somehow manages to log into the metaverse to reunite with his friend, piloting the SB-011 Star Burning Gundam. Sekai Kamiki (カミキ・セカイ, Kamiki Sekai) Voiced by: Kazumi Togashi A veteran builder and former member of Team Try Fighters. He is currently the Japanese National representative Champion. In the series he develops a rivalry relationship with Hiroto similar to that of Kyoya and Rommel. His current Gunpla is the Shin Burning Gundam, the latest version of the original KMK-B01 Kamiki Burning Gundam from Gundam Build Fighters Try which is based on the Burning Gundam and Master Gundam. Hiroto Kuga (クガ・ヒロト, Kuga Hiroto) / Hiroto (ヒロト, Hiroto) Voiced by: Chiaki Kobayashi A veteran diver, the one responsible for discovering more EL-Divers, and a former member of the legendary force "Avalon", who later joined the unofficial, "BUILD DiVERS" and eventually became the current Force Leader, and as well as the current title holder of "Hero of Gunpla". In the third episode he is the only Build Diver member who participates in the tournament, while his fellow force-mates are in the audience routing for him and Rio. His Gunpla is the Plutine Gundam, which is a combination of his Core Gundam II Plus, upgraded from the Core Gundam II featured in Gundam Build Divers Re:Rise equipped with the Pluto Armor. Magee (マギー, Magī) Voiced by: Taishi Murata A flamboyant veteran Diver who owns a shop in the metaverse and is an acquaintance of Seria's. Freddie (フレディ, Furedi) Voiced by: Ai Kakuma An alien anthropomorphic dog boy from planet Eldora, a support member to both Build Diver teams, who manages to access the metaverse from his home planet along his fellow Eldorans. Ogre (オーガ, Ōga) Voiced by: Wataru Hatano Kyoya Kisugi (キスギ・キョウヤ, Kisugi Kyōya) / Kyoya Kujo (クジョウ・キョウヤ, Kujō Kyōya) Voiced by: Jun Kasama Leader of the legendary force "Avalon" and the reigning and current title holder of "World Champion". He along with Hiroto Kuga, Maria Urutsuki, and Tatsuya Yuuki are currently at the top of the entire gunpla world community. His current gunpla is an recolored version of his AGE-TRYMAG Gundam TRY AGE Magnum from Gundam Build Divers Re:Rise. Susumu Sazaki (サザキ・ススム, Sazaki Susumu) Voiced by: Ryo Hirohashi Kaoruko Sazaki (サザキ・カオルコ, Sazaki Kaoruko) Voiced by: Ryo Hirohashi Mahiru Shigure (シグレ・マヒル, Shigure Mahiru) Voiced by: Rinko Natsuhi Keiko Sano (サノ・ケイコ, Sano Keiko) Voiced by: Ami Naito === Others === Maria Urutsuki (ウルツキ・マリア, Urutsuki Maria) / Mascarilla (マスカリージャ, Masukarīja) Voiced by: Ai Kakuma A mysterious masked woman with a harsh rivalry with Seria and a similar avatar as hers, she is later revealed as Seria's younger sister Maria, who began to loathe her sister after she quit on their dream to fight for the title of Lady Kawaguchi. She later obtains the title, becoming "Lady Kawaguchi VII". Jeff (ジェフさん, Jefu-san) Voiced by: Kenta Miyake A distant relative of Seria and Maria's and owner of the hobby shop where Seria lives. Mellow Neige (メロウ・ネージュ, Merō Nēju) Voiced by: Chikano Ibuki A sentient A.I. who is the current publicity face of the Gunpla Metaverse. == Episodes ==

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  Computational law

  Computational law is the branch of legal informatics concerned with the automation of legal reasoning. What distinguishes Computational Law systems from other instances of legal technology is their autonomy, i.e. the ability to answer legal questions without additional input from human legal experts. While there are many possible applications of Computational Law, the primary focus of work in the field today is compliance management, i.e. the development and deployment of computer systems capable of assessing, facilitating, or enforcing compliance with rules and regulations. Some systems of this sort already exist. TurboTax is a good example. And the potential is particularly significant now due to recent technological advances – including the prevalence of the Internet in human interaction and the proliferation of embedded computer systems (such as smart phones, self-driving cars, and robots). There are also applications that do not involve governmental laws. The regulations can just as well be the terms of contracts (e.g. delivery schedules, insurance covenants, real estate transactions, financial agreements). They can be the policies of corporations (e.g. constraints on travel, expenditure reporting, pricing rules). They can even be the rules of games (embodied in computer game playing systems). == History == Speculation about potential benefits to legal practice through applying methods from computational science and AI research to automate parts of the law date back at least to the middle 1940s. Further, AI and law and computational law do not seem easily separable, as perhaps most of AI research focusing on the law and its automation appears to utilize computational methods. The forms that speculation took are multiple and not all related in ways to readily show closeness to one another. This history will sketch them as they were, attempting to show relationships where they can be found to have existed. By 1949, a minor academic field aiming to incorporate electronic and computational methods to legal problems had been founded by American legal scholars, called jurimetrics. Though broadly said to be concerned with the application of the "methods of science" to the law, these methods were actually of a quite specifically defined scope. Jurimetrics was to be "concerned with such matters as the quantitative analysis of judicial behavior, the application of communication and information theory to legal expression, the use of mathematical logic in law, the retrieval of legal data by electronic and mechanical means, and the formulation of a calculus of legal predictability". These interests led in 1959 to the founding a journal, Modern Uses of Logic in Law, as a forum wherein articles would be published about the applications of techniques such as mathematical logic, engineering, statistics, etc. to the legal study and development. In 1966, this Journal was renamed as Jurimetrics. Today, however, the journal and meaning of jurimetrics seems to have broadened far beyond what would fit under the areas of applications of computers and computational methods to law. Today the journal not only publishes articles on such practices as found in computational law, but has broadened jurimetrical concerns to mean also things like the use of social science in law or the "policy implications [of] and legislative and administrative control of science". Independently in 1958, at the Conference for the Mechanization of Thought held at the National Physical Laboratory in Teddington, Middlesex, UK, the French jurist Lucien Mehl presented a paper both on the benefits of using computational methods for law and on the potential means to use such methods to automate law for a discussion that included AI luminaries like Marvin Minsky. Mehl believed that the law could by automated by two basic distinct, though not wholly separable, types of machine. These were the "documentary or information machine", which would provide the legal researcher quick access to relevant case precedents and legal scholarship, and the "consultation machine", which would be "capable of answering any question put to it over a vast field of law". The latter type of machine would be able to basically do much of a lawyer's job by simply giving the "exact answer to a [legal] problem put to it". By 1970, Mehl's first type of machine, one that would be able to retrieve information, had been accomplished but there seems to have been little consideration of further fruitful intersections between AI and legal research. There were, however, still hopes that computers could model the lawyer's thought processes through computational methods and then apply that capacity to solve legal problems, thus automating and improving legal services via increased efficiency as well as shedding light on the nature of legal reasoning. By the late 1970s, computer science and the affordability of computer technology had progressed enough that the retrieval of "legal data by electronic and mechanical means" had been achieved by machines fitting Mehl's first type and were in common use in American law firms. During this time, research focused on improving the goals of the early 1970s occurred, with programs like Taxman being worked on in order to both bring useful computer technology into the law as practical aids and to help specify the exact nature of legal concepts. Nonetheless, progress on the second type of machine, one that would more fully automate the law, remained relatively inert. Research into machines that could answer questions in the way that Mehl's consultation machine would picked up somewhat in the late 1970s and 1980s. A 1979 convention in Swansea, Wales marked the first international effort solely to focus upon applying artificial intelligence research to legal problems in order to "consider how computers can be used to discover and apply the legal norms embedded within the written sources of the law". Considerable progress on the development of the second type of machine was made in the following decade, with the development of a variety of expert systems. According to Thorne McCarty, "these systems all have the following characteristics: They do backward chaining inference from a specified goal; they ask questions to elicit information from the user; and they produce a suggested answer along with a trace of the supporting legal rules." According to Prakken and Sartor the representation of the British Nationality Act as a logic program, which introduced this approach, was "hugely influential for the development of computational representations of legislation, showing how logic programming enables intuitively appealing representations that can be directly deployed to generate automatic inferences". In 2021, this work received the Inaugural CodeX Prize as "one of the first and best-known works in computational law, and one of the most widely cited papers in the field." In a 1988 review of Anne Gardner's book An Artificial Intelligence Approach to Legal Reasoning (1987), the Harvard academic legal scholar and computer scientist Edwina Rissland wrote that "She plays, in part, the role of pioneer; artificial intelligence ("AI") techniques have not yet been widely applied to perform legal tasks. Therefore, Gardner, and this review, first describe and define the field, then demonstrate a working model in the domain of contract offer and acceptance." Eight years after the Swansea conference had passed, and still AI and law researchers merely trying to delineate the field could be described by their own kind as "pioneer[s]". In the 1990s and early 2000s more progress occurred. Computational research generated insights for law. The First International Conference on AI and the Law occurred in 1987, but it is in the 1990s and 2000s that the biannual conference began to build up steam and to delve more deeply into the issues involved with work intersecting computational methods, AI, and law. Classes began to be taught to undergraduates on the uses of computational methods to automating, understanding, and obeying the law. Further, by 2005, a team largely composed of Stanford computer scientists from the Stanford Logic group had devoted themselves to studying the uses of computational techniques to the law. Computational methods in fact advanced enough that members of the legal profession began in the 2000s to both analyze, predict and worry about the potential future of computational law and a new academic field of computational legal studies seems to be now well established. As insight into what such scholars see in the law's future due in part to computational law, here is quote from a recent conference about the "New Normal" for the legal profession: "Over the last 5 years, in the fallout of the Great Recession, the legal profession has entered the era of the New Normal. Notably, a series of forces related to technological change, globalization, and the pressure to do more with less (in both corpo

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  Multicloud

  Multicloud (also written as multi-cloud or multi cloud) is a term with varying interpretations, generally referring to a system using multiple cloud computing providers. According to ISO/IEC 22123-1: "multi-cloud is a cloud deployment model in which a customer uses public cloud services provided by two or more cloud service providers". Multi-cloud can involve various deployment models, including public, private, and hybrid clouds, and multiple service models, such as Infrastructure as a Service (IaaS), Platform as a Service (PaaS), and Software as a Service (SaaS). Multicloud incorporates workload, data, traffic, and workflow portability options, which can result in varying implementation complexity. When effectively implemented, multicloud solutions can enhance architectural resilience, reduce dependence on a single vendor, and improve flexibility by leveraging services from different providers. However, multicloud strategies also present challenges, including increased operational complexity, security risks, higher costs, and integration difficulties. According to the 2024 State of the Cloud Report by Flexera, multi-cloud adoption has continued to rise in 2024. Enterprises increasingly silo applications into specific clouds and select best-fit services. Key use cases include data analysis in separate clouds and cross-cloud disaster recovery. == Advantages and challenges == There are several advantages to using a multicloud approach, including the ability to negotiate better pricing with cloud providers, the ability to quickly switch to another provider if needed, and the ability to avoid vendor lock-in. Multicloud can also be a good way to hedge against the risks of obsolescence, as it allows you to rely on multiple vendors and open standards, which can prolong the life of your systems. Additional benefits of the multicloud architecture include adherence to local policies that require certain data to be physically present within the area/country, geographical distribution of processing requests from physically closer cloud unit which in turn reduces latency and protect against disasters. Various issues and challenges also present themselves in a multicloud environment. Security and governance is more complicated, and more "moving parts" may create resiliency issues. == Difference between multicloud and hybrid cloud == Multicloud differs from hybrid cloud in that it refers to multiple cloud services from different vendors rather than multiple deployment modes (on-premises hardware, and public and private, cloud hosting). However, when considering a broad definition of multi-cloud, hybrid cloud can still be regarded as a special form of multi-cloud.

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  Vidby

  Vidby AG (stylized in lower-case) is a start-up based in Rotkreuz, Switzerland specializing in AI language translation for videos. Founded by Alexander Konovalov (uk:Олександр Коновалов) and Eugen von Rubinberg in September 2021, the company has especially garnered attention for its use in translating speeches given by President Volodymyr Zelenskyy during the Russian invasion of Ukraine. == History == Vidby AG was founded by Alexander Konovalov and Eugen von Rubinberg. Konovalov is a native of Ukraine and retains Ukrainian citizenship; Rubinberg came to Switzerland from Germany and holds German citizenship. Both are residents of Switzerland. The latter founded his first business, a trading company, at age 16. In 2013, the business partners launched a consumer-oriented video-call translation service called DROTR (Droid Translator) AG, utilizing a Konovalov-created AI-powered language translation technology enabling simultaneous translation of messages, voice and video calls in 104 languages (written), with 44 available in spoken form. This was the world's first video calling app with translation. The technology was pronounced a competitor of Skype and Viber by Forbes and claimed first prize at the "Innovative Breakthrough 2013" Competition. In 2021, with a new business-oriented focus, DROTR became Vidby, with the former Google technology partners Konovalov and Rubinberg remaining at the helm, each with the title Co-CEO. While headquartered in Switzerland, Vidby's development team is, according to the company's founders, based in Ukraine. The technology behind Vidby has an accuracy level variously reported as up to 99 percent or 99 to 100 percent, equalling the highest level of human translation. Additionally, the technology is capable of removing the original language while maintaining ambient sounds. Currently, some 70 languages plus 60 dialects are possible with the algorithm-based technology. == Notable use == In addition to its use with speeches delivered by Pope Francis, the technology has been provided to Ukrainian authorities and embassies during the ongoing military conflict with Russia free of remuneration. By July, 2022, some 70 speeches given by President Zelenskyy totalling 650 minutes had been translated into 30 languages, for a total of over 10,000 minutes of video material. Of its use in translating Zelenskyy's wartime speeches, Konovalov has said, "Like any citizen, I want to help defend my country." Notable corporate clients of Vidby include Samsung, Siemens, Cisco, Kärcher, Generali and McDonald's Corporation; an academic client is Harvard University. Google Cloud Technology Partner status of Vidby was confirmed officially after a six-month audit in December 2022. Denys Krasnikov, a Vidby co-founder, is responsible for cooperation with Google, YouTube, Microsoft, and other key partners. After the launch of multilingual YouTube channels, Vidby started AI translating and dubbing creators' videos for this new type of channel at the end of February 2023. == Accolades == Vidby headed a list of the five best video translation services as named by TechRadar Deutschland in September, 2022. In the same month, Tech Times named Vidby #1 in their list of the five best such services. It similarly topped a list of the five best content translation technologies as judged by European Business Review in October, 2022. Prior to these lead-position rankings (August, 2022), it was featured as Business Insider's special start-up recommendation (German: "Unser Lesetipp auf Gründerszene"). In 2023, YouTube recognized Vidby as its recommended vendor.

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  Murderbot (TV series)

  Murderbot is an American science fiction action comedy television series created by Paul Weitz and Chris Weitz for Apple TV+. It is based on All Systems Red, the first book of the series The Murderbot Diaries by Martha Wells, who serves as a consulting producer. The series stars Alexander Skarsgård as the titular character. The first season premiered on May 16, 2025 and received positive reviews. In July 2025, the series was renewed for a second season. == Premise == A media-obsessed private security construct (manufactured from cloned human tissue and mechanical parts) calling itself Murderbot must hide its newly acquired autonomy while completing dangerous assignments and being simultaneously drawn to humans, and appalled by their weakness. == Cast and characters == === Main === Alexander Skarsgård as Murderbot Noma Dumezweni as Ayda Mensah, a terraforming specialist, the President of Preservation Alliance and the leader of the science team protected by Murderbot David Dastmalchian as Gurathin, a tech expert and augmented human Sabrina Wu as Pin-Lee, a scientist and legal counsel to the team Akshay Khanna as Ratthi, a wormhole expert Tamara Podemski as Bharadwaj, a geochemist Tattiawna Jones as Arada, a biologist === Recurring === Cast of show-within-a-show The Rise and Fall of Sanctuary Moon John Cho as Eknie Jef Chem (playing Captain Hossein) Jack McBrayer as Breiller MocJac (playing Navigation Officer Hordööp-Sklanch) Clark Gregg as Arletty (playing Lieutenant Kullervv) DeWanda Wise as Pordron Bretney III Roche (playing NawBot 337 Alt 66) === Guest === Anna Konkle as Leebeebee, a member of another survey team on the planet. The character does not appear in the novella. Amanda Brugel as GrayCris Blue Leader David Reale as GrayCris Yellow == Episodes == == Production == The book series was optioned in the late 2010s, and its film adaptation was considered. In 2021, book series author Martha Wells said that a potential TV series adaptation was in development and that she had read the script and was "really excited about it". The series was green lit by Apple TV+ in 2022, with Wells serving as a consulting producer. The production design team, led by Sue Chan, started work in the autumn. Tommy Arnold, the Murderbot Diaries special edition illustrator, created the concept art for the show. After the casting was delayed by the 2023 SAG-AFTRA strike, in December 2023 it was announced that Alexander Skarsgård would produce and star in the series. He developed the character and the world of Murderbot with the showrunners. In February 2024, David Dastmalchian and Noma Dumezweni joined the cast. In March, Sabrina Wu, Tattiawna Jones, Akshay Khanna, and Tamara Podemski joined the cast. On July 10, 2025, the series was renewed for a second season. Showrunners Chris and Paul Weitz suggested the second season would combine the next three books of the series and will have longer episodes. === Filming === Principal photography for the first season took place from March–June 2024, in Toronto and parts of Ontario, Canada. Most of the filming was done on location, with the Sanctuary Moon scenes filmed on a virtual production stage. Principal photography for the second season began in mid-2026, in Madrid, Spain. It is planned to last 71 days, with Martha Wells also visiting the set. == Release == The first two episodes of Murderbot premiered on Apple TV+ on May 16, 2025, with subsequent episodes released weekly. The first season consists of ten episodes. == Reception == Even before the release of the show, numerous media sources had commented on the titular character as being coded as autistic and agender. On the review aggregator website Rotten Tomatoes, Murderbot has an approval rating of 96% with an average score of 7.5/10, based on 76 critics' reviews. The website's critical consensus states, "Alexander Skarsgård's superbly dry wit brings a lot of heart to Murderbot, making for a refreshingly jaunty sci-fi saga about finally coming out of one's shell". Metacritic, which uses a weighted average, assigned a score of 70 out of 100, based on 28 critics, indicating "generally favorable" reviews. Some reviewers have criticized Murderbot's changes to Wells' original books. Angela Watercutter of Wired noted that the series has significant tonal differences from the books and noted the show's changes to characters, particularly Murderbot and Dr. Mensah, and Wells' social commentary. === Accolades === Murderbot was a finalist for the 2025 Dragon Award for Best Science Fiction or Fantasy TV Series. Tommy Arnold won the 2025 Concept Art Association Award in the category of Live-Action Series Character Art for his work on Murderbot. Alexander Skarsgård was nominated for a Critics' Choice Award for Best Actor in a Comedy Series. Carrie Grace and Laura Jean Shannon were nominated for a Costume Designers Guild Award in the category of Excellence in Sci-Fi/Fantasy Television for their work on FreeCommerce. Amanda Jones was nominated for a Composers & Lyricists Award for Outstanding Original Title Sequence for a Television Production.

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  Feeding the Machine (book)

  Feeding the Machine: The Hidden Human Labour Powering AI is a 2024 book by James Muldoon, Mark Graham and Callum Cant. == Writing == The authors developed the concept for the book while doing fieldwork studying data annotation in developing countries in East Africa. == Synopsis == The book examines the human input needed to develop and sustain AI ecosystems. == Reception == The book received positive reviews. Rosalie Waelen of Capital & Class gave it a mostly positive review. Tim Hornyak of Literary Review praised it. Kirkus Reviews called it "A sobering and timely—if sometimes distracted—study of AI.". Publishers Weekly gave the book a starred review, writing that "The grim real-life stories read like dystopian parables, such as the account of a European voice actor whose recordings were legally used without her consent to create an inexpensive synthetic clone whom she now competes with for business. Driven by striking reporting and finely observed profiles, this unsettles."

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  Information space analysis

  Within the field of information science, information space analysis is a deterministic method, enhanced by machine intelligence, for locating and assessing resources for team-centric efforts. Organizations need to be able to quickly assemble teams backed by the support services, information, and material to do the job. To do so, these teams need to find and assess sources of services that are potential participants in the team effort. To support this initial team and resource development, information needs to be developed via analysis tools that help make sense of sets of data sources in an Intranet or Internet. Part of the process is to characterize them, partition them, and sort and filter them. These tools focus on three key issues in forming a collaborative team: Help individuals responsible for forming the team understand what is available. Assist team members in identifying the structure and categorize the information available to them in a manner specifically suited to the task at hand. Aid team members to understand the mappings of their information between their organization and that used by others who might participate. Information space analysis tools combine multiple methods to assist in this task. This causes the tools to be particularly well-suited to integrating additional technologies in order to create specialized systems.

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  Speech synthesis

  Speech synthesis is the artificial production of human speech. A computer system used for this purpose is called a speech synthesizer, and can be implemented in software or hardware products. A text-to-speech (TTS) system converts normal language text into speech; other systems render symbolic linguistic representations like phonetic transcriptions into speech. The reverse process is speech recognition. Synthesized speech can be created by concatenating pieces of recorded speech that are stored in a database. Systems differ in the size of the stored speech units; a system that stores phones or diphones provides the largest output range, but may lack clarity. For specific usage domains, the storage of entire words or sentences allows for high-quality output. Alternatively, a synthesizer can incorporate a model of the vocal tract and other human voice characteristics to create a completely "synthetic" voice output. The quality of a speech synthesizer is judged by its similarity to the human voice and by its ability to be understood clearly. An intelligible text-to-speech program allows people with visual impairments or reading disabilities to listen to written words on a home computer. The earliest computer operating system to have included a speech synthesizer was Unix in 1974, through the Unix speak utility. In 2000, Microsoft Sam was the default text-to-speech voice synthesizer used by the narrator accessibility feature, which shipped with all Windows 2000 operating systems, and subsequent Windows XP systems. A text-to-speech system (or "engine") is composed of two parts: a front-end and a back-end. The front-end has two major tasks. First, it converts raw text containing symbols like numbers and abbreviations into the equivalent of written-out words. This process is often called text normalization, pre-processing, or tokenization. The front-end then assigns phonetic transcriptions to each word, and divides and marks the text into prosodic units, like phrases, clauses, and sentences. The process of assigning phonetic transcriptions to words is called text-to-phoneme or grapheme-to-phoneme conversion. Phonetic transcriptions and prosody information together make up the symbolic linguistic representation that is output by the front-end. The back-end—often referred to as the synthesizer—then converts the symbolic linguistic representation into sound. In certain systems, this part includes the computation of the target prosody (pitch contour, phoneme durations), which is then imposed on the output speech. == History == Long before the invention of electronic signal processing, some people tried to build machines to emulate human speech. There were also legends of the existence of "Brazen Heads", such as those involving Pope Silvester II (d. 1003 AD), Albertus Magnus (1198–1280), and Roger Bacon (1214–1294). In 1779, the German-Danish scientist Christian Gottlieb Kratzenstein won the first prize in a competition announced by the Russian Imperial Academy of Sciences and Arts for models he built of the human vocal tract that could produce the five long vowel sounds (in International Phonetic Alphabet notation: [aː], [eː], [iː], [oː] and [uː]). There followed the bellows-operated "acoustic-mechanical speech machine" of Wolfgang von Kempelen of Pressburg, Hungary, described in a 1791 paper. This machine added models of the tongue and lips, enabling it to produce consonants as well as vowels. In 1837, Charles Wheatstone produced a "speaking machine" based on von Kempelen's design, and in 1846, Joseph Faber exhibited the "Euphonia". In 1923, Paget resurrected Wheatstone's design. In the 1930s, Bell Labs developed the vocoder, which automatically analyzed speech into its fundamental tones and resonances. From his work on the vocoder, Homer Dudley developed a keyboard-operated voice-synthesizer called The Voder (Voice Demonstrator), which he exhibited at the 1939 New York World's Fair. Franklin S. Cooper and his colleagues at Haskins Laboratories built the pattern playback in the late 1940s and completed it in 1950. There were several different versions of this hardware device; only one currently survives. The machine converts pictures of the acoustic patterns of speech in the form of a spectrogram back into sound. Using this device, Alvin Liberman and colleagues discovered acoustic cues for the perception of phonetic segments (consonants and vowels). === Electronic devices === The first computer-based speech-synthesis systems originated in the late 1950s. Noriko Umeda et al. developed the first general English text-to-speech system in 1968, at the Electrotechnical Laboratory in Japan. In 1961, physicist John Larry Kelly, Jr and his colleague Louis Gerstman used an IBM 704 computer to synthesize speech, an event among the most prominent in the history of Bell Labs. Kelly's voice recorder synthesizer (vocoder) recreated the song "Daisy Bell", with musical accompaniment from Max Mathews. Coincidentally, Arthur C. Clarke was visiting his friend and colleague John Pierce at the Bell Labs Murray Hill facility. Clarke was so impressed by the demonstration that he used it in the climactic scene of his screenplay for his novel 2001: A Space Odyssey, where the HAL 9000 computer sings the same song as astronaut Dave Bowman puts it to sleep. Despite the success of purely electronic speech synthesis, research into mechanical speech-synthesizers continues. Linear predictive coding (LPC), a form of speech coding, began development with the work of Fumitada Itakura of Nagoya University and Shuzo Saito of Nippon Telegraph and Telephone (NTT) in 1966. Further developments in LPC technology were made by Bishnu S. Atal and Manfred R. Schroeder at Bell Labs during the 1970s. LPC was later the basis for early speech synthesizer chips, such as the Texas Instruments LPC Speech Chips used in the Speak & Spell toys from 1978. In 1975, Fumitada Itakura developed the line spectral pairs (LSP) method for high-compression speech coding, while at NTT. From 1975 to 1981, Itakura studied problems in speech analysis and synthesis based on the LSP method. In 1980, his team developed an LSP-based speech synthesizer chip. LSP is an important technology for speech synthesis and coding, and in the 1990s was adopted by almost all international speech coding standards as an essential component, contributing to the enhancement of digital speech communication over mobile channels and the internet. In 1975, MUSA was released, and was one of the first Speech Synthesis systems. It consisted of a stand-alone computer hardware and a specialized software that enabled it to read Italian. A second version, released in 1978, was also able to sing Italian in an "a cappella" style. Dominant systems in the 1980s and 1990s were the DECtalk system, based largely on the work of Dennis Klatt at MIT, and the Bell Labs system; the latter was one of the first multilingual language-independent systems, making extensive use of natural language processing methods. Handheld electronics featuring speech synthesis began emerging in the 1970s. One of the first was the Telesensory Systems Inc. (TSI) Speech+ portable calculator for the blind in 1976. Other devices had primarily educational purposes, such as the Speak & Spell toy produced by Texas Instruments in 1978. Fidelity released a speaking version of its electronic chess computer in 1979. The first video game to feature speech synthesis was the 1980 shoot 'em up arcade game, Stratovox (known in Japan as Speak & Rescue), from Sun Electronics. The first personal computer game with speech synthesis was Manbiki Shoujo (Shoplifting Girl), released in 1980 for the PET 2001, for which the game's developer, Hiroshi Suzuki, developed a "zero cross" programming technique to produce a synthesized speech waveform. Another early example, the arcade version of Berzerk, also dates from 1980. The Milton Bradley Company produced the first multi-player electronic game using voice synthesis, Milton, in the same year. In 1976, Computalker Consultants released their CT-1 Speech Synthesizer. Designed by D. Lloyd Rice and Jim Cooper, it was an analog synthesizer built to work with microcomputers using the S-100 bus standard. Synthesized voices typically sounded male until 1990, when Ann Syrdal, at AT&T Bell Laboratories, created a female voice. Ray Kurzweil predicted in 2005 that as the cost-performance ratio caused speech synthesizers to become cheaper and more accessible, more people would benefit from the use of text-to-speech programs. === Artificial intelligence === In September 2016, DeepMind released WaveNet, which demonstrated that deep learning models are capable of modeling raw waveforms and generating speech from acoustic features like spectrograms or mel-spectrograms, starting the field of deep learning speech synthesis. Although WaveNet was initially considered to be computationally expensive and slow to be used in consumer products at the time, a year after its

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  Random-fuzzy variable

  In measurements, the measurement obtained can suffer from two types of uncertainties. The first is the random uncertainty which is due to the noise in the process and the measurement. The second contribution is due to the systematic uncertainty which may be present in the measuring instrument. Systematic errors, if detected, can be easily compensated as they are usually constant throughout the measurement process as long as the measuring instrument and the measurement process are not changed. But it can not be accurately known while using the instrument if there is a systematic error and if there is, how much? Hence, systematic uncertainty could be considered as a contribution of a fuzzy nature. This systematic error can be approximately modeled based on our past data about the measuring instrument and the process. Statistical methods can be used to calculate the total uncertainty from both systematic and random contributions in a measurement. However, the computational complexity is very high, and hence not desirable. L.A.Zadeh introduced the concepts of fuzzy variables and fuzzy sets. Fuzzy variables are based on the theory of possibility and hence are possibility distributions. This makes them suitable to handle any type of uncertainty, i.e., both systematic and random contributions to the total uncertainty. Random-fuzzy variable (RFV) is a type 2 fuzzy variable, defined using the mathematical possibility theory, used to represent the entire information associated to a measurement result. It has an internal possibility distribution and an external possibility distribution called membership functions. The internal distribution is the uncertainty contributions due to the systematic uncertainty and the bounds of the RFV are because of the random contributions. The external distribution gives the uncertainty bounds from all contributions. == Definition == A random-fuzzy Variable (RFV) is defined as a type 2 fuzzy variable which satisfies the following conditions: Both the internal and the external functions of the RFV can be identified. Both the internal and the external functions are modeled as possibility distributions (PD). Both the internal and external functions have a unitary value for possibility to the same interval of values. An RFV can be seen in the figure. The external membership function is the distribution in blue and the internal membership function is the distribution in red. Both the membership functions are possibility distributions. Both the internal and external membership functions have a unitary value of possibility only in the rectangular part of the RFV. Therefore, all three conditions have been satisfied. If there are only systematic errors in the measurement, then the RFV simply becomes a fuzzy variable which consists of just the internal membership function. Similarly, if there is no systematic error, then the RFV becomes a fuzzy variable with just the random contributions and therefore, is just the possibility distribution of the random contributions. == Construction == A random-fuzzy variable can be constructed using an internal possibility distribution (rinternal) and a random possibility distribution (rrandom). === The random distribution (rrandom) === rrandom is the possibility distribution of the random contributions to the uncertainty. Any measurement instrument or process suffers from random error contributions due to intrinsic noise or other effects. This is completely random in nature and is a normal probability distribution when several random contributions are combined according to the central limit theorem. However, there can also be random contributions from other probability distributions, such as a uniform distribution, gamma distribution and so on. The probability distribution can be modeled from the measurement data. Then, the probability distribution can be used to model an equivalent possibility distribution using the maximally specific probability-possibility transformation. Some common probability distributions and the corresponding possibility distributions can be seen in the figures. === The internal distribution (rinternal) === rinternal is the internal distribution in the RFV which is the possibility distribution of the systematic contribution to the total uncertainty. This distribution can be built based on the information that is available about the measuring instrument and the process. The largest possible distribution is the uniform or rectangular possibility distribution. This means that every value in the specified interval is equally possible. This actually represents the state of total ignorance according to the theory of evidence which means it represents a scenario in which there is maximum lack of information. This distribution is used for the systematic error when we have absolutely no idea about the systematic error except that it belongs to a particular interval of values. This is quite common in measurements. However, in certain cases, it may be known that certain values have a higher or lower degrees of belief than certain other values. In this case, depending on the degrees of belief for the values, an appropriate possibility distribution could be constructed. === The construction of the external distribution (rexternal) and the RFV === After modeling the random and internal possibility distribution, the external membership function, rexternal, of the RFV can be constructed by using the following equation: where x ∗ {\displaystyle x^{}} is the mode of r random {\displaystyle r_{\textit {random}}} , which is the peak in the membership function of r r a n d o m {\displaystyle r_{random}} and Tmin is the minimum triangular norm. RFV can also be built from the internal and random distributions by considering the α-cuts of the two possibility distributions (PDs). An α-cut of a fuzzy variable F can be defined as Therefore, essentially an α-cut is the set of values for which the value of the membership function μ F ( a ) {\displaystyle \mu _{\rm {F}}(a)} of the fuzzy variable is greater than α. This gives the upper and lower bounds of the fuzzy variable F for each α-cut. The α-cut of an RFV, however, has 4 specific bounds and is given by R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} . X a α {\displaystyle X_{a}^{\alpha }} and X d α {\displaystyle X_{d}^{\alpha }} are the lower and upper bounds respectively of the external membership function (rexternal) which is a fuzzy variable on its own. X b α {\displaystyle X_{b}^{\alpha }} and X c α {\displaystyle X_{c}^{\alpha }} are the lower and upper bounds respectively of the internal membership function (rinternal) which is a fuzzy variable on its own. To build the RFV, let us consider the α-cuts of the two PDs i.e., rrandom and rinternal for the same value of α. This gives the lower and upper bounds for the two α-cuts. Let them be [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} and [ X L I α , X U I α ] {\displaystyle [X_{LI}^{\alpha },X_{UI}^{\alpha }]} for the random and internal distributions respectively. [ X L R α , X U R α ] {\displaystyle [X_{LR}^{\alpha },X_{UR}^{\alpha }]} can be again divided into two sub-intervals [ X L R α , x ∗ ] {\displaystyle [X_{LR}^{\alpha },x^{}]} and [ x ∗ , X U R α ] {\displaystyle [x^{},X_{UR}^{\alpha }]} where x ∗ {\displaystyle x^{}} is the mode of the fuzzy variable. Then, the α-cut for the RFV for the same value of α, R F V α = [ X a α , X b α , X c α , X d α ] {\displaystyle RFV^{\alpha }=[X_{a}^{\alpha },X_{b}^{\alpha },X_{c}^{\alpha },X_{d}^{\alpha }]} can be defined by Using the above equations, the α-cuts are calculated for every value of α which gives us the final plot of the RFV. A random-fuzzy variable is capable of giving a complete picture of the random and systematic contributions to the total uncertainty from the α-cuts for any confidence level as the confidence level is nothing but 1-α. An example for the construction of the corresponding external membership function (rexternal) and the RFV from a random PD and an internal PD can be seen in the following figure.

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