Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units (nodes, vertices, actors), based on specific patterns, which form a distinctive structure through interconnectivity. It is primarily used in statistics, machine learning and network science. As an empirical procedure, blockmodeling assumes that all the units in a specific network can be grouped together to such extent to which they are equivalent. Regarding equivalency, it can be structural, regular or generalized. Using blockmodeling, a network can be analyzed using newly created blockmodels, which transforms large and complex network into a smaller and more comprehensible one. At the same time, the blockmodeling is used to operationalize social roles. While some contend that the blockmodeling is just clustering methods, Bonacich and McConaghy state that "it is a theoretically grounded and algebraic approach to the analysis of the structure of relations". Blockmodeling's unique ability lies in the fact that it considers the structure not just as a set of direct relations, but also takes into account all other possible compound relations that are based on the direct ones. The principles of blockmodeling were first introduced by Francois Lorrain and Harrison C. White in 1971. Blockmodeling is considered as "an important set of network analytic tools" as it deals with delineation of role structures (the well-defined places in social structures, also known as positions) and the discerning the fundamental structure of social networks. According to Batagelj, the primary "goal of blockmodeling is to reduce a large, potentially incoherent network to a smaller comprehensible structure that can be interpreted more readily". Blockmodeling was at first used for analysis in sociometry and psychometrics, but has now spread also to other sciences. == Definition == A network as a system is composed of (or defined by) two different sets: one set of units (nodes, vertices, actors) and one set of links between the units. Using both sets, it is possible to create a graph, describing the structure of the network. During blockmodeling, the researcher is faced with two problems: how to partition the units (e.g., how to determine the clusters (or classes), that then form vertices in a blockmodel) and then how to determine the links in the blockmodel (and at the same time the values of these links). In the social sciences, the networks are usually social networks, composed of several individuals (units) and selected social relationships among them (links). Real-world networks can be large and complex; blockmodeling is used to simplify them into smaller structures that can be easier to interpret. Specifically, blockmodeling partitions the units into clusters and then determines the ties among the clusters. At the same time, blockmodeling can be used to explain the social roles existing in the network, as it is assumed that the created cluster of units mimics (or is closely associated with) the units' social roles. Blockmodeling can thus be defined as a set of approaches for partitioning units into clusters (also known as positions) and links into blocks, which are further defined by the newly obtained clusters. A block (also blockmodel) is defined as a submatrix, that shows interconnectivity (links) between nodes, present in the same or different clusters. Each of these positions in the cluster is defined by a set of (in)direct ties to and from other social positions. These links (connections) can be directed or undirected; there can be multiple links between the same pair of objects or they can have weights on them. If there are not any multiple links in a network, it is called a simple network. A matrix representation of a graph is composed of ordered units, in rows and columns, based on their names. The ordered units with similar patterns of links are partitioned together in the same clusters. Clusters are then arranged together so that units from the same clusters are placed next to each other, thus preserving interconnectivity. In the next step, the units (from the same clusters) are transformed into a blockmodel. With this, several blockmodels are usually formed, one being core cluster and others being cohesive; a core cluster is always connected to cohesive ones, while cohesive ones cannot be linked together. Clustering of nodes is based on the equivalence, such as structural and regular. The primary objective of the matrix form is to visually present relations between the persons included in the cluster. These ties are coded dichotomously (as present or absent), and the rows in the matrix form indicate the source of the ties, while the columns represent the destination of the ties. Equivalence can have two basic approaches: the equivalent units have the same connection pattern to the same neighbors or these units have same or similar connection pattern to different neighbors. If the units are connected to the rest of network in identical ways, then they are structurally equivalent. Units can also be regularly equivalent, when they are equivalently connected to equivalent others. With blockmodeling, it is necessary to consider the issue of results being affected by measurement errors in the initial stage of acquiring the data. == Different approaches == Regarding what kind of network is undergoing blockmodeling, a different approach is necessary. Networks can be one–mode or two–mode. In the former all units can be connected to any other unit and where units are of the same type, while in the latter the units are connected only to the unit(s) of a different type. Regarding relationships between units, they can be single–relational or multi–relational networks. Further more, the networks can be temporal or multilevel and also binary (only 0 and 1) or signed (allowing negative ties)/values (other values are possible) networks. Different approaches to blockmodeling can be grouped into two main classes: deterministic blockmodeling and stochastic blockmodeling approaches. Deterministic blockmodeling is then further divided into direct and indirect blockmodeling approaches. Among direct blockmodeling approaches are: structural equivalence and regular equivalence. Structural equivalence is a state, when units are connected to the rest of the network in an identical way(s), while regular equivalence occurs when units are equally related to equivalent others (units are not necessarily sharing neighbors, but have neighbour that are themselves similar). Indirect blockmodeling approaches, where partitioning is dealt with as a traditional cluster analysis problem (measuring (dis)similarity results in a (dis)similarity matrix), are: conventional blockmodeling, generalized blockmodeling: generalized blockmodeling of binary networks, generalized blockmodeling of valued networks and generalized homogeneity blockmodeling, prespecified blockmodeling. According to Brusco and Steinley (2011), the blockmodeling can be categorized (using a number of dimensions): deterministic or stochastic blockmodeling, one–mode or two–mode networks, signed or unsigned networks, exploratory or confirmatory blockmodeling. == Blockmodels == Blockmodels (sometimes also block models) are structures in which: vertices (e.g., units, nodes) are assembled within a cluster, with each cluster identified as a vertex; from such vertices a graph can be constructed; combinations of all the links (ties), represented in a block as a single link between positions, while at the same time constructing one tie for each block. In a case, when there are no ties in a block, there will be no ties between the two positions that define the block. Computer programs can partition the social network according to pre-set conditions. When empirical blocks can be reasonably approximated in terms of ideal blocks, such blockmodels can be reduced to a blockimage, which is a representation of the original network, capturing its underlying 'functional anatomy'. Thus, blockmodels can "permit the data to characterize their own structure", and at the same time not seek to manifest a preconceived structure imposed by the researcher. Blockmodels can be created indirectly or directly, based on the construction of the criterion function. Indirect construction refers to a function, based on "compatible (dis)similarity measure between paris of units", while the direct construction is "a function measuring the fit of real blocks induced by a given clustering to the corresponding ideal blocks with perfect relations within each cluster and between clusters according to the considered types of connections (equivalence)". === Types === Blockmodels can be specified regarding the intuition, substance or the insight into the nature of the studied network; this can result in such models as follows: parent-child role systems, organizational hierarchies, systems of
Scanimate
Scanimate is an analog computer animation (video synthesizer) system created by Lee Harrison III of Denver, Colorado. Harrison had developed its predecessor, ANIMAC, which generated used a motion capture system, based on a body suit with potentiometers. In contrast, Scanimate included TV technology. Scanimate's successor was called Caesar, and used a digital computer to control the analog system. The eight Scanimate systems were used to produce much of the video-based animation seen on television between most of the 1970s and early 1980s in commercials, promotions, and show openings. One of the major advantages the Scanimate system had over film-based animation and computer animation was the ability to create animations in real time. The speed with which animation could be produced on the system because of this, as well as its range of possible effects, helped it to supersede film-based animation techniques for television graphics. By the mid-1980s, it was superseded by digital computer animation, which produced sharper images and more sophisticated 3D imagery. Animations created on Scanimate and similar analog computer animation systems have a number of characteristic features that distinguish them from film-based animation: the motion is extremely fluid, using all 60 fields per second (in NTSC format video) or 50 fields (in PAL format video) rather than the 24 frames per second that film uses; the colors are much brighter and more saturated; and the images have a very "electronic" look that results from the direct manipulation of video signals through which the Scanimate produces the images. == How it works == A special high-resolution (around 945 lines) monochrome camera records high-contrast artwork. The image is then displayed on a high-resolution screen. Unlike a normal monitor, its deflection signals are passed through a special analog computer that enables the operator to bend the image in a variety of ways. The image is then shot from the screen by either a film camera or a video camera. In the case of a video camera, this signal is then fed into a colorizer, a device that takes certain shades of grey and turns it into color as well as transparency. The idea behind this is that the output of the Scanimate itself is always monochrome. Another advantage of the colorizer is that it gives the operator the ability to continuously add layers of graphics. This makes possible the creation of very complex graphics. This is done by using two video recorders. The background is played by one recorder and then recorded by another one. This process is repeated for every layer. This requires very high-quality video recorders (such as both the Ampex VR-2000 or IVC's IVC-9000 of Scanimate's era, the IVC-9000 being used quite frequently for Scanimate composition due to its very high generational quality between re-recordings). == Current usage == Two of the Scanimates are still in use at ZFx studios in Asheville, North Carolina. The original "Black Swan" R&D machine has been updated with more modern power supplies and can produce material in standard or 1080P high definition video. The "white Pearl" machine is the last one produced and is being kept in its original configuration for historical purposes by David Sieg at ZFx inc. The machines are installed in a working production environment with Grass Valley switchers, Kaleidoscope digital video effects systems, and Accom digital disk recorders for layering. == Use in television, music and films == === Music videos === Let's Groove by Earth, Wind & Fire Get Down on It by Kool & the Gang Blame It on the Boogie by The Jacksons Knock on Wood by Amii Stewart Popcorn Love by New Edition === TV programs/movies === === TV channels/home video/TV productions ===
Belief–desire–intention software model
The belief–desire–intention software model (BDI) is a software model developed for programming intelligent agents. Superficially characterized by the implementation of an agent's beliefs, desires and intentions, it actually uses these concepts to solve a particular problem in agent programming. In essence, it provides a mechanism for separating the activity of selecting a plan (from a plan library or an external planner application) from the execution of currently active plans. Consequently, BDI agents are able to balance the time spent on deliberating about plans (choosing what to do) and executing those plans (doing it). A third activity, creating the plans in the first place (planning), is not within the scope of the model, and is left to the system designer and programmer. == Overview == In order to achieve this separation, the BDI software model implements the principal aspects of Michael Bratman's theory of human practical reasoning (also referred to as Belief-Desire-Intention, or BDI). That is to say, it implements the notions of belief, desire and (in particular) intention, in a manner inspired by Bratman. For Bratman, desire and intention are both pro-attitudes (mental attitudes concerned with action). He identifies commitment as the distinguishing factor between desire and intention, noting that it leads to (1) temporal persistence in plans and (2) further plans being made on the basis of those to which it is already committed. The BDI software model partially addresses these issues. Temporal persistence, in the sense of explicit reference to time, is not explored. The hierarchical nature of plans is more easily implemented: a plan consists of a number of steps, some of which may invoke other plans. The hierarchical definition of plans itself implies a kind of temporal persistence, since the overarching plan remains in effect while subsidiary plans are being executed. An important aspect of the BDI software model (in terms of its research relevance) is the existence of logical models through which it is possible to define and reason about BDI agents. Research in this area has led, for example, to the axiomatization of some BDI implementations, as well as to formal logical descriptions such as Anand Rao and Michael Georgeff's BDICTL. The latter combines a multiple-modal logic (with modalities representing beliefs, desires and intentions) with the temporal logic CTL. More recently, Michael Wooldridge has extended BDICTL to define LORA (the Logic Of Rational Agents), by incorporating an action logic. In principle, LORA allows reasoning not only about individual agents, but also about communication and other interaction in a multi-agent system. The BDI software model is closely associated with intelligent agents, but does not, of itself, ensure all the characteristics associated with such agents. For example, it allows agents to have private beliefs, but does not force them to be private. It also has nothing to say about agent communication. Ultimately, the BDI software model is an attempt to solve a problem that has more to do with plans and planning (the choice and execution thereof) than it has to do with the programming of intelligent agents. This approach has recently been proposed by Steven Umbrello and Roman Yampolskiy as a means of designing autonomous vehicles for human values. == BDI agents == A BDI agent is a particular type of bounded rational software agent, imbued with particular mental attitudes, viz: Beliefs, Desires and Intentions (BDI). === Architecture === This section defines the idealized architectural components of a BDI system. Beliefs: Beliefs represent the informational state of the agent–its beliefs about the world (including itself and other agents). Beliefs can also include inference rules, allowing forward chaining to lead to new beliefs. Using the term belief rather than knowledge recognizes that what an agent believes may not necessarily be true (and in fact may change in the future). Beliefset: Beliefs are stored in database (sometimes called a belief base or a belief set), although that is an implementation decision. Desires: Desires represent the motivational state of the agent. They represent objectives or situations that the agent would like to accomplish or bring about. Examples of desires might be: find the best price, go to the party or become rich. Goals: A goal is a desire that has been adopted for active pursuit by the agent. Usage of the term goals adds the further restriction that the set of active desires must be consistent. For example, one should not have concurrent goals to go to a party and to stay at home – even though they could both be desirable. Intentions: Intentions represent the deliberative state of the agent – what the agent has chosen to do. Intentions are desires to which the agent has to some extent committed. In implemented systems, this means the agent has begun executing a plan. Plans: Plans are sequences of actions (recipes or knowledge areas) that an agent can perform to achieve one or more of its intentions. Plans may include other plans: my plan to go for a drive may include a plan to find my car keys. This reflects that in Bratman's model, plans are initially only partially conceived, with details being filled in as they progress. Events: These are triggers for reactive activity by the agent. An event may update beliefs, trigger plans or modify goals. Events may be generated externally and received by sensors or integrated systems. Additionally, events may be generated internally to trigger decoupled updates or plans of activity. BDI was also extended with an obligations component, giving rise to the BOID agent architecture to incorporate obligations, norms and commitments of agents that act within a social environment. === BDI interpreter === This section defines an idealized BDI interpreter that provides the basis of SRI's PRS lineage of BDI systems: initialize-state repeat options: option-generator (event-queue) selected-options: deliberate(options) update-intentions(selected-options) execute() get-new-external-events() drop-unsuccessful-attitudes() drop-impossible-attitudes() end repeat === Limitations and criticisms === The BDI software model is one example of a reasoning architecture for a single rational agent, and one concern in a broader multi-agent system. This section bounds the scope of concerns for the BDI software model, highlighting known limitations of the architecture. Learning: BDI agents lack any specific mechanisms within the architecture to learn from past behavior and adapt to new situations. Three attitudes: Classical decision theorists and planning research questions the necessity of having all three attitudes, distributed AI research questions whether the three attitudes are sufficient. Logics: The multi-modal logics that underlie BDI (that do not have complete axiomatizations and are not efficiently computable) have little relevance in practice. Multiple agents: In addition to not explicitly supporting learning, the framework may not be appropriate to learning behavior. Further, the BDI model does not explicitly describe mechanisms for interaction with other agents and integration into a multi-agent system. Explicit goals: Most BDI implementations do not have an explicit representation of goals. Lookahead: The architecture does not have (by design) any lookahead deliberation or forward planning. This may not be desirable because adopted plans may use up limited resources, actions may not be reversible, task execution may take longer than forward planning, and actions may have undesirable side effects if unsuccessful. == BDI agent implementations == === 'Pure' BDI === Procedural Reasoning System (PRS) IRMA (not implemented but can be considered as PRS with non-reconsideration) UM-PRS OpenPRS Distributed Multi-Agent Reasoning System (dMARS) AgentSpeak(L) – see Jason below AgentSpeak(RT) Agent Real-Time System (ARTS) (ARTS) JAM JACK Intelligent Agents JADEX (open source project) JaKtA JASON GORITE SPARK 3APL 2APL GOAL agent programming language CogniTAO (Think-As-One) Living Systems Process Suite PROFETA Gwendolen (Part of the Model Checking Agent Programming Languages Framework) === Extensions and hybrid systems === JACK Teams CogniTAO (Think-As-One) Living Systems Process Suite Brahms JaCaMo
Fuzzy associative matrix
A fuzzy associative matrix expresses fuzzy logic rules in tabular form. These rules usually take two variables as input, mapping cleanly to a two-dimensional matrix, although theoretically a matrix of any number of dimensions is possible. From the perspective of neuro-fuzzy systems, the mathematical matrix is called a "Fuzzy associative memory" because it stores the weights of the perceptron. == Applications == In the context of game AI programming, a fuzzy associative matrix helps to develop the rules for non-player characters. Suppose a professional is tasked with writing fuzzy logic rules for a video game monster. In the game being built, entities have two variables: hit points (HP) and firepower (FP): This translates to: IF MonsterHP IS VeryLowHP AND MonsterFP IS VeryWeakFP THEN Retreat IF MonsterHP IS LowHP AND MonsterFP IS VeryWeakFP THEN Retreat IF MonsterHP IS MediumHP AND MonsterFP is VeryWeakFP THEN Defend Multiple rules can fire at once, and often will, because the distinction between "very low" and "low" is fuzzy. If it is more "very low" than it is low, then the "very low" rule will generate a stronger response. The program will evaluate all the rules that fire and use an appropriate defuzzification method to generate its actual response. An implementation of this system might use either the matrix or the explicit IF/THEN form. The matrix makes it easy to visualize the system, but it also makes it impossible to add a third variable just for one rule, so it is less flexible. == Identify a rule set == There is no inherent pattern in the matrix. It appears as if the rules were just made up, and indeed they were. This is both a strength and a weakness of fuzzy logic in general. It is often impractical or impossible to find an exact set of rules or formulae for dealing with a specific situation. For a sufficiently complex game, a mathematician would not be able to study the system and figure out a mathematically accurate set of rules. However, this weakness is intrinsic to the realities of the situation, not of fuzzy logic itself. The strength of the system is that even if one of the rules is wrong, even greatly wrong, other rules that are correct are likely to fire as well and they may compensate for the error. This does not mean a fuzzy system should be sloppy. Depending on the system, it might get away with being sloppy, but it will underperform. While the rules are fairly arbitrary, they should be chosen carefully. If possible, an expert should decide on the rules, and the sets and rules should be tested vigorously and refined as needed. In this way, a fuzzy system is like an expert system. (Fuzzy logic is used in many true expert systems, as well.)
Taylor Swift deepfake pornography controversy
In late January 2024, sexually explicit AI-generated deepfake images of American musician Taylor Swift were proliferated on social media platforms 4chan and X (formerly Twitter). Several artificial images of Swift of a sexual or violent nature were quickly spread, with one post reported to have been seen over 47 million times before its eventual removal. The images led Microsoft to enhance Microsoft Designer's text-to-image model to prevent future abuse. Moreover, these images prompted responses from anti-sexual assault advocacy groups, US politicians, Swifties, and Microsoft CEO Satya Nadella, among others, and it has been suggested that Swift's influence could result in new legislation regarding the creation of deepfake pornography. A similar controversy emerged in August 2025, when The Verge reported AI image and video tool Grok Imagine generated sexually explicit images and videos of Swift from an otherwise innocuous text prompt. == Background == American musician Taylor Swift has been the target of misogyny and slut-shaming throughout her career. American technology corporation Microsoft offers AI image creators called Microsoft Designer and Bing Image Creator, which employ censorship safeguards to prevent users from generating unsafe or objectionable content. Members of a Telegram group discussed ways to circumvent these censors to create pornographic images of celebrities. Graphika, a disinformation research firm, traced the creation of the images back to a 4chan community. == Reactions == For some, the deepfake images of Swift immediately became a source of controversy and outrage. Other internet users found them humorous and absurd, such as the image making it appear as though Swift was to engage in sexual intercourse with Oscar the Grouch. The images drew condemnations from Rape, Abuse & Incest National Network and SAG-AFTRA. The latter group, who had been following issues regarding AI-generated media prior to Swift's involvement, considered the images "upsetting, harmful and deeply concerning." Microsoft CEO Satya Nadella, whose company's products were believed to be used to make these images, responded to the controversy as "alarming and terrible", further stating his belief that "we all benefit when the online world is a safe world." === Taylor Swift === A source close to Swift told the Daily Mail that she would be considering legal action, saying, "Whether or not legal action will be taken is being decided, but there is one thing that is clear: These fake AI-generated images are abusive, offensive, exploitative, and done without Taylor's consent and/or knowledge." === Politicians === White House press secretary Karine Jean-Pierre expressed concern over the counterfeit images, deeming them "alarming", and emphasized the obligation of social media platforms to curb the dissemination of misinformation. Several members of American politics called for legislation against AI-generated pornography. Later in the month, a bipartisan bill was introduced by US senators Dick Durbin, Lindsey Graham, Amy Klobuchar and Josh Hawley. The bill would allow victims to sue individuals who produced or possessed "digital forgeries" with intent to distribute, or those who received the material knowing it was made without consent. The European Union struck a deal in February 2024 on a similar bill that would criminalize deepfake pornography, as well as online harassment and revenge porn, by mid-2027. === Social media platforms === X responded to the sharing of these images on their own website with claims they would suspend accounts that participated in their spread. Despite this, the photos continued to be reshared among accounts of X, and spread to other platforms including Instagram and Reddit. X enforces a "synthetic and manipulated media policy", which has been criticized for its efficacy. They briefly blocked searches of Swift's name on January 27, 2024, reinstating them two days later. === Swifties === Fans of Taylor Swift, known as Swifties, responded to the circulation of these images by pushing the hashtag #ProtectTaylorSwift to trend on X. They also flooded other hashtags related to the images with more positive images and videos of her live performances. == Cultural significance == Deepfake pornography has remained highly controversial and has affected figures from other celebrities to ordinary people, most of whom are women. Journalists have opined that the involvement of a prominent public figure such as Swift in the dissemination of AI-generated pornography could bring public awareness and political reform to the issue.
Automated machine learning
Automated machine learning (AutoML) is the process of automating the tasks of applying machine learning to real-world problems. It is the combination of automation and ML. AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was proposed as an artificial intelligence-based solution to the growing challenge of applying machine learning. The high degree of automation in AutoML aims to allow non-experts to make use of machine learning models and techniques without requiring them to become experts in machine learning. Automating the process of applying machine learning end-to-end additionally offers the advantages of producing simpler solutions, faster creation of those solutions, and models that often outperform hand-designed models. Common techniques used in AutoML include hyperparameter optimization, meta-learning and neural architecture search. == Comparison to the standard approach == In a typical machine learning application, practitioners have a set of input data points to be used for training. The raw data may not be in a form that all algorithms can be applied to. To make the data amenable for machine learning, an expert may have to apply appropriate data pre-processing, feature engineering, feature extraction, and feature selection methods. After these steps, practitioners must then perform algorithm selection and hyperparameter optimization to maximize the predictive performance of their model. If deep learning is used, the architecture of the neural network must also be chosen manually by the machine learning expert. Each of these steps may be challenging, resulting in significant hurdles to using machine learning. AutoML aims to simplify these steps for non-experts, and to make it easier for them to use machine learning techniques correctly and effectively. AutoML plays an important role within the broader approach of automating data science, which also includes challenging tasks such as data engineering, data exploration and model interpretation and prediction. == Targets of automation == Automated machine learning can target various stages of the machine learning process. Steps to automate are: Data preparation and ingestion (from raw data and miscellaneous formats) Column type detection; e.g., Boolean, discrete numerical, continuous numerical, or text Column intent detection; e.g., target/label, stratification field, numerical feature, categorical text feature, or free text feature Task detection; e.g., binary classification, regression, clustering, or ranking Feature engineering Feature selection Feature extraction Meta-learning and transfer learning Detection and handling of skewed data and/or missing values Model selection - choosing which machine learning algorithm to use, often including multiple competing software implementations Ensembling - a form of consensus where using multiple models often gives better results than any single model Hyperparameter optimization of the learning algorithm and featurization Neural architecture search Pipeline selection under time, memory, and complexity constraints Selection of evaluation metrics and validation procedures Problem checking Leakage detection Misconfiguration detection Analysis of obtained results Creating user interfaces and visualizations == Challenges and Limitations == There are a number of key challenges being tackled around automated machine learning. A big issue surrounding the field is referred to as "development as a cottage industry". This phrase refers to the issue in machine learning where development relies on manual decisions and biases of experts. This is contrasted to the goal of machine learning which is to create systems that can learn and improve from their own usage and analysis of the data. Basically, it's the struggle between how much experts should get involved in the learning of the systems versus how much freedom they should be giving the machines. However, experts and developers must help create and guide these machines to prepare them for their own learning. To create this system, it requires labor intensive work with knowledge of machine learning algorithms and system design. Additionally, other challenges include meta-learning and computational resource allocation.
Fuzzy concept
A fuzzy concept is an idea of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. That means the idea is somewhat vague or imprecise. Yet it is not unclear or meaningless. It has a definite meaning, which can often be made more exact with further elaboration and specification — including a closer definition of the context in which the concept is used. The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept). Fuzzy concepts are often used to navigate imprecision in the real world, when precise information is not available and an approximate indication is sufficient to be helpful. Although the linguist George Philip Lakoff already defined the semantics of a fuzzy concept in 1973 (inspired by an unpublished 1971 paper by Eleanor Rosch,) the term "fuzzy concept" rarely received a standalone entry in dictionaries, handbooks and encyclopedias. Sometimes it was defined in encyclopedia articles on fuzzy logic, or it was simply equated with a mathematical “fuzzy set”. A fuzzy concept can be "fuzzy" for many different reasons in different contexts. This makes it harder to provide a precise definition that covers all cases. Paradoxically, the definition of fuzzy concepts may itself be somewhat "fuzzy". Lotfi A. Zadeh, known as "the father of fuzzy logic", claimed that "vagueness connotes insufficient specificity, whereas fuzziness connotes unsharpness of class boundaries". Not all scholars agree. With increasing academic literature on the subject, the term "fuzzy concept" is now more widely recognized as a philosophical, linguistic or scientific category, and the study of the characteristics of fuzzy concepts and fuzzy language is known as fuzzy semantics. “Fuzzy logic” has become a generic term for many different kinds of many-valued logics, and is applied in many different areas of research, computer programming and industrial design. For engineers, "Fuzziness is imprecision or vagueness of definition." For computer scientists, a fuzzy concept is an idea which is "to an extent applicable" in a situation. It means that the concept can have gradations of significance or unsharp (variable) boundaries of application — a "fuzzy statement" is a statement which is true "to some extent", and that extent can often be represented by a scaled value (a score). For mathematicians, a "fuzzy concept" is usually a fuzzy set or a combination of such sets (see fuzzy mathematics and fuzzy set theory). In cognitive linguistics, the things that belong to a "fuzzy category" exhibit gradations of family resemblance, and the borders of the category are not clearly defined. Through most of the 20th century, the idea of reasoning with fuzzy concepts faced considerable resistance from Western academic elites. They did not want to endorse the use of imprecise concepts in research or argumentation, and they often regarded fuzzy logic with suspicion, derision or even hostility. That may partly explain why the idea of a "fuzzy concept" did not get a separate entry in encyclopedias, handbooks and dictionaries. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward. That is mainly due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows very complex inferences about "variations on a theme" to be anticipated and fixed in a program. The Perseverance Mars rover, a driverless NASA vehicle used to explore the Jezero crater on the planet Mars, features fuzzy logic programming that steers it through rough terrain. Similarly, to the North, the Chinese Mars rover Zhurong used fuzzy logic algorithms to calculate its travel route in Utopia Planitia from sensor data. New neuro-fuzzy computational methods make it possible for machines to identify, measure, adjust and respond to fine gradations of significance with great precision. It means that practically useful concepts can be coded, sharply defined, and applied to all kinds of tasks, even if ordinarily these concepts are never exactly defined. Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets (see also fuzzy set theory). Fuzzy logic is not "woolly thinking", but a "precise logic of imprecision" which reasons with graded concepts and gradations of truth. Fuzzy concepts and fuzzy logic often play a significant role in artificial intelligence programming, for example because they can model human cognitive processes more easily than other methods. == Origins == Vagueness and fuzziness have probably always been a part of human experience. In the West, ancient texts show that philosophers and scientists were already thinking critically about this in classical antiquity. Most often, they regarded vagueness as a problem: as an obstacle to clear thinking, as a source of confusion, or as an evasive tactic. It got in the way of providing clear orientation, guidance, direction and leadership. Therefore, vagueness became associated with a hermeneutic of suspicion — it was considered as something to avoid, as something undesirable. By contrast, in the ancient Chinese tradition of Daoist thought of Laozi and Zhuang Zhou, "vagueness is not regarded with suspicion, but is simply an acknowledged characteristic of the world around us" — a subject for meditation and a source of insight. === Sorites paradox === The ancient Sorites paradox raised the logical problem, of how we could exactly define the threshold at which a change in quantitative gradation turns into a qualitative or categorical difference. With some physical processes, this threshold seems relatively easy to identify. For example, water turns into steam at 100 °C or 212 °F. Of course, the boiling point depends partly on atmospheric pressure, which decreases at higher altitudes; it is also affected by the level of humidity — in that sense, the boiling point is "somewhat fuzzy", because it can vary under different conditions. Nevertheless, for every altitude, level of air pressure and degree of humidity, we can predict accurately what the boiling point will be, if we know the relevant conditions. With many other processes and gradations, however, the point of change is much more difficult to locate, and remains somewhat vague. Thus, the boundaries between qualitatively different things may be unsharp: we know that there are boundaries, but we cannot define them exactly. For example, to identify "the oldest city in the world", we have to define what counts as a city, and at what point a growing human settlement becomes a city. === The continuum fallacy and Loki's wager === According to the modern idea of the continuum fallacy, the fact that a statement is to an extent vague, does not automatically mean that it has no validity. The question then arises, of how (by what method or approach) we could ascertain and define the validity that the fuzzy statement does have. The Nordic myth of Loki's wager suggested that concepts that lack precise meanings or lack precise boundaries of application cannot be operated with, because they evade any clear definition. However, the 20th-century idea of "fuzzy concepts" proposes that "somewhat vague terms" can be operated with, because we can explicate and define the variability of their application — by assigning numbers to gradations of applicability. This idea sounds simple enough, but it had large implications. === Precursors and pioneers === In Western civilization, the intellectual recognition of fuzzy concepts has been traced back to a diversity of famous and less well-known thinkers, including (among many others) Eubulides, Epicurus, Plato, Cicero, William Ockham and John Buridan, Georg Wilhelm Friedrich Hegel, Karl Marx and Friedrich Engels, Friedrich Nietzsche, William James, Hugh MacColl, Charles S. Peirce, Hans Reichenbach, Carl Gustav Hempel, Max Black, Arto Salomaa, Ludwig Wittgenstein, Jan Łukasiewicz, Emil Leon Post, Alfred Tarski, Georg Cantor, Nicolai A. Vasiliev, Kurt Gödel, Stanisław Jaśkowski, Willard Van Orman Quine, George J. Klir, Petr Hájek, Joseph Goguen, Ronald R. Yager, Enrique Héctor Ruspini, Jan Pavelka, Didier Dubois, Bernadette Bouchon-Meunier, and Donald Knuth. Across at least two and a half millennia, all of them had something to say about graded concepts with unsharp boundaries. This suggests at least that the awareness of the existence of concepts with "fuzzy" characteristics, in one form or another, has a very long history in human thought. Quite a few 20th century logicians, mathematicians and philosophers also tried to analyze the characteristics of fuzzy concepts as a recognized species, sometimes with the aid of some kind of many-valued logic or substructural logic. An early attempt in the post-WW2 era to create a mathematical theory of sets with gradations of