AI Chat Character Talkie

AI Chat Character Talkie — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

  • Machine learning

    Machine learning

    Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of statistical algorithms that can learn from data and generalize to unseen data, and thus perform tasks without being explicitly programmed. Advances in the field of deep learning have allowed neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. Statistics and mathematical optimisation methods compose the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysis (EDA) through unsupervised learning. From a theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional machine learning and deep learning algorithms can be described as empirical risk minimisation under this framework. == History == The term machine learning was coined in 1959 by Arthur Samuel, an IBM employee and pioneer in the field of computer gaming and artificial intelligence. The synonym self-teaching computers was also used during this time period. The earliest machine learning program was introduced in the 1950s, when Samuel invented a computer program that calculated the chance of winning in checkers for each side, but the history of machine learning is rooted in decades of efforts to study human cognitive processes. In 1949, Canadian psychologist Donald Hebb published the book The Organization of Behavior, in which he introduced a theoretical neural structure formed by certain interactions among nerve cells. The Hebbian theory of neuron interaction set the groundwork for how many machine learning algorithms work, with connected artificial neurons changing the strength of their connections based on data. Other researchers who have studied human cognitive systems contributed to the modern machine learning technologies as well, including Walter Pitts and Warren McCulloch, who proposed the first mathematical model of neural networks including algorithms that mirror human thought processes. By the early 1960s, an experimental "learning machine" with punched tape memory, called Cybertron, had been developed by Raytheon Company to analyse sonar signals, electrocardiograms, and speech patterns using rudimentary reinforcement learning. It was repetitively "trained" by a human operator/teacher to recognise patterns and equipped with a "goof" button to cause it to reevaluate incorrect decisions. A representative book on research into machine learning during the 1960s was Nils Nilsson's book "Learning Machines", dealing mostly with machine learning for pattern classification. Interest related to pattern recognition continued into the 1970s, as described by Duda and Hart in 1973. In 1981, a report was given on using teaching strategies so that an artificial neural network learns to recognise 40 characters (26 letters, 10 digits, and 4 special symbols) from a computer terminal. Tom M. Mitchell provided a widely quoted, more formal definition of the algorithms studied in the machine learning field: "A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P if its performance at tasks in T, as measured by P, improves with experience E." This definition of the tasks in which machine learning is concerned is fundamentally operational rather than defining the field in cognitive terms. This follows Alan Turing's proposal in his paper "Computing Machinery and Intelligence", in which the question, "Can machines think?", is replaced by asking whether machines can convincingly imitate a human in its responses to human-posed questions. In 2014 Ian Goodfellow and others introduced generative adversarial networks (GANs) which could produce realistic synthetic data. By 2016 AlphaGo had won against top human players in Go using reinforcement learning techniques. == Relationships to other fields == === Artificial intelligence === As a scientific endeavour, machine learning grew out of the quest for artificial intelligence (AI). In the early days of AI as an academic discipline, some researchers were interested in having machines learn from data. They attempted to approach the problem with various symbolic methods, as well as what were then termed "neural networks"; these were mostly perceptrons and other models that were later found to be reinventions of the generalised linear models of statistics. Probabilistic reasoning was also employed, especially in automated medical diagnosis. However, an increasing emphasis on the logical, knowledge-based approach caused a rift between AI and machine learning. Probabilistic systems were plagued by theoretical and practical problems of data acquisition and representation. By 1980, expert systems had come to dominate AI, and statistics was out of favour. Work on symbolic/knowledge-based learning continued within AI, leading to inductive logic programming (ILP), but the more statistical line of research was now outside the field of AI proper, in pattern recognition and information retrieval. Neural network research was abandoned by AI and computer science around the same time. This subfield, termed "connectionism", was continued by researchers from other disciplines, including John Hopfield, David Rumelhart, and Geoffrey Hinton. Their main success came in the mid-1980s with the reinvention of backpropagation. Machine learning (ML), reorganised and recognised as its own field, started to flourish in the 1990s. The field changed its goal from achieving artificial intelligence to tackling solvable problems of a practical nature. It shifted focus away from the symbolic approaches it had inherited from AI, and toward methods and models borrowed from statistics, fuzzy logic, and probability theory. === Data compression === === Data mining === Machine learning and data mining often employ the same methods and overlap significantly, but while machine learning focuses on prediction based on known properties learned from the training data, data mining focuses on the discovery of previously unknown properties in the data (this is the analysis step of knowledge discovery in databases). Data mining uses many machine learning methods, but with different goals; on the other hand, machine learning also employs data mining methods as "unsupervised learning" or as a preprocessing step to improve learner accuracy. Much of the confusion between these two research communities comes from the basic assumptions they work with: in machine learning, performance is usually evaluated with respect to the ability to reproduce known knowledge, while in knowledge discovery and data mining (KDD) the key task is the discovery of previously unknown knowledge. Evaluated with respect to known knowledge, an uninformed (unsupervised) method will easily be outperformed by other supervised methods, while in a typical KDD task, supervised methods cannot be used due to the unavailability of training data. Machine learning also has intimate ties to optimization: Many learning problems are formulated as minimisation of some loss function on a training set of examples. Loss functions express the discrepancy between the predictions of the model being trained and the actual problem instances (for example, in classification, one wants to assign a label to instances, and models are trained to correctly predict the preassigned labels of a set of examples). === Generalization === Characterizing the generalisation of various learning algorithms is an active topic of current research, especially for deep learning algorithms. === Statistics === Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalisable predictive patterns. Conventional statistical analyses require the a priori selection of a model most suitable for the study data set. In addition, only significant or theoretically relevant variables based on previous experience are included for analysis. In contrast, machine learning is not built on a pre-structured model; rather, the data shape the model by detecting underlying patterns. The more variables (input) used to train the model, the more accurate the ultimate model will be. Leo Breiman distinguished two statistical modelling paradigms: the data model and the algorithmic model, wherein "algorithmic model" means more or less the machine learning algorithms like Random forest. Some statisticians have adopted methods from machine learning, producing the field of statistical learning. === Statistical physics === Analytical and computational techniques derived from deep-rooted physics of disordered systems can be extended to large-scale problems, including machine learning, e.g., to analyse the weight space of deep neural networks. Statistical physics is thus

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  • AI Action Summit 2025

    AI Action Summit 2025

    The Artificial Intelligence (AI) Action Summit (French: Sommet pour l'action sur l'intelligence artificielle or Sommet pour l'action sur l'IA, SAIA) was held at the Grand Palais in Paris, France, from 10 to 11 February 2025. The summit was co-chaired by French President Emmanuel Macron and Indian Prime Minister Narendra Modi. The 2025 AI Action Summit followed the 2023 AI Safety Summit hosted at Bletchley Park in the UK, and the 2024 AI Seoul Summit in South Korea. This series of AI summits continued with the AI Impact Summit in Delhi, which was hosted by India in February 2026. Whereas the 2023 AI Safety Summit was attended by representatives from 29 governments and executives from only a handful of AI companies, over 1,000 participants from more than 100 countries attended the 2025 Paris AI Summit, representing government leaders, international organisations, the academic and research community, the private sector, and civil society. == Background == The First International AI Safety Report was published on 29 January 2025. Commissioned after the Bletchley Park AI Safety Summit, the report focused on the risks and threats posed by general-purpose AI, and was slated for discussion at the Paris summit as part of the "Trust in AI" pillar. Whereas the first summit was focused on the catastrophic risks of AI and their mitigation, the Paris meeting was recast as an "AI Action Summit" emphasising innovation, practical implementation, and potential economic opportunities of AI, while also exploring a broader range of risks including its environmental impact and disruptions to the labour market. In the weeks leading up to the Paris summit, government leaders had also started to rally around "national champions" in AI, partly in response to Chinese AI startup DeepSeek, which had released a new model rivalling OpenAI o1. On Sunday 9 February, French President Emmanuel Macron posted a compilation of AI-generated deepfake video clips of himself on Instagram to help publicise the start of the 2025 AI Action Summit the following day. While acknowledging the humour of the deepfakes, the real Macron states in the video that using artificial intelligence, "we can do some very big things: change healthcare, energy, life in our society". == Proceedings == === Day 1 === In her opening address, French special envoy Anne Bouverot discussed the environmental impact of AI, acknowledging the technology's "current trajectory is unsustainable". General secretary Christy Hoffman of the UNI Global Union said that "AI-driven productivity gains risk turning the technology into yet another engine of inequality, further straining our democracies". Chinese Vice Premier Zhang Guoqing made a speech expressing China's willingness "to work with other countries to promote development, safeguard security, and share achievements in the field of artificial intelligence". Google CEO Sundar Pichai said in his speech that while the rise of AI brings many risks, "The biggest risk is missing out". He discussed Google's long track record of AI research and said that the company is investing further into "deep research" agents that can autonomously search the Internet and compile a full analysis for users. A new coalition, the Robust Open Online Safety Tools (ROOST) initiative, debuted at the summit. Supported by Google, Discord, OpenAI, and Roblox, and incubated at the Institute of Global Politics at Columbia University, the organisation is developing free, open-source tools to detect and report child sexual abuse material (CSAM). In his speech closing the first day, President Emmanuel Macron emphasized that France has the capability to deliver the power required by AI companies, thanks to its production of nuclear energy. While declaring that Europe was "back in the race" for AI, Macron said that the region was "too slow" for investors, and called on the EU to "simplify regulation" and "resynchronize with the rest of the world". === Day 2 === On 11 February 2025, the French government announced its $400 million endowment of Current AI, a new foundation to support the creation of AI "public goods" including high-quality datasets and open-source tools and infrastructure. Launched by President Macron, Current AI is backed by nine governments – Finland, France, Germany, Chile, India, Kenya, Morocco, Nigeria, Slovenia, and Switzerland – plus various philanthropic organisations such as the Omidyar Group and the McGovern Foundation, and private companies such as Google and Salesforce. Another initiative launched at the summit was the Coalition for Sustainable AI. Led by France, the UN Environment Programme (UNEP), and the International Telecommunication Union (ITU), the coalition has the support of 11 countries, five international organisations, and 37 tech companies including EDF, IBM, Nvidia, and SAP. The Summit of Heads of State and Government took place with a plenary session in the Grand Palais. Prime Minister Narendra Modi of India stressed the need to "democratise technology" and "[ensure] access to all, especially in the Global South". Vice President JD Vance of the United States used his speech to warn against "excessive regulation of the AI" which "could kill a transformative sector just as it's taking off". Vance also warned other leaders against cooperating with "authoritarian regimes" on AI, a comment widely interpreted as a reference to China. == Investments == At the summit, the European Union made several announcements related to planned investments supporting AI development. President Ursula von der Leyen of the European Commission launched InvestAI, a €200 billion initiative, including €20 billion to build four AI gigafactories to train highly complex, very large models. In addition, a coalition of more than 60 European companies launched the EU AI Champions Initiative. Led by venture capital firm General Catalyst, the coalition plans to invest €150 billion in AI-related businesses and infrastructure in Europe over five years. President Emmanuel Macron announced that private investors had pledged to invest nearly €110 billion in the AI sector in France. Financing of between €30 and €50 billion is expected from the United Arab Emirates to build a very large data centre campus, with another €20 billion from the Canadian investment firm Brookfield Corporation. French startup Mistral AI and Helsing, a German-British company, announced their partnership in developing vision-language-action models helping soldiers use AI on the battlefield. == Reactions == The Financial Times editorial board noted that the Paris summit "highlighted a shift in the dynamics towards geopolitical competition", which it characterised as "a new AI arms race" between the US and China, with Europe "trying to carve out its role". Fortune.com AI editor Jeremy Kahn described the 2025 Paris Summit as an "AI festival, complete with glitzy corporate side events and even a late night dance party", contrasting it with the "decidedly sober" mood of the inaugural AI Safety Summit at Bletchley Park. Many experts of the AI Safety Community expressed disappointment that the Paris Summit did not do enough to address AI risks, with Anthropic CEO Dario Amodei calling it a "missed opportunity". Others voicing similar concerns included David Leslie of the Alan Turing Institute and Max Tegmark of the Future of Life Institute. Reporting from Paris, technology columnist Kevin Roose of The New York Times wrote, "The biggest surprise of the Paris summit, for me, has been that policymakers can't seem to grasp how soon powerful AI systems could arrive, or how disruptive they could be." == Statement on inclusive and sustainable AI == At the summit, 58 countries, including France, China, and India, signed a joint declaration, the Statement on Inclusive and Sustainable Artificial Intelligence for People and the Planet. The statement outlines general principles such as accessibility and overcoming the digital divide; developing AI that is open, transparent, ethical, safe, and trustworthy; avoiding market concentration of AI development to encourage innovation; positive outcomes for labour markets; making AI sustainable; and promoting international cooperation and governance. The US and UK refused to sign the declaration on inclusive and sustainable AI. The UK government said in a brief statement that the international agreement did not go far enough in defining global governance of AI and addressing concerns about its impact on national security. === Signatories === The list of signatory countries to the statement for inclusive and sustainable AI in alphabetical order: Additional signatories included the following international bodies and research institutes: ALAI (Latin American Association on Internet) African Union (AU) Commission BEUC The European Consumer Organisation Center for Democracy and Technology Council of Europe European Commission (and the 27 member states) Hugging Face INRIA Institute of Advanced Study OEC

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  • The Fractal Prince

    The Fractal Prince

    The Fractal Prince is the second science fiction novel by Hannu Rajaniemi and the second novel to feature the post-human gentleman thief Jean le Flambeur. It was published in Britain by Gollancz in September 2012, and by Tor in the same year in the US. The novel is the second in the trilogy, following The Quantum Thief (2010) and preceding The Causal Angel (2014). == Plot summary == After the events of The Quantum Thief, Jean le Flambeur and Mieli are on their way to Earth. Jean is trying to open the Schrödinger's Box he retrieved from the memory palace on the Oubliette. After making little progress, he is prodded by the ship Perhonen to talk to Mieli, who turns out to be possessed by the pellegrini again. This time, Jean identifies Mieli's employer as a Sobornost Founder, Joséphine Pellegrini, and gets her to reveal how he got captured, thereby picking up the clues to make plans for his next heist. No sooner is that done than an attack comes from the Hunter. The ship and crew barely survived that, and Jean realizes that he has to find a better way to open the Box - fast. Mieli has been very quiet after they left Mars. She has given up almost everything to the pellegrini, even her identity, as she has promised to let the pellegrini make gogols of her in exchange for rescuing the thief. Yet, having to work with the thief is testing her, especially when the thief eventually does something even more unforgivable than stealing Sydän's jewel from her. In the city of Sirr, on an Earth ravaged by wildcode, Tawaddud and Dunyazad are sisters and members of the powerful Gomelez family. Tawaddud is the black sheep of the family, having run away from her husband and consorted with a notorious jinn, a disembodied intelligence from the wildcode desert. Now Cassar Gomelez, her father, hopes to get her to curry favor with a gogol merchant, Abu Nuwas, so that he has enough votes in the Council for the upcoming decision to renegotiate the Cry of Wrath Accords with the Sobornost. Soon, Tawaddud is embroiled in an investigation with a Sobornost envoy into the murder that triggered the need for her father to forge a new alliance in the first place, and forced to confront old secrets that will change Sirr forever. Somewhere else, in a bookshop and on a beach, a young boy is at play. His mother has told him not to talk to strangers, but there has never been anyone here before. Until now. Should he talk to them? == Influences == In the acknowledgments, Rajaniemi cites the influence of "Andy Clark, Douglas Hofstadter, Maurice Leblanc, Jan Potocki and [...] The Arabian Nights." === Self-loops === In the novel, the idea that the mind is a self-loop may have been influenced by the theories of the Professor of Philosophy, Andy Clark, and the book I Am a Strange Loop by Douglas Hofstadter. === Frame stories === The novel uses frame stories rather extensively, a feature also of The Arabian Nights and Jan Potocki's The Manuscript Found in Saragossa. Several characters in Sirr are the namesakes of characters in these two earlier works as well. The events in The Quantum Thief are also retold at least once by Jean le Flambeur in the course of the events in this novel. == Reception == The novel has received generally positive reviews. However, criticisms of the novel still revolve around Rajaniemi's uncompromising "show, don't tell" style. For example, Amy Goldschlager, writing for the Los Angeles Review of Books, suggested that "[a] bit more explication of the physics involved (“surfing the deficit angle”?) would really be helpful, more helpful than the description of the Schrödinger’s Cat problem given earlier in the book".

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  • Smart speaker

    Smart speaker

    A smart speaker is a type of loudspeaker and voice command device with an integrated virtual assistant that offers interactive actions and hands-free activation with the help of one "wake word" (or several "wake words"). Some smart speakers also act as smart home hubs by using Wi-Fi, Bluetooth, Thread, and other protocol standards to extend usage beyond audio playback and control home automation devices connected through a local area network. == History == Early voice-activated devices began in 2013 with MIT's Jasper project, which used multiple microphones and cloud software to power hands-free interactions from across a room. The first commercial smart speaker was the Amazon Echo, which was released in 2014 powered by Alexa and a ring of far-field microphones. Google followed in 2016 with Home, powered by Google Assistant. By 2017, devices like the Echo Show and Home Hub (later called Nest Hub) added touchscreens and video, creating the "smart display" subcategory. In 2018, Apple joined the smart speaker trend by launching the HomePod, which focused on high-quality audio alongside their built-in assistant Siri. ASUS release its own smart Speaker Xiao-Bu in 2019 with Artificial Intelligence, it terminates the Cloud Service on June 1st, 2025, which means all real-time service such as weather, news, currency conversion is affected. Sonos's 1st smart speaker Sonos One released in 2017, powered by Alexa. Invoke by Harman Kardon was powered by Microsoft's intelligent personal assistant, Cortana. In the early 2020s, smart speakers gained on-device voice processing for faster responses and improved privacy. New standards such as Matter and Thread allowed multitudes of smart-home devices (even from completely different brands) to work together. == Features == === Audio and Voice === Smart speakers use multiple microphones along with noise-cancelling software to pick up your voice from across the room, even when music is playing or the assistant is already talking. Noise suppression and echo cancellation is also used by the speaker so it can focus in on who is talking and ignore any background noises. Most smart speaker models can recognize who is speaking by voiceprint, which allows the speaker to grab information from that person's calendar, preferences, or music playlists. Listening to music on a speaker is when importance for good audio quality becomes apparent. Entry-level (cheaper) speakers such as the Home Mini or the Echo Dot have a single full-range driver. These lower-end speakers typically aren't great for listening to music as the audio quality is pretty poor. More advanced units such as the Home Max or Echo Studio have separate tweeters and woofers meant for listening to music in high quality. === Connectivity and smart-home control === Most connect over Wi-Fi or Bluetooth and support hub protocols like Thread and Matter. That lets them not only stream and play music but also allows you to control various brands of smart lights, thermostats, door locks, cameras, and much more-all from one point of control. Each can have its own designated interface and features in-house, usually launched or controlled via application or home automation software. These devices are able to communicate with each other via peer-to-peer connection through mesh networking. These speakers and related smart devices are typically controlled with one smartphone application. === Assistant services and skills === The built-in assistants handle timers, alarms, reminders, news briefings, weather updates, send messages to other smart devices, send texts, make calls, and simple questions. You can combine actions together in what are typically known as routines (for example saying "good morning" turns on lights, starts the coffee, says the weather, and reads the news) and add extra functions known as skills or actions (for things like ordering food or playing trivia games). This hands-free use of smart speakers can help assist those with disabilities. Most other technologies need the user to be able to physically interact with the device. Smart speakers are not bound by these limitations and can serve as an excellent tool for those who are unable to use their arms or legs or have vision issues. Although these tasks can be completed by a phone or computer, consumers tend to lean towards smart speakers due to factors such as their range being much greater than that of a phone and the need to not have to physically interact with the speaker to get the voice assistant as with most smartphones, certain parts of a phone may need to be interacted with to activate the speaking assistant. === Smart displays === Some smart speakers also include a screen to show the user a visual response. A smart speaker with a touchscreen is known as a smart display; these integrate a conversational user interface with display screens to augment voice interaction with images and video. They are powered by one of the common voice assistants and offer additional controls for smart home devices, feature streaming apps, and web browsers with touch controls for selecting content. The first smart displays were introduced in 2017 by Amazon (Amazon Echo Show) and Google (Google/Nest Home Hub). Hotel chain Marriott International partnered with Amazon to install Echo devices in select hotels since 2018. A Taiwanese startup, Aiello, launched the Aiello Voice Assistant (AVA) in the Asian hotel market in 2019, claiming it is powered by a multi-AI model system. Angie by Nomadix, which is similar to the Amazon Echo, launched its first product in 2017, specifically targeting hotel properties in the North America. In May 2019, Angie Hospitality acquired the assets of Roxy, a competitor that also built its own speech-enabled virtual assistant technology for hotels. This acquisition merged two proprietary NLP stacks into the current Nomadix product. === Artificial intelligence === The newest speakers can use on-device AI or cloud-based generative models to allow the smart speaker to carry on much more natural conversations, draft emails or recipes, suggest ideas based on context, or even create short pieces of music or art. This AI evolution allows these speakers to do far more than what they could do before. == Accuracy == According to a study by Proceedings of the National Academy of Sciences of the United States of America released In March 2020, the six biggest tech development companies, Amazon, Apple, Google, Yandex, IBM and Microsoft, have misidentified more words spoken by "black people" than "white people". The systems tested errors and unreadability, with a 19 and 35 percent discrepancy for the former and a 2 and 20 percent discrepancy for the latter. The North American Chapter of the Association for Computational Linguistics (NAACL) also identified a discrepancy between male and female voices. According to their research, Google's speech recognition software is 13 percent more accurate for men than women. It performs better than the systems used by Bing, AT&T, and IBM. == Privacy concerns == The built-in microphone in smart speakers is continuously listening for wake words followed by a command. However, these continuously listening microphones also raise privacy concerns among users. According to a survey taken by 1,007 people in Western Europe, it is clear that privacy is the biggest concern holding consumers back from buying "smart" products. these concerns include what is being recorded, how the data will be used, how it will be protected, and whether it will be used for invasive advertising. Furthermore, an analysis of Amazon Echo Dots showed that 30–38% of "spurious audio recordings were human conversations", suggesting that these devices capture audio other than strictly detection of the wake word. === As a wiretap === There are strong concerns that the ever-listening microphone of smart speakers presents a perfect candidate for wiretapping. In 2017, British security researcher Mark Barnes showed that pre-2017 Echos have exposed pins which allow for a compromised OS to be booted. According to Umar Iqbal, an assistant professor at Washington University in St. Louis, research indicates that data from consumer interactions with Alexa was used to targeted advertisements and products to consumer with over 40% of transmitted data lacking proper encryption raising privacy concerns. Further data indicates that due to the Smart Speakers ability to always capture audio, it begins to pick up on external conversations from consumers not related to commands given to the smart speaker. Things such as other members in the household, consumers on the phone and even TV audio can be picked up by these speakers and stored for future use by companies. === Voice assistance vs privacy === While voice assistants provide a valuable service, there can be some hesitation towards using them in various social contexts, such as in public or around other users. However, only more recently have users begun interac

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  • Multimedia database

    Multimedia database

    A Multimedia database (MMDB) is a collection of related for multimedia data. The multimedia data include one or more primary media data types such as text, images, graphic objects (including drawings, sketches and illustrations) animation sequences, audio and video. A Multimedia Database Management System (MMDBMS) is a framework that manages different types of data potentially represented in a wide diversity of formats on a wide array of media sources. It provides support for multimedia data types, and facilitate for creation, storage, access, query and control of a multimedia database. == Contents of MMDB == A Multimedia Database (MMDB) hosts one or more multimedia data types (i.e. text, images, graphic objects, audio, video, animation sequences). These data types are broadly categorized into three classes: Static media (time-independent: image and graphic object). Dynamic media (time-dependent: audio, video and animation). Dimensional media(3D game and computer aided drafting programs). === Comparison of multimedia data types === Additionally, a Multimedia Database (MMDB) needs to manage additional information pertaining to the actual multimedia data. The information is about the following: Media data: the actual data representing an object. Media format data: information about the format of the media data after it goes through the acquisition, processing, and encoding phases. Media keyword data: the keyword descriptions, usually relating to the generation of the media data. Media feature data: content dependent data such as contain information about the distribution of colours, the kinds of textures and the different shapes present in an image. The last three types are called metadata as they describe several different aspects of the media data. The media keyword data and media feature data are used as indices for searching purpose. The media format data is used to present the retrieved information. == Requirements of Multimedia databases == Like the traditional databases, Multimedia databases should address the following requirements: Integration Data items do not need to be duplicated for different programs invocations Data independence Separate the database and the management from the application programs Concurrency control Allows concurrent transactions Persistence Data objects can be saved and re-used by different transactions and program invocations Privacy Access and authorization control Integrity control Ensures database consistency between transactions Recovery Failures of transactions should not affect the persistent data storage Query support Allows easy querying of multimedia data Multimedia databases should have the ability to uniformly query data (media data, textual data) represented in different formats and have the ability to simultaneously query different media sources and conduct classical database operations across them. (Query support) They should have the ability to retrieve media objects from a local storage device in a good manner. (Storage support) They should have the ability to take the response generated by a query and develop a presentation of that response in terms of audio-visual media and have the ability to deliver this presentation. (Presentation and delivery support) == Issues and challenges == Multimedia data consists of a variety of media formats or file representations including TIFF, BMP, PPT, IVUE, FPX, JPEG, MPEG, AVI, MID, WAV, DOC, GIF, EPS, PNG, etc. Because of restrictions on the conversion from one format to the other, the use of the data in a specific format has been limited as well. Usually, the data size of multimedia is large such as video; therefore, multimedia data often require a large storage. Multimedia database consume a lot of processing time, as well as bandwidth. Some multimedia data types such as video, audio, and animation sequences have temporal requirements that have implications on their storage, manipulation and presentation, but images, video and graphics data have special constraints in terms of their content. == Application areas == Examples of multimedia database application areas: Digital Libraries News-on-Demand Video-on-Demand Music database Geographic Information Systems (GIS) Telemedicine

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  • Degree of truth

    Degree of truth

    In classical logic, propositions are typically unambiguously considered as being true or false. For instance, the proposition one is both equal and not equal to itself is regarded as simply false, being contrary to the Law of Noncontradiction; while the proposition one is equal to one is regarded as simply true, by the Law of Identity. However, some mathematicians, computer scientists, and philosophers have been attracted to the idea that a proposition might be more or less true, rather than wholly true or wholly false. Consider this pizza is hot. In mathematics, this idea can be developed in terms of fuzzy logic. In computer science, it has found application in artificial intelligence. In philosophy, the idea has proved particularly appealing in the case of vagueness. Degrees of truth is an important concept in law. The term is an older concept than conditional probability. Instead of determining the objective probability, only a subjective assessment is defined. In adjudicative processes, 'substantive truth' is distinct from 'formal legal truth' which comes in four degrees: hearsay, balance of probabilities, proven beyond reasonable doubt and absolute truth (knowledge reserved unto God).

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  • Possibility theory

    Possibility theory

    Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively. Professor Lotfi Zadeh first introduced possibility theory in 1978 as an extension of his theory of fuzzy sets and fuzzy logic. Didier Dubois and Henri Prade further contributed to its development. Earlier, in the 1950s, economist G. L. S. Shackle proposed the min/max algebra to describe degrees of potential surprise. == Formalization of possibility == For simplicity, assume that the universe of discourse Ω is a finite set. A possibility measure is a function Π {\displaystyle \Pi } from 2 Ω {\displaystyle 2^{\Omega }} to [0, 1] such that: Axiom 1: Π ( ∅ ) = 0 {\displaystyle \Pi (\varnothing )=0} Axiom 2: Π ( Ω ) = 1 {\displaystyle \Pi (\Omega )=1} Axiom 3: Π ( U ∪ V ) = max ( Π ( U ) , Π ( V ) ) {\displaystyle \Pi (U\cup V)=\max \left(\Pi (U),\Pi (V)\right)} for any disjoint subsets U {\displaystyle U} and V {\displaystyle V} . It follows that, like probability on finite probability spaces, the possibility measure is determined by its behavior on singletons: Π ( U ) = max ω ∈ U Π ( { ω } ) . {\displaystyle \Pi (U)=\max _{\omega \in U}\Pi (\{\omega \}).} Axiom 1 can be interpreted as the assumption that Ω is an exhaustive description of future states of the world, because it means that no belief weight is given to elements outside Ω. Axiom 2 could be interpreted as the assumption that the evidence from which Π {\displaystyle \Pi } was constructed is free of any contradiction. Technically, it implies that there is at least one element in Ω with possibility 1. Axiom 3 corresponds to the additivity axiom in probabilities. However, there is an important practical difference. Possibility theory is computationally more convenient because Axioms 1–3 imply that: Π ( U ∪ V ) = max ( Π ( U ) , Π ( V ) ) {\displaystyle \Pi (U\cup V)=\max \left(\Pi (U),\Pi (V)\right)} for any subsets U {\displaystyle U} and V {\displaystyle V} . Because one can know the possibility of the union from the possibility of each component, it can be said that possibility is compositional with respect to the union operator. Note however that it is not compositional with respect to the intersection operator. Generally: Π ( U ∩ V ) ≤ min ( Π ( U ) , Π ( V ) ) ≤ max ( Π ( U ) , Π ( V ) ) . {\displaystyle \Pi (U\cap V)\leq \min \left(\Pi (U),\Pi (V)\right)\leq \max \left(\Pi (U),\Pi (V)\right).} When Ω is not finite, Axiom 3 can be replaced by: For all index sets I {\displaystyle I} , if the subsets U i , i ∈ I {\displaystyle U_{i,\,i\in I}} are pairwise disjoint, Π ( ⋃ i ∈ I U i ) = sup i ∈ I Π ( U i ) . {\displaystyle \Pi \left(\bigcup _{i\in I}U_{i}\right)=\sup _{i\in I}\Pi (U_{i}).} == Necessity == Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, possibility theory uses two concepts, the possibility and the necessity of the event. For any set U {\displaystyle U} , the necessity measure is defined by N ( U ) = 1 − Π ( U ¯ ) {\displaystyle N(U)=1-\Pi ({\overline {U}})} . In the above formula, U ¯ {\displaystyle {\overline {U}}} denotes the complement of U {\displaystyle U} , that is the elements of Ω {\displaystyle \Omega } that do not belong to U {\displaystyle U} . It is straightforward to show that: N ( U ) ≤ Π ( U ) {\displaystyle N(U)\leq \Pi (U)} for any U {\displaystyle U} and that: N ( U ∩ V ) = min ( N ( U ) , N ( V ) ) {\displaystyle N(U\cap V)=\min(N(U),N(V))} . Note that contrary to probability theory, possibility is not self-dual. That is, for any event U {\displaystyle U} , we only have the inequality: Π ( U ) + Π ( U ¯ ) ≥ 1 {\displaystyle \Pi (U)+\Pi ({\overline {U}})\geq 1} However, the following duality rule holds: For any event U {\displaystyle U} , either Π ( U ) = 1 {\displaystyle \Pi (U)=1} , or N ( U ) = 0 {\displaystyle N(U)=0} Accordingly, beliefs about an event can be represented by a number and a bit. == Interpretation == There are four cases that can be interpreted as follows: N ( U ) = 1 {\displaystyle N(U)=1} means that U {\displaystyle U} is necessary. U {\displaystyle U} is certainly true. It implies that Π ( U ) = 1 {\displaystyle \Pi (U)=1} . Π ( U ) = 0 {\displaystyle \Pi (U)=0} means that U {\displaystyle U} is impossible. U {\displaystyle U} is certainly false. It implies that N ( U ) = 0 {\displaystyle N(U)=0} . Π ( U ) = 1 {\displaystyle \Pi (U)=1} means that U {\displaystyle U} is possible. I would not be surprised at all if U {\displaystyle U} occurs. It leaves N ( U ) {\displaystyle N(U)} unconstrained. N ( U ) = 0 {\displaystyle N(U)=0} means that U {\displaystyle U} is unnecessary. I would not be surprised at all if U {\displaystyle U} does not occur. It leaves Π ( U ) {\displaystyle \Pi (U)} unconstrained. The intersection of the last two cases is N ( U ) = 0 {\displaystyle N(U)=0} and Π ( U ) = 1 {\displaystyle \Pi (U)=1} meaning that I believe nothing at all about U {\displaystyle U} . Because it allows for indeterminacy like this, possibility theory relates to the graduation of a many-valued logic, such as intuitionistic logic, rather than the classical two-valued logic. Note that unlike possibility, fuzzy logic is compositional with respect to both the union and the intersection operator. The relationship with fuzzy theory can be explained with the following classic example. Fuzzy logic: When a bottle is half full, it can be said that the level of truth of the proposition "The bottle is full" is 0.5. The word "full" is seen as a fuzzy predicate describing the amount of liquid in the bottle. Possibility theory: There is one bottle, either completely full or totally empty. The proposition "the possibility level that the bottle is full is 0.5" describes a degree of belief. One way to interpret 0.5 in that proposition is to define its meaning as: I am ready to bet that it's empty as long as the odds are even (1:1) or better, and I would not bet at any rate that it's full. == Possibility theory as an imprecise probability theory == There is an extensive formal correspondence between probability and possibility theories, where the addition operator corresponds to the maximum operator. A possibility measure can be seen as a consonant plausibility measure in the Dempster–Shafer theory of evidence. The operators of possibility theory can be seen as a hyper-cautious version of the operators of the transferable belief model, a modern development of the theory of evidence. Possibility can be seen as an upper probability: any possibility distribution defines a unique credal set of admissible probability distributions by K = { P ∣ ∀ S P ( S ) ≤ Π ( S ) } . {\displaystyle K=\{\,P\mid \forall S\ P(S)\leq \Pi (S)\,\}.} This allows one to study possibility theory using the tools of imprecise probabilities. == Necessity logic == We call generalized possibility every function satisfying Axiom 1 and Axiom 3. We call generalized necessity the dual of a generalized possibility. The generalized necessities are related to a very simple and interesting fuzzy logic called necessity logic. In the deduction apparatus of necessity logic the logical axioms are the usual classical tautologies. Also, there is only a fuzzy inference rule extending the usual modus ponens. Such a rule says that if α and α → β are proved at degree λ and μ, respectively, then we can assert β at degree min{λ,μ}. It is easy to see that the theories of such a logic are the generalized necessities and that the completely consistent theories coincide with the necessities (see for example Gerla 2001).

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  • Residuated Boolean algebra

    Residuated Boolean algebra

    In mathematics, a residuated Boolean algebra is a residuated lattice whose lattice structure is that of a Boolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet Σ {\displaystyle \Sigma } under concatenation, the set of all binary relations on a given set X {\displaystyle X} under relational composition, and more generally the power set of any equivalence relation, again under relational composition. The original application was to relation algebras as a finitely axiomatized generalization of the binary relation example, but there exist interesting examples of residuated Boolean algebras that are not relation algebras, such as the language example. == Definition == A residuated Boolean algebra is an algebraic structure ( L , ∧ , ∨ , ¬ , 0 , 1 , ∙ , I , / , ∖ ) {\displaystyle (L,\wedge ,\vee ,\neg ,0,1,\bullet ,\mathbf {I} ,/,\backslash )} such that An equivalent signature better suited to the relation algebra application is ( L , ∧ , ∨ , ¬ , 0 , 1 , ∙ , I , ▹ , ◃ ) {\displaystyle (L,\wedge ,\vee ,\neg ,0,1,\bullet ,\mathbf {I} ,\triangleright ,\triangleleft )} where the unary operations x ∖ {\displaystyle x\backslash } and x ▹ {\displaystyle x\triangleright } are intertranslatable in the manner of De Morgan's laws via x ∖ y = ¬ ( x ▹ ¬ y ) {\displaystyle x\backslash y=\neg (x\triangleright \neg y)} , x ▹ y = ¬ ( x ∖ ¬ y ) {\displaystyle x\triangleright y=\neg (x\backslash \neg y)} , and dually / y {\displaystyle /y} and ◃ y {\displaystyle \triangleleft y} as x / y = ¬ ( ¬ x ◃ y ) {\displaystyle x/y=\neg (\neg x\triangleleft y)} , x ◃ y = ¬ ( ¬ x / y ) {\displaystyle x\triangleleft y=\neg (\neg x/y)} , with the residuation axioms in the residuated lattice article reorganized accordingly (replacing z {\displaystyle z} by ¬ z {\displaystyle \neg z} ) to read ( x ▹ z ) ∧ y = 0 ⇔ ( x ∙ y ) ∧ z = 0 ⇔ ( z ◃ y ) ∧ x = 0 {\displaystyle (x\triangleright z)\wedge y=0\ \Leftrightarrow \ (x\bullet y)\wedge z=0\ \Leftrightarrow \ (z\triangleleft y)\wedge x=0} This De Morgan dual reformulation is motivated and discussed in more detail in the section below on conjugacy. Since residuated lattices and Boolean algebras are each definable with finitely many equations, so are residuated Boolean algebras, whence they form a finitely axiomatizable variety. == Examples == Any Boolean algebra, with the monoid multiplication ∙ {\displaystyle \bullet } taken to be conjunction and both residuals taken to be material implication x → y {\displaystyle x\to y} . Of the remaining 15 binary Boolean operations that might be considered in place of conjunction for the monoid multiplication, only five meet the monotonicity requirement, namely 0 , 1 , x , y {\displaystyle 0,1,x,y} and x ∨ y {\displaystyle x\vee y} . Setting y = z = 0 {\displaystyle y=z=0} in the residuation axiom y ≤ x ∖ z ⇔ x ∙ y ≤ z {\displaystyle y\leq x\backslash z\ \Leftrightarrow \ x\bullet y\leq z} , we have 0 ≤ x ∖ 0 ⇔ x ∙ 0 ≤ 0 {\displaystyle 0\leq x\backslash 0\ \Leftrightarrow \ x\bullet 0\leq 0} , which is falsified by taking x = 1 {\displaystyle x=1} when x ∙ y = 1 {\displaystyle x\bullet y=1} , x {\displaystyle x} , or x ∨ y {\displaystyle x\vee y} . The dual argument for z / y {\displaystyle z/y} rules out x ∙ y = y {\displaystyle x\bullet y=y} . This just leaves x ∙ y = 0 {\displaystyle x\bullet y=0} (a constant binary operation independent of x {\displaystyle x} and y {\displaystyle y} ), which satisfies almost all the axioms when the residuals are both taken to be the constant operation x / y = x ∖ y = 1 {\displaystyle x/y=x\backslash y=1} . The axiom it fails is x ∙ I = x = I ∙ x {\displaystyle x\bullet \mathbf {I} =x=\mathbf {I} \bullet x} , for want of a suitable value for I {\displaystyle \mathbf {I} } . Hence conjunction is the only binary Boolean operation making the monoid multiplication that of a residuated Boolean algebra. The power set 2 X 2 {\displaystyle 2^{X^{2}}} made a Boolean algebra as usual with ∩ {\displaystyle \cap } , ∪ {\displaystyle \cup } and complement relative to X 2 {\displaystyle X^{2}} , and made a monoid with relational composition. The monoid unit I {\displaystyle \mathbf {I} } is the identity relation { ( x , x ) | x ∈ X } {\displaystyle \{(x,x)|x\in X\}} . The right residual R ∖ S {\displaystyle R\backslash S} is defined by x ( R ∖ S ) y ⇔ ∀ z ∈ X , z R x ⇒ z S y {\displaystyle x(R\backslash S)y\ \Leftrightarrow \ \forall z\in X,zRx\Rightarrow zSy} . Dually the left residual S / R {\displaystyle S/R} is defined by y ( S / R ) x ⇔ ∀ z ∈ X , x R z ⇒ y S z {\displaystyle y(S/R)x\ \Leftrightarrow \ \forall z\in X,xRz\Rightarrow ySz} . The power set 2 Σ ∗ {\displaystyle 2^{\Sigma ^{}}} made a Boolean algebra as for Example 2, but with language concatenation for the monoid. Here the set Σ {\displaystyle \Sigma } is used as an alphabet while Σ ∗ {\displaystyle \Sigma ^{}} denotes the set of all finite (including empty) words over that alphabet. The concatenation L M {\displaystyle LM} of languages L {\displaystyle L} and M {\displaystyle M} consists of all words u v {\displaystyle uv} such that u ∈ L {\displaystyle u\in L} and v ∈ M {\displaystyle v\in M} . The monoid unit is the language { ε } {\displaystyle \{\varepsilon \}} consisting of just the empty word ε {\displaystyle \varepsilon } . The right residual M ∖ L {\displaystyle M\backslash L} consists of all words w {\displaystyle w} over Σ {\displaystyle \Sigma } such that M w ⊆ L {\displaystyle Mw\subseteq L} . The left residual L / M {\displaystyle L/M} is the same with w M {\displaystyle wM} in place of M w {\displaystyle Mw} . == Conjugacy == The De Morgan duals ▹ {\displaystyle \triangleright } and ◃ {\displaystyle \triangleleft } of residuation arise as follows. Among residuated lattices, Boolean algebras are special by virtue of having a complementation operation ¬ {\displaystyle \neg } . This permits an alternative expression of the three inequalities y ≤ x ∖ z ⇔ x ∙ y ≤ z ⇔ x ≤ z / y {\displaystyle y\leq x\backslash z\ \Leftrightarrow \ x\bullet y\leq z\ \Leftrightarrow \ x\leq z/y} in the axiomatization of the two residuals in terms of disjointness, via the equivalence x ≤ y ⇔ x ∧ ¬ y = 0 {\displaystyle x\leq y\ \Leftrightarrow \ x\wedge \neg y=0} . Abbreviating x ∧ y = 0 {\displaystyle x\wedge y=0} to x # y {\displaystyle x\#y} as the expression of their disjointness, and substituting ¬ z {\displaystyle \neg z} for z {\displaystyle z} in the axioms, they become with a little Boolean manipulation ¬ ( x ∖ ¬ z ) # y ⇔ x ∙ y # z ⇔ ¬ ( ¬ z / y ) # x {\displaystyle \neg (x\backslash \neg z)\#y\ \Leftrightarrow \ x\bullet y\#z\ \Leftrightarrow \ \neg (\neg z/y)\#x} Now ¬ ( x ∖ ¬ z ) {\displaystyle \neg (x\backslash \neg z)} is reminiscent of De Morgan duality, suggesting that x ∖ {\displaystyle x\backslash } be thought of as a unary operation f {\displaystyle f} , defined by f ( y ) = x ∖ y {\displaystyle f(y)=x\backslash y} , that has a De Morgan dual ¬ f ( ¬ y ) {\displaystyle \neg f(\neg y)} , analogous to ∀ x ϕ ( x ) = ¬ ∃ x ¬ ϕ ( x ) {\displaystyle \forall x\phi (x)=\neg \exists x\neg \phi (x)} . Denoting this dual operation as x ▹ {\displaystyle x\triangleright } , we define x ▹ z {\displaystyle x\triangleright z} as ¬ x ∖ ¬ z {\displaystyle \neg x\backslash \neg z} . Similarly we define another operation z ◃ y {\displaystyle z\triangleleft y} as ¬ ( ¬ z / y ) {\displaystyle \neg (\neg z/y)} . By analogy with x ∖ {\displaystyle x\backslash } as the residual operation associated with the operation x ∙ {\displaystyle x\bullet } , we refer to x ▹ {\displaystyle x\triangleright } as the conjugate operation, or simply conjugate, of x ∙ {\displaystyle x\bullet } . Likewise ◃ y {\displaystyle \triangleleft y} is the conjugate of ∙ y {\displaystyle \bullet y} . Unlike residuals, conjugacy is an equivalence relation between operations: if f {\displaystyle f} is the conjugate of g {\displaystyle g} then g {\displaystyle g} is also the conjugate of f {\displaystyle f} , i.e. the conjugate of the conjugate of f {\displaystyle f} is f {\displaystyle f} . Another advantage of conjugacy is that it becomes unnecessary to speak of right and left conjugates, that distinction now being inherited from the difference between x ∙ {\displaystyle x\bullet } and ∙ x {\displaystyle \bullet x} , which have as their respective conjugates x ▹ {\displaystyle x\triangleright } and ◃ x {\displaystyle \triangleleft x} . (But this advantage accrues also to residuals when x ∖ {\displaystyle x\backslash } is taken to be the residual operation to x ∙ {\displaystyle x\bullet } .) All this yields (along with the Boolean algebra and monoid axioms) the following equivalent axiomatization of a residuated Boolean algebra. y # x ▹ z ⇔ x ∙ y # z ⇔ x # z ◃ y {\displaystyle y\#x\triangleright z\ \Leftrightarrow \ x\bullet y\#z\ \Leftrightarrow \ x\#z\triangleleft y} With this signature it remains the case that this axiomatization can be expressed as

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  • Personality computing

    Personality computing

    Personality computing is a research field related to artificial intelligence and personality psychology that studies personality by means of computational techniques from different sources, including text, multimedia, and social networks. == Overview == Personality computing addresses three main problems involving personality: automatic personality recognition, perception, and synthesis. Automatic personality recognition is the inference of the personality type of target individuals from their digital footprint. Automatic personality perception is the inference of the personality attributed by an observer to a target individual based on some observable behavior. Automatic personality synthesis is the generation of the style or behaviour of artificial personalities in Avatars and virtual agents. Self-assessed personality tests or observer ratings are always exploited as the ground truth for testing and validating the performance of artificial intelligence algorithms for the automatic prediction of personality types. There is a wide variety of personality tests, such as the Myers Briggs Type Indicator (MBTI) or the MMPI, but the most used are tests based on the Five Factor Model such as the Revised NEO Personality Inventory. Personality computing can be considered as an extension or complement of Affective computing, where the former focuses on personality traits and the latter on affective states. A further extension of the two fields is Character Computing which combines various character states and traits including but not limited to personality and affect. == History == Personality computing began around 2005 with the pioneering research in personality recognition by Shlomo Argamon and later by François Mairesse. These works showed that personality traits could be inferred with reasonable accuracy from text, such as blogs, self-presentations, and email addresses. In 2008, the concept of "portable personality" for the distributed management of personality profiles has been developed. A few years later, research began in personality recognition and perception from multimodal and social signals, such as recorded meetings and voice calls. In the 2010s, the research focused mainly on personality recognition and perception from social media, helped by the first workshops organized by Fabio Celli. In particular personality was extracted from Facebook, Twitter and Instagram. In the same years, automatic personality synthesis helped improve the coherence of simulated behavior in virtual agents. Scientific works by Michal Kosinski demonstrated the validity of Personality Computing from different digital footprints, in particular from user preferences such as Facebook page likes, showed that machines can recognize personality better than humans and raised a warning against Cambridge Analytica and misuse of this kind of technology. == Applications == Personality computing techniques, in particular personality recognition and perception, have applications in Social media marketing, where they can help reducing the cost of advertising campaigns through psychological targeting.

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  • IJCAI Award for Research Excellence

    IJCAI Award for Research Excellence

    The IJCAI Award for Research Excellence is a biannual award before given at the IJCAI conference to researcher in artificial intelligence as a recognition of excellence of their career. Beginning in 2016, the conference is held annually and so is the award. == Laureates == The recipients of this award have been: John McCarthy (1985) Allen Newell (1989) Marvin Minsky (1991) Raymond Reiter (1993) Herbert A. Simon (1995) Aravind Joshi (1997) Judea Pearl (1999) Donald Michie (2001) Nils Nilsson (2003) Geoffrey E. Hinton (2005) Alan Bundy (2007) Victor R. Lesser (2009) Robert Kowalski (2011) Hector Levesque (2013) Barbara Grosz (2015) for her pioneering research in Natural Language Processing and in theories and applications of Multiagent Collaboration. Michael I. Jordan (2016) for his groundbreaking and impactful research in both the theory and application of statistical machine learning. Andrew Barto (2017) for his pioneering work in the theory of reinforcement learning. Jitendra Malik (2018) Yoav Shoham (2019) Eugene Freuder (2020) Richard S. Sutton (2021) Stuart J. Russell (2022) Sarit Kraus (2023) for her pioneering work of the study of interactions among self-interested agents, creating the field of automated negotiation, and developing methods for coalition formation and teamwork, both as formal models and real-world implementations. == Winners of also Turing Award == John McCarthy (1971) Allen Newell (1975) Marvin Minsky (1969) Herbert A. Simon (1975) Judea Pearl (2011) Geoffrey Hinton (2018) Andrew Barto (2024) Richard S. Sutton (2024)

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  • Paranoia (role-playing game)

    Paranoia (role-playing game)

    Paranoia is a dystopian science-fiction tabletop role-playing game originally designed and written by Greg Costikyan, Dan Gelber, and Eric Goldberg, and first published in 1984 by West End Games. Since 2004 the game has been published under license by Mongoose Publishing. The game won the Origins Award for Best Roleplaying Rules of 1984 and was inducted into the Origins Awards Hall of Fame in 2007. Paranoia is notable among tabletop games for being more competitive than co-operative, with players encouraged to betray one another for their own interests, as well as for keeping a light-hearted, tongue in cheek tone despite its dystopian setting. Several editions of the game have been published since the original version, and the franchise has spawned several spin-offs, novels and comic books based on the game. == Premise == The game is set in a dystopian future city controlled by the Computer (also known as "Friend Computer"), and where information (including the game rules) are restricted by color-coded "security clearance". Player characters are initially enforcers of the Computer's authority known as Troubleshooters, and are given missions to seek out and eliminate threats to the Computer's control. They are also part of prohibited underground movements, and have secret objectives including theft from and murder of other player characters. == Tone == Paranoia is a humorous role-playing game set in a dystopian future along the lines of Nineteen Eighty-Four, Brave New World, Logan's Run, and THX 1138; however, the tone of the game is rife with black humor, frequently tongue-in-cheek rather than dark and heavy. Most of the game's humor is derived from the players' (usually futile) attempts to complete their assignment while simultaneously adhering to the Computer's arbitrary, contradictory and often nonsensical security directives. The Paranoia rulebook is unusual in a number of ways; demonstrating any knowledge of the rules is forbidden, and most of the rulebook is written in an easy, conversational tone that often makes fun of the players and their characters, while occasionally taking digs at other notable role-playing games. === Setting === The game's main setting is an immense, futuristic city called Alpha Complex. Alpha Complex is controlled by the Computer, a civil service AI construct (a literal realization of the "Influencing Machine" that some schizophrenics fear). The Computer serves as the game's principal antagonist, and fears a number of threats to its 'perfect' society, such as the Outdoors, mutants, and secret societies (especially Communists). To deal with these threats, the Computer employs Troubleshooters, whose job is to go out, find trouble, and shoot it. Player characters are usually Troubleshooters, although later game supplements have allowed the players to take on other roles, such as High-Programmers of Alpha Complex. The player characters frequently receive mission instructions from the Computer that are incomprehensible, self-contradictory, or obviously fatal if adhered to, and side-missions (such as Mandatory Bonus Duties) that conflict with the main mission. Failing a mission generally results in termination of the player character, but succeeding can just as often result in the same fate, after being rewarded for successfully concluding the mission. They are issued equipment that is uniformly dangerous, faulty, or "experimental" (i.e., almost certainly dangerous and faulty). Additionally, each player character is generally an unregistered mutant and a secret society member (which are both termination offenses in Alpha Complex), and has a hidden agenda separate from the group's goals, often involving stealing from or killing teammates. Thus, missions often turn into a comedy of errors, as everyone on the team seeks to double-cross everyone else while keeping their own secrets. The game's manual encourages suspicion between players, offering several tips on how to make the gameplay as paranoid as possible. Every player's character is assigned six clones, known as a six-pack, which are used to replace the preceding clone upon his or her death. The game lacks a conventional health system; most wounds the player characters can suffer are assumed to be fatal. As a result, Paranoia allows characters to be routinely killed, yet the player can continue instead of leaving the game. This easy spending of clones tends to lead to frequent firefights, gruesome slapstick, and the horrible yet humorous demise of most if not all of the player character's clone family. Additional clones can be purchased if one gains sufficient favour with the Computer. === Security clearances === Paranoia features a security clearance system based on colors of the visible spectrum which heavily restricts what the players can and cannot legally do; everything from corridors to food and equipment have security restrictions. The lowest rating is Infrared, but the lowest playable security clearance is Red; the game usually begins with the characters having just been promoted to Red grade. Interfering with anything which is above that player's clearance carries significant risk. The full order of clearances from lowest to highest is Infrared (visually represented by black), Red, Orange, Yellow, Green, Blue, Indigo, Violet, and Ultraviolet (visually represented by white). Within the game, Infrared-clearance citizens live dull lives of mindless drudgery and are heavily medicated, while higher clearance characters may be allowed to demote or even summarily execute those of a lower rank and those with Ultraviolet clearance are almost completely unrestricted and have a great deal of access to the Computer; they are the only citizens that may (legally) access and modify the Computer's programming, and thus Ultraviolet citizens are also referred to as "High Programmers". Security clearance is not related to competence but is instead the result of the Computer's often insane and unjustified calculus of trust concerning a citizen. It is suggested that it may in fact be the High Programmers' meddling with The Computer's programming that resulted in its insanity. === Secret societies === In the game, secret societies tend to be based on sketchy and spurious knowledge of historical matters. For example, previous editions included societies such as the "Seal Club" that idolizes the Outdoors but is unsure what plants and animals actually look like. Other societies include the Knights of the Circular Object (based on the Knights of the Round Table), the Trekkies, and the First Church of Christ Computer Programmer. In keeping with the theme of paranoia, many secret societies have spies or double agents in each other's organizations. The first edition also included secret societies such as Programs Groups (the personal agents and spies of the High Programmers at the apex of Alpha Complex society) and Spy For Another Alpha Complex. The actual societies which would be encountered in a game depends on the play style; some societies are more suited for more light-hearted games (Zap-style, or the lighter end of Classic), whereas others represent a more serious threat to Alpha Complex and are therefore more suitable for Straight or the more dark sort of Classic games. == Publication history == Six editions have been published. Three of these were published by West End Games — the first, second, and fifth editions — whereas the later three editions (Paranoia XP, the 25th Anniversary edition and the "Red Clearance" edition) were published by Mongoose Publishing. In addition to these six published editions, it is known that West End Games were working on a third edition — to replace the poorly received fifth edition — in the late 1990s, but their financial issues would prevent this edition from being published, except for being included in one tournament adventure. === First edition === The first edition, was written by Greg Costikyan, Dan Gelber, and Eric Goldberg, and published in 1984 by West End Games. In 1985, this edition of Paranoia won the Origins Award for Best Roleplaying Rules of 1984. This edition, while encouraging dark humour in-game, took a fairly serious dystopian tone; the supplements and adventures released to accompany it emphasised the lighter side, however, establishing the freewheeling mix of slapstick, intra-team backstabbing and satire that is classically associated with a game of Paranoia. === Second edition === The second edition, is credited to Costikyan, Gelber, Goldberg, Ken Rolston, and Paul Murphy, was published in 1987 by West End Games. This edition can be seen as a response to the natural development of the line towards a rules-light, fast and entertaining play style. Here, the humorous possibilities of life in a paranoid dystopia are emphasised, and the rules are simplified. ==== Metaplot and the second edition ==== Many of the supplements released for the second edition fall into a story arc set up by new writers and line editors

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  • The Future of Truth (Rosenbaum book)

    The Future of Truth (Rosenbaum book)

    The Future of Truth: How AI Reshapes Reality is a 2026 book by American filmmaker and author Steven Rosenbaum about how artificial intelligence affects the concept of truth. It was published by Matt Holt Books on May 12, 2026, to positive media attention; on May 19, in response to an inquiry from The New York Times, Rosenbaum acknowledged that the book itself contains multiple misattributed or false quotes that were hallucinated by AIs. == Synopsis == == Development == Rosenbaum has said that he developed the book using AI chatbots as research tools, indicating in his notes what information came from AI and sending those claims to a fact-checker affiliated with the publisher. He has said that he did not use AI tools to write the book itself. He has described AI tools as "a delightful writing companion ... strangely creative and crafty and unusual in all these ways", while acknowledging that sometimes "then it betrays you in ways that are just really quite horrible". Journalist and Nobel laureate Maria Ressa wrote the book's foreword. Taylor Lorenz, Michael Wolff, and Nicholas Thompson wrote blurbs promoting it. == Release and reception == The Future of Truth was published by Matt Holt Books, an imprint of BenBella Books, and distributed by Simon & Schuster. The book's release on May 12, 2026, was described by Futurism as "buzzy" and by The New York Times as "to great fanfare". On May 14, an excerpt was published in Wired under the title "Gen Z Is Pioneering a New Understanding of Truth". On May 17, the Times contacted Rosenbaum regarding a number of quotes that appeared to be falsified or misattributed; the following evening he confirmed that they were the result of AI hallucinations:As I disclosed in the book's acknowledgments, I used AI tools ChatGPT and Claude during the research, writing and editing process. That does not excuse these errors, of which I take full responsibility. I am now working with the editors to thoroughly review and quickly correct any affected passages; any future editions will be corrected. The Times documented several of the errors, including a quote from Kara Swisher that Swisher described as making it "sound like I have a stick up my butt" and a quote from Lisa Feldman Barrett that Barrett described as misrepresenting her views on the nature of emotions, social signals, and truth. The book also misattributed a quote by Meredith Broussard from an interview with Marketplace Tech as having been from her book Artificial Unintelligence and hallucinated several words in a quote from Lee McIntyre, although according to McIntyre it did not misrepresent his views. Wired's editors, in an addendum to the excerpt they published, said that all quotes included in it had been verified as part of their fact-checking process. Rosenbaum told the Times that the series of errors "serves as a warning about the risks of AI-assisted research and verification, that is why I wrote the book. These AI errors do not, in fact, diminish the larger questions that the book raises about truth, trust and AI and its impact on society, democracy and editorial." Maggie Harrison Dupré in Futurism expressed skepticism, writing "The risk of AI hallucinations ... is well-known. If you're going to literally write the book on post-AI truth, you should probably put some more elbow grease into fact-checking your AI-assisted research." Kyle Orland in Ars Technica, responding to Rosenbaum's statement that his error "demonstrates the problem more vividly than any abstract argument could", was similarly skeptical, writing that "if we accept this take, every avoidably obvious mess in the world might be a disguised good because it really helps illuminate the huge mistake. And that can't be right; sometimes 'negligence' is just that." Subsequent comments by Rosenbaum placed more blame on the chatbots, which he told The Atlantic "fucked up the book". Rosenbaum told Ars Technica that fact-checking occurred "incredibly effectively, but not a hundred percent"; Orland observed that "it's worth noting that most writers manage to include zero made-up quotes when they write a book". Rosenbaum said that he had "learned a lesson" and would be "much more suspicious" of AI in the future, but would continue to use AI in his research. Orland responded to Rosenbaum's characterization of AI as "magical" by comparing it to the One Ring from The Lord of the Rings, in that it "convinces many of those who use it that they can control its power properly" when many cannot. Orland highlighted the limits of traditional fact-checking regarding AI, given that fact-checkers are used to assuming that direct quotes are copied word-for-word from the source. Rosenbaum told Orland that the future of fact-checking for AI-researched works "probably includes mandatory source tracing for quotations, better provenance tracking, clearer standards around AI-assisted research, and potentially (more irony here) AI tools that audit citations against primary materials". Patrick Redford in Defector criticized Rosenbaum, alongside other artists tricked by AI, for failing to recognize AI as "the enemy". Will Oremus in The Atlantic described Redford's approach of stigmatizing AI writing as "reasonable", noting the presence of low-quality, seemingly AI-generated verbiage in The Future of Truth—a claim denied by Rosenbaum—before saying that the greater issue is finding the line at which AI assistance in writing becomes a problem. Oremus concluded, "The scandal can't just be that [Rosenbaum] used AI while working on his book, because he acknowledged that up front. He got in trouble because he had used AI badly, failing to check its work on a task at which it is famously unreliable."

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  • Contrast-to-noise ratio

    Contrast-to-noise ratio

    Contrast-to-noise ratio (CNR) is a measure used to determine image quality. CNR is similar to the metric signal-to-noise ratio (SNR), but subtracts a term before taking the ratio. This is important when there is a significant bias in an image, such as from haze. As can be seen in the picture at right, the intensity is rather high even though the features of the image are washed out by the haze. Thus this image may have a high SNR metric, but will have a low CNR metric. One way to define contrast-to-noise ratio is: C = | S A − S B | σ o {\displaystyle C={\frac {|S_{A}-S_{B}|}{\sigma _{o}}}} where SA and SB are signal intensities for signal producing structures A and B in the region of interest and σo is the standard deviation of the pure image noise.

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  • Ghost in the Shell

    Ghost in the Shell

    Ghost in the Shell is a Japanese cyberpunk military science fiction media franchise that began with the eponymous manga series, written and illustrated by Masamune Shirow. The manga, first serialized from 1989 to 1991, is set in the mid-21st-century and follows the fictional counter-cyberterrorist organization Public Security Section 9, led by protagonist Major Motoko Kusanagi. Animation studio Production I.G has produced several anime adaptations of the series. These include the 1995 film of the same name and its 2004 sequel, Ghost in the Shell 2: Innocence; the 2002 television series Ghost in the Shell: Stand Alone Complex and its 2020 follow-up, Ghost in the Shell: SAC_2045; and the Ghost in the Shell: Arise original video animation series. In addition, an American-produced live-action film was released in March 2017. == Overview == === Title === The original editor Koichi Yuri says: At first, Ghost in the Shell came from Shirow, but when Yuri asked for "something more flashy", Shirow came up with "攻殻機動隊 Koukaku Kidou Tai (Shell Squad)" for Yuri. But Shirow was attached to including "Ghost in the Shell" as well even if in smaller type. === Setting === Primarily set in the mid-twenty-first century in the fictional Japanese city of Niihama, Niihama Prefecture (新浜県新浜市, Niihama-ken Niihama-shi), otherwise known as New Port City (ニューポートシティ, Nyū Pōto Shiti), the manga and the many anime adaptations follow the members of Public Security Section 9, a task-force consisting of various professionals skilled at solving and preventing crime, mostly with some sort of police background. Political intrigue and counter-terrorism operations are standard fare for Section 9, but the various actions of corrupt officials, companies, and cyber-criminals in each scenario are unique and require the diverse skills of Section 9's staff to prevent a series of incidents from escalating. In this post-cyberpunk iteration of a possible future, computer technology has advanced to the point that many members of the public possess cyberbrains, technology that allows them to interface their biological brain with various networks. The level of cyberization varies from simple minimal interfaces to almost complete replacement of the brain with cybernetic parts, in cases of severe trauma. This can also be combined with various levels of prostheses, with a fully prosthetic body enabling a person to become a cyborg. The main character of Ghost in the Shell, Major Motoko Kusanagi, is such a cyborg, having had a terrible accident befall her as a child that ultimately required her to use a full-body prosthesis to house her cyberbrain. This high level of cyberization, however, opens the brain up to attacks from highly skilled hackers, with the most dangerous being those who will hack a person to bend to their whims. == Media == === Literature === ==== Original manga ==== The original Ghost in the Shell manga ran in Japan from April 1989 to November 1990 in Kodansha's manga anthology Young Magazine, and was released in a tankōbon volume on October 2, 1991. Ghost in the Shell 2: Man-Machine Interface followed in 1997 for nine issues in Young Magazine, and was collected in the Ghost in the Shell: Solid Box on December 1, 2000. Then a standard version with modifications and new pages was published on June 26, 2001. Four stories from Man-Machine Interface that were not released in tankobon format from previous releases were later collected in Ghost in the Shell 1.5: Human-Error Processor, and published by Kodansha on July 17, 2003. Several art books have also been published for the manga. === Films === ==== Animated films ==== Two animated films based on the original manga have been released, both directed by Mamoru Oshii and animated by Production I.G. Ghost in the Shell was released in 1995 and follows the "Puppet Master" storyline from the manga. It was re-released in 2008 as Ghost in the Shell 2.0 with new audio and updated 3D computer graphics in certain scenes. Innocence, otherwise known as Ghost in the Shell 2: Innocence, was released in 2004, with its story based on a chapter from the first manga. ==== Live-action film ==== In 2008, DreamWorks and producer Steven Spielberg acquired the rights to a live-action film adaptation of the original Ghost in the Shell manga. On January 24, 2014, Rupert Sanders was announced as director, with a screenplay by William Wheeler. In April 2016, the full cast was announced, which included Juliette Binoche, Chin Han, Lasarus Ratuere and Kaori Momoi, and Scarlett Johansson in the lead role; the casting of Johansson drew accusations of whitewashing. Principal photography on the film began on location in Wellington, New Zealand, on February 1, 2016. Filming wrapped in June 2016. Ghost in the Shell premiered in Tokyo on March 16, 2017, and was released in the United States on March 31, 2017, in 2D, 3D and IMAX 3D. It received mixed reviews, with praise for its visuals and Johansson's performance but criticism for its script. === Television === ==== Stand Alone Complex TV series, film and ONA ==== In 2002, Ghost in the Shell: Stand Alone Complex premiered on Animax, presenting a new telling of Ghost in the Shell independent from the original manga, focusing on Section 9's investigation of the Laughing Man hacker. It was followed in 2004 by a second season titled Ghost in the Shell: S.A.C. 2nd GIG, which focused on the Individual Eleven terrorist group. The primary storylines of both seasons were compressed into OVAs broadcast as Ghost in the Shell: Stand Alone Complex The Laughing Man in 2005 and Ghost in the Shell: Stand Alone Complex Individual Eleven in 2006. Also in 2006, Ghost in the Shell: Stand Alone Complex - Solid State Society, featuring Section 9's confrontation with a hacker known as the Puppeteer, was broadcast, serving as a finale to the anime series. The extensive score for the series and its films was composed by Yoko Kanno. On April 7, 2017, Kodansha and Production I.G announced that Kenji Kamiyama and Shinji Aramaki would be co-directing a new Kōkaku Kidōtai anime production. On December 7, 2018, it was reported by Netflix that they had acquired the worldwide streaming rights to the original net animation (ONA) anime series, titled Ghost in the Shell: SAC_2045, and that it would premiere on April 23, 2020. The series is in 3DCG and Sola Digital Arts collaborated with Production I.G on the project. Ilya Kuvshinov handled character designs. The series had two seasons of 12 episodes each. In addition to the anime, a series of published books, two separate manga adaptations, and several video games for consoles and mobile phones have been released for Stand Alone Complex. ==== Arise OVA, TV series and film ==== In 2013, a new iteration of the series titled Ghost in the Shell: Arise premiered, taking an original look at the Ghost in the Shell world, set before the original manga. It was released as a series of four original video animation (OVA) episodes (with limited theatrical releases) from 2013 to 2014, then recompiled as a 10-episode television series under the title of Kōkaku Kidōtai: Arise - Alternative Architecture. An additional fifth OVA titled Pyrophoric Cult, originally premiering in the Alternative Architecture broadcast as two original episodes, was released on August 26, 2015. Kazuchika Kise served as the chief director of the series, with Tow Ubukata as head writer. Cornelius was brought onto the project to compose the score for the series, with the Major's new voice actress Maaya Sakamoto also providing vocals for certain tracks. Ghost in the Shell: The New Movie, also known as Ghost in the Shell: Arise − The Movie or New Ghost in the Shell, is a 2015 film directed by Kazuya Nomura that serves as a finale to the Ghost in the Shell: Arise story arc. The film is a continuation to the plot of the Pyrophoric Cult episode of Arise, and ties up loose ends from that arc. A manga adaptation was serialized in Kodansha's Young Magazine, which started on March 13 and ended on August 26, 2013. ==== 2026 anime ==== On May 25, 2024, it was announced that a new anime television series adaptation will be produced by Science Saru for a July 2026 premiere. Saru will be in a production committee with Bandai Namco Filmworks, Kodansha and Production I.G. The series will be directed by Monkochan, with a script by EnJoe Toh. === Video games === Ghost in the Shell was developed by Exact and released for the PlayStation on July 17, 1997, in Japan by Sony Computer Entertainment. It is a third-person shooter featuring an original storyline where the character plays a rookie member of Section 9. The video game's soundtrack Megatech Body features various techno artists, such as Takkyu Ishino, Scan X and Mijk Van Dijk. Several video games were also developed to tie into the Stand Alone Complex television series, in addition to a first-person shooter by Nexon and Neople titled Ghost in the Shell: Stand Alone Complex - First Assault Online,

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  • Random-fuzzy variable

    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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