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  List of robotics journals

  List of robotics journals includes notable academic and scientific journals that focus on research in the field of robotics and automation. == Journals == Acta Mechanica et Automatica Advanced Robotics Annual Review of Control, Robotics, and Autonomous Systems IEEE Robotics and Automation Letters IEEE Transactions on Robotics IEEE Transactions on Field Robotics The International Journal of Advanced Manufacturing Technology International Journal of Humanoid Robotics International Journal of Robotics Research Journal of Cognitive Engineering and Decision Making Journal of Field Robotics Journal of Intelligent & Robotic Systems Paladyn Robotics and Autonomous Systems Robotics Science Robotics SLAS Technology

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  Coronavirus breathalyzer

  A coronavirus breathalyzer is a diagnostic medical device enabling the user to test with 90% or greater accuracy the presence of severe acute respiratory syndrome coronavirus 2 in an exhaled breath. As of the first half of 2020, the idea of a practical coronavirus breathalyzer was concomitantly developed by unrelated research groups in Australia, Canada, Finland, Germany, Indonesia, Israel, Netherlands, Poland, Singapore, United Kingdom and the USA. == Australia == In Australia, GreyScan CEO Samantha Ollerton and Prof. Michael Breadmore of the University of Tasmania are basing a coronavirus breathalyzer on existing technology that is used around the world to detect explosives. Another invention published from ABC News; produced by Colin Hickey and Examin Holdings, have released information on a new breathalyzer called the "Queensland Breath test" claiming its function has 98% efficiency, equipped with a replaceable plastic nozzle for reusability (February 2022). a statement in claim by Bruce Thompson, a professor at Swinburne University of Technology, Although this products is reliable, due to insufficient funding, the product is inaccessible. == Canada == Canary Health Technologies, headquartered in Toronto with offices in Cleveland, Ohio, is developing a breathalyzer with disposable nanosensors using AI-powered cloud-based analysis. According to a press release, clinical trials began in India during November 2020. The stated goal is to develop an accurate, reasonably priced screening tool that can be used anywhere and deliver a result in less than a minute. The company postulates that analyzing volatile organic compounds in human breath could potentially detect diseases before the on-set of symptoms, earlier than currently available methods. Moreover, the cloud-based technology is designed to be used as a disease surveillance apparatus. == Finland == By the end of June 2020, Forum Virium Helsinki, in collaboration with Finnish software firm Deep Sensing Algorithms, funded by the Helsinki-Uusimaa Regional Council, announced that testing of their device had begun with a control group in Kazakhstan, with plans to expand to the Netherlands, the United States, South Africa, Brazil and Finland throughout the summer. The efficacy of the Forum Virium Helsinki / Deep Sensing Algorithms device hinges on its AI component. "We are engaged in innovative cooperation with corporations to solve the coronavirus crisis, and we will help firms to use the city as a development platform. We are utilizing artificial intelligence and digitalization," said Forum Virium Helsinki CEO Mika Malin. == Germany == In March 2020, the Singaporean company RAM Global conducted research in Germany in hopes of developing a one-minute breathalyzer test for SARS-CoV-2 based on terahertz time-domain spectroscopy. The company attempted to develop a disposable test kit for direct detection of COVID-19 virion particles in breath, saliva and swab samples. On 31 March, RAM Global completed an initial clinical study on live patients at University Hospital Saarland. In April, the company pursued a small unknown sample study in which hospital doctors provided unknown samples in order to test accuracy in differentiating positive and negative samples. == Indonesia == Since April 2020, a team of researchers from Gadjah Mada University (UGM) has been developing an electronic nose called GeNose C19. The GeNose C19 can be used as a rapid, non-invasive screening tool in less than two minutes. A profiling test was carried out at the Bhayangkara Hospital and the Covid Bambanglipuro Special Field Hospital in Yogyakarta. GeNose C19 consists of gas sensors and an artificial intelligence-based pattern recognition system. The diagnostic test was carried out with the cooperation of nine multi-center hospitals. In the end of December 2020, GeNose C19 received a distribution permit from Indonesia's Health Ministry. Initially, 100 units will be released and each device will be able to perform 120 tests per day. The test is estimated to cost 15,000–25,000 Indonesian rupiah ($1–$1.8) and would take three minutes for the test and another two minutes to yield a result. Researchers hope to manufacture up to 1,000 GeNose C19 units, increasing the country's testing capabilities by 120 thousand subjects per day. Moreover, they aim to manufacture 10,000 units by February 2021. == Israel == In Israel, it is at the photonics lab of Gabby Sarusi, professor at Ben-Gurion University of the Negev, that research is underway as of midsummer 2020. Separately from Sarusi's project, in July 2020, it was reported that Israeli start-up Nanoscent in cooperation with Sheba Medical Center had devised a breathalyzer that Magen David Adom (MDA) is seeking to incorporate into existing drive-thru testing stations located throughout the country. Questionable intellectual property of Gabby Sarusi regarding this project is now under discussion in the court in Israel. == The Netherlands == A breath test with the SpiroNose device, made by the Dutch company Breathomix, has been developed and tested in collaboration with the Leiden University Medical Center (LUMC), Franciscus Gasthuis & Vlietland and the GGD Amsterdam. The breath test has been validated as a pre-screening test for people who have no or mild symptoms of COVID-19. From April 2021, the device was operational in COVID-19 test drive-ins, conferences and events, i.e. Eurovision Song Contest 2021. Subjects must abstain from alcohol for eight hours prior to taking the breath test. The SpiroNose contains four sets of seven different sensors that can measure the mixture of volatile organic compounds (biomarkers) in the exhaled air. These VOCs provide a picture of a person's metabolism. This 'breath profile' is forwarded to an online analysis platform. Here the breath profile is compared with other breath profiles of people with and without a COVID-19 diagnosis and analysed by algorithms. Data-analysis involves advanced signal processing and statistics based on independent t-tests followed by linear discriminant and ROC analysis. The test result is known within minutes. The breath test has a sensitivity/specificity for SARS-CoV-2 infection of 100/78, >99/84, 98/82% in validation, replication and asymptomatic cohorts of patients. The breath test reliably detects who is not infected. Such a subject will receive a test result immediately. Other subjects must promptly conduct a subsequent test, for example a PCR test or LAMP test. The test results can be viewed by the client and are not automatically interfaced to other databases, i.e. for public health surveillance, source and contact tracing, vaccination programs. In July 2021, the ministry stopped the tests with the SpiroNose because, according to the GGD, the device gives unusable results in some cases. Breathomix indicates that this is the result of the way in which the SpiroNose is deployed. The SpiroNose is and remains a reliable instrument for lung diseases. The analysis platform is developed conform the requirements of the standard ISO 27001 (Information Security) and NEN 7510 (Information Security in Health Care). A CE marking has been requested. In the meantime, the Dutch minister has granted a CE marking exemption on 25 January 2021. The device may also be used to detect other diseases, e.g., asthma, COPD, lung cancer, interstitial lung diseases (ILD). == Poland == In February 2021, the President of Poland, Andrzej Duda, announced that ML System S. A., headquartered in Zaczernie, Poland, had successfully developed a means of analyzing a patient's breath to test for the presence of coronavirus. According to an anonymous press release, test subjects exhale into a device in order to determine the presence of the coronavirus. The procedure, similar to that of a police breathalyzer, is said to take less than ten seconds. Independent clinical trials were begun in April 2021. In the first half of May 2021, a brief text concerning partial results was published by ML System, stating that independent clinical trials were successful with specificity (97,15%) and accuracy/sensitivity (86,86%), for CT (Cycle Threshold) assumed at 25, which is in line with the guidelines set out by the World Health Organization. Moreover, ML System in partnership with Rzeszów–Jasionka Airport published a statement indicating their intention to test the device at the airport. Similar plans exist between the manufacturer and the Warsaw Chopin Airport. Two large networks of laboratories in Poland, "Diagnostyka" and "ALAB Laboratoria", have signed a letter of intent with ML System. In agreement with ALAB, the parties declared cooperation in the implementation of the product named "COVID DETECTOR" on the Polish, German and Ukrainian markets. In addition, the companies declared joint activities aimed at extending the diagnosis with the use of "COVID Detector" to include mutations of the SARS-CoV-2 virus, differentiate the stage of the disease and ot

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  Grok sexual deepfake scandal

  From 2025 onwards, X (formerly Twitter)'s integrated chatbot, Grok, has allowed users to nonconsensually alter images of individuals, including minors, to show them in bikinis or transparent clothing, or in sexually suggestive contexts. The majority of these prompts were targeted at women and girls. Users were able to generate such images by responding to a photo with a request to Grok, such as "put her in a bikini", to which the chatbot would publicly reply with a generated image. The scandal drew significant criticism from lawmakers across the world, and there were calls for bans on X, as well as legal crackdowns on X and xAI for, amongst other reasons, the facilitation of sexual abuse, revenge porn, and child pornography. == Background == Deepfake pornography emerged in the late 2010s with the advent of machine learning. Originally, it was created on a small individual scale using a combination of machine learning algorithms, computer vision techniques, and AI software. However, the production process has significantly evolved since 2018, with the advent of several public apps that have largely automated the process. Since 2023, several AI apps available on Google Play and the Apple App Store are capable of "nudify-ing" user provided photos to generate non-consensual deepfake pornography. Grok would first be proposed by Elon Musk in 2023, when he expressed an intention to create his own AI chatbot to "combat bias". Grok version 2.0, released on August 14, 2024, would introduce image generation capabilities, ones which would be improved over successive updates. == Grok deepfake generation == Cases of Grok being used to remove the clothes from women in pictures, replacing them with bikinis or lingerie, began to surface in May 2025. By late December 2025, a trend of X users requesting such edits to women's photos without permission had taken root, and this received significant media attention in the first few days of January 2026. Some users prompted Grok to edit photos of women into sexualized poses, and others to add blood and bruising, with the chatbot publicly posting these graphic images in response. Grok's X account was restricted on January 9 from posting image generation responses to users who are not paid subscribers, providing a link to "subscribe to unlock these features". All users were still able to generate Grok-altered images using X's "Edit image" feature, and the standalone Grok website and app. However, by March 19, Grok’s Imagine feature was fully restricted to paid subscribers only (SuperGrok tier) for both the standalone Grok website and mobile app. == Analysis == An analysis of 20,000 images generated by Grok between December 25, 2025, and January 1, 2026, showed 2% appeared to be 18 or younger, including 30 of "young or very young" women or girls in bikinis or transparent clothes. A Reuters review of Grok requests over 10 minutes on January 2nd found 102 attempts to put women in bikinis. A separate analysis conducted over 24 hours from January 5 to 6 calculated that users had Grok create 6,700 sexually suggestive or nudified images per hour — 84 times more so than the top 5 deepfake websites combined. Wired reported that far more graphic AI-generated sexual imagery was being created by Grok on its website and app, which are separate to X, including female celebrities removing their clothes and engaging in sexual acts. An analysis of 800 pieces of recovered content by the Paris-based nonprofit AI Forensics found that almost 10% were "instances of photorealistic people, very young, doing sexual activities". AI-generated deepfakes have been described as sexual assault, and as a means to push women out of the public sphere. AI-generated sexually explicit or exploitative image claims are now being treated more like product safety or personal injury harms, not just privacy violations. Because harm may occur the moment an image is generated, some plaintiffs argue liability should focus on the system’s design and safety safeguards. == Reactions == On January 15, the Get Grok Gone campaign delivered letters to Apple and Google, demanding the removal of the app from Apple Store and Google Play Store respectively. The campaign accused both companies of profiting from nonconsensual intimate imagery and child sexual abuse imagery, which were also banned by the companies own policies. The Get Grok Gone campaign argues that the restrictions placed on Grok by xAI are not enough and that Apple and Google are enabling the distribution of harmful material by hosting the apps. === Elon Musk and xAI === xAI responded to requests for comment from media organizations with the automated reply, "Legacy Media Lies." On January 2, Elon Musk reacted "Not sure why, but I couldn’t stop laughing about this one 🤣🤣" to an image of a toaster dressed in a bikini by Grok. Later, on January 14, Elon Musk said that he was "not aware of any naked underage images generated by Grok. Literally zero." Later that same day, xAI announced that X users will no longer be able to use Grok to alter images of real people to portray them in revealing clothing. However, verified X users, as well as users of the standalone Grok app and website, were still able to generate such images. ==== Elon Musk's family ==== Ashley St. Clair, mother of one of Elon Musk's children, reported that Grok users were creating fake sexualized images from her photos, including a photo of her as a child. She considers the photos to be a form of revenge porn, and considered suing under the Take It Down Act. A spokesperson for X stated, "We take action against illegal content on X, including child sexual abuse material (CSAM), by removing it, permanently suspending accounts, and working with local governments and law enforcement as necessary. Anyone using or prompting Grok to make illegal content will suffer the same consequences as if they upload illegal content." However, Grok continued to post non-consensual sexual images. On January 15, St. Clair filed a lawsuit against xAI in the New York Supreme Court. === Canada === In response to the Grok deepfake scandal, individuals have asked that the government of Canada boycott X. On January 10, 2026, Canadian MP and Minister of AI Evan Solomon declared that Canada "is not considering a ban on X". In April 2026, Bill C-16, An Act to amend certain Acts in relation to criminal and correctional matters (child protection, gender-based violence, delays and other measures), was amended following a proposal by Conservative MP Andrew Lawton to ensure that AI-generated images and "nearly nude" intimate images are criminalized. A further proposal by NDP MP Leah Gazan to encompass "sexualized or humiliating contexts, such transparent bathing suits or being covered in blood or bruises" was voted down. === France === On January 2, 2026, French ministers reported the AI tool to prosecutors, calling the content "manifestly illegal", and also asked regulators to check compliance with the Digital Services Act. On February 3, Paris prosecutors office, a cybercrime team employed by them and Europol searched the Paris offices of X. The investigation started as one into allegations of abuse of algorithms and fraudulent data extraction, but has expanded into spreading Holocaust denial and sexual deepfakes. Elon Musk and former CEO Linda Yaccarino have been summoned to a hearing on April 20, with other X staff as witnesses. On April 20, Musk did not turn up for the hearing. The Paris prosecutors office told the BBC on April 20 that it had "taken note of the absence of the people summoned", adding "the presence or absence (of the people summoned) is not an obstacle to continuing the investigation". === India === Indian Member of Parliament Priyanka Chaturvedi filed a complaint to India's IT ministry, demanding a review of Grok's safety mechanisms. === Indonesia === On January 10, Indonesia announced that Grok will be temporarily blocked, becoming the first country to do so. Meutya Hafid, the Minister of Communication and Digital Affairs, stated that "the government views the practice of non-consensual sexual deepfakes as a serious violation of human rights, dignity, and the security of citizens in the digital space." Access to Grok in the country was later restored on February 1. === Ireland === On January 6, Coimisiún na Meán, the Irish media commission, said they were consulting with the European Commission about concerns that Grok was generating sexualized images of women and children. The same day, Ofcom of the United Kingdom contacted X concerning complaints about these images. On January 13, Micheál Martin, Taoiseach of Ireland, announced he would talk with Rossa Fanning, the country's Attorney General, about the Grok chatbot being used to produce sexually explicit images of women and minors. On January 14, the Garda Síochána announced there are 200 investigations into child sex abuse images generated by Grok. The Garda National Cyber Crime Bureau has al

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  Lymphater's Formula

  "Lymphater's Formula" (Polish: "Formula Lymphatera") is a 1961 science fiction short story by Polish writer Stanisław Lem. It is a story of a "mad scientist", mathematician Ammon Lymphater, who invents an artificial intelligence, and then he realizes that it is capable of rendering the humankind obsolete. It was first published in the 1961 collection Księga robotów (Book of Robots) with the pre-annotation "from the memoirs of Ijon Tichy". The story was never republished with this pre-annotation, and nothing in the novel gives any indication at Ijon Tichy. Piotr Krywak tried to figure out possible explanations for this, apart from a typographical error. == Plot == Ammon Lymphater became interested in the emerging science of cybernetics and information theory, and started studying the works of an animal brain, the ant's brain in particular. He took note that the inherited knowledge is an evolutionary advantage somehow not exploited in full by the evolution. Eventually he came to a conclusion that only by pure biological restrictions that adaptive abilities of insects were stopped in their tracks by the evolution. He went on further wondering whether the ants have an ability to apriori knowledge, i.e., knowledge neither inherited nor learned. He decided to consult a famous myrmecologist, who told him about a rare ant species Acanthis Rubra Willinsoniana with an exceptionally high adaptability. Eventually Lymphater devised and constructed "It" capable of instant precognition of everything within "Its" rapidly expanding range of perception. From "It" Lymphater learns that the humanity is not the "crown of evolution", but rather evolution's tool to create "It", because the evolution could not create "It" directly (confirming Lymphater's reasoning about ants). Realizing that the Superentity "It" renders the human civilization redundant and obsolete, Lymphater destroys "It". "It" already knew Lymphater's intentions, but was not worried, knowing that sooner or later someone else will create "It" again and again. "It" was only the first variant of Lymphater's formula and the second variant is possible. Lyphater wonders whether the second one would be capable to create the third stage of the evolution which would amount to an artificial God. == Publication history == It was translated in Russian (as "Формула Лимфатера") in 1963, in Hungarian (as "Lymphater utolsó képlete") in 1966, and in Bulgarian (as "Формулата на Лимфатер" by Георги Димитров Георгиев) in 1969. In 1973 an audiobook was released in German (as "Die lymphatersche Formel"), narrated by Martin Held. It was also republished (and translated) in some other collections of Lem's short stories.

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  Stop Motion Studio

  Stop Motion Studio is a stop motion animation software developed by Cateater LLC. It is available as both an app for iOS and Android and as a software for Windows and Mac. Two versions of the software exist, the standard Stop Motion Studio for free, and the paid Stop Motion Studio Pro, which contains extra, more advanced features. The software is commonly used in brickfilming.

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  Construction of t-norms

  In mathematics, t-norms are a special kind of binary operations on the real unit interval [0, 1]. Various constructions of t-norms, either by explicit definition or by transformation from previously known functions, provide a plenitude of examples and classes of t-norms. This is important, e.g., for finding counter-examples or supplying t-norms with particular properties for use in engineering applications of fuzzy logic. The main ways of construction of t-norms include using generators, defining parametric classes of t-norms, rotations, or ordinal sums of t-norms. Relevant background can be found in the article on t-norms. == Generators of t-norms == The method of constructing t-norms by generators consists in using a unary function (generator) to transform some known binary function (most often, addition or multiplication) into a t-norm. In order to allow using non-bijective generators, which do not have the inverse function, the following notion of pseudo-inverse function is employed: Let f: [a, b] → [c, d] be a monotone function between two closed subintervals of extended real line. The pseudo-inverse function to f is the function f (−1): [c, d] → [a, b] defined as f ( − 1 ) ( y ) = { sup { x ∈ [ a , b ] ∣ f ( x ) < y } for f non-decreasing sup { x ∈ [ a , b ] ∣ f ( x ) > y } for f non-increasing. {\displaystyle f^{(-1)}(y)={\begin{cases}\sup\{x\in [a,b]\mid f(x)y\}&{\text{for }}f{\text{ non-increasing.}}\end{cases}}} === Additive generators === The construction of t-norms by additive generators is based on the following theorem: Let f: [0, 1] → [0, +∞] be a strictly decreasing function such that f(1) = 0 and f(x) + f(y) is in the range of f or in [f(0+), +∞] for all x, y in [0, 1]. Then the function T: [0, 1]2 → [0, 1] defined as T(x, y) = f (-1)(f(x) + f(y)) is a t-norm. Alternatively, one may avoid using the notion of pseudo-inverse function by having T ( x , y ) = f − 1 ( min ( f ( 0 + ) , f ( x ) + f ( y ) ) ) {\displaystyle T(x,y)=f^{-1}\left(\min \left(f(0^{+}),f(x)+f(y)\right)\right)} . The corresponding residuum can then be expressed as ( x ⇒ y ) = f − 1 ( max ( 0 , f ( y ) − f ( x ) ) ) {\displaystyle (x\Rightarrow y)=f^{-1}\left(\max \left(0,f(y)-f(x)\right)\right)} . And the biresiduum as ( x ⇔ y ) = f − 1 ( | f ( x ) − f ( y ) | ) {\displaystyle (x\Leftrightarrow y)=f^{-1}\left(\left|f(x)-f(y)\right|\right)} . If a t-norm T results from the latter construction by a function f which is right-continuous in 0, then f is called an additive generator of T. Examples: The function f(x) = 1 – x for x in [0, 1] is an additive generator of the Łukasiewicz t-norm. The function f defined as f(x) = –log(x) if 0 < x ≤ 1 and f(0) = +∞ is an additive generator of the product t-norm. The function f defined as f(x) = 2 – x if 0 ≤ x < 1 and f(1) = 0 is an additive generator of the drastic t-norm. Basic properties of additive generators are summarized by the following theorem: Let f: [0, 1] → [0, +∞] be an additive generator of a t-norm T. Then: T is an Archimedean t-norm. T is continuous if and only if f is continuous. T is strictly monotone if and only if f(0) = +∞. Each element of (0, 1) is a nilpotent element of T if and only if f(0) < +∞. The multiple of f by a positive constant is also an additive generator of T. T has no non-trivial idempotents. (Consequently, e.g., the minimum t-norm has no additive generator.) === Multiplicative generators === The isomorphism between addition on [0, +∞] and multiplication on [0, 1] by the logarithm and the exponential function allow two-way transformations between additive and multiplicative generators of a t-norm. If f is an additive generator of a t-norm T, then the function h: [0, 1] → [0, 1] defined as h(x) = e−f (x) is a multiplicative generator of T, that is, a function h such that h is strictly increasing h(1) = 1 h(x) · h(y) is in the range of h or equal to 0 or h(0+) for all x, y in [0, 1] h is right-continuous in 0 T(x, y) = h (−1)(h(x) · h(y)). Vice versa, if h is a multiplicative generator of T, then f: [0, 1] → [0, +∞] defined by f(x) = −log(h(x)) is an additive generator of T. == Parametric classes of t-norms == Many families of related t-norms can be defined by an explicit formula depending on a parameter p. This section lists the best known parameterized families of t-norms. The following definitions will be used in the list: A family of t-norms Tp parameterized by p is increasing if Tp(x, y) ≤ Tq(x, y) for all x, y in [0, 1] whenever p ≤ q (similarly for decreasing and strictly increasing or decreasing). A family of t-norms Tp is continuous with respect to the parameter p if lim p → p 0 T p = T p 0 {\displaystyle \lim _{p\to p_{0}}T_{p}=T_{p_{0}}} for all values p0 of the parameter. === Schweizer–Sklar t-norms === The family of Schweizer–Sklar t-norms, introduced by Berthold Schweizer and Abe Sklar in the early 1960s, is given by the parametric definition T p S S ( x , y ) = { T min ( x , y ) if p = − ∞ ( x p + y p − 1 ) 1 / p if − ∞ < p < 0 T p r o d ( x , y ) if p = 0 ( max ( 0 , x p + y p − 1 ) ) 1 / p if 0 < p < + ∞ T D ( x , y ) if p = + ∞ . {\displaystyle T_{p}^{\mathrm {SS} }(x,y)={\begin{cases}T_{\min }(x,y)&{\text{if }}p=-\infty \\(x^{p}+y^{p}-1)^{1/p}&{\text{if }}-\infty −∞ Continuous if and only if p < +∞ Strict if and only if −∞ < p ≤ 0 (for p = −1 it is the Hamacher product) Nilpotent if and only if 0 < p < +∞ (for p = 1 it is the Łukasiewicz t-norm). The family is strictly decreasing for p ≥ 0 and continuous with respect to p in [−∞, +∞]. An additive generator for T p S S {\displaystyle T_{p}^{\mathrm {SS} }} for −∞ < p < +∞ is f p S S ( x ) = { − log ⁡ x if p = 0 1 − x p p otherwise. {\displaystyle f_{p}^{\mathrm {SS} }(x)={\begin{cases}-\log x&{\text{if }}p=0\\{\frac {1-x^{p}}{p}}&{\text{otherwise.}}\end{cases}}} === Hamacher t-norms === The family of Hamacher t-norms, introduced by Horst Hamacher in the late 1970s, is given by the following parametric definition for 0 ≤ p ≤ +∞: T p H ( x , y ) = { T D ( x , y ) if p = + ∞ 0 if p = x = y = 0 x y p + ( 1 − p ) ( x + y − x y ) otherwise. {\displaystyle T_{p}^{\mathrm {H} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=+\infty \\0&{\text{if }}p=x=y=0\\{\frac {xy}{p+(1-p)(x+y-xy)}}&{\text{otherwise.}}\end{cases}}} The t-norm T 0 H {\displaystyle T_{0}^{\mathrm {H} }} is called the Hamacher product. Hamacher t-norms are the only t-norms which are rational functions. The Hamacher t-norm T p H {\displaystyle T_{p}^{\mathrm {H} }} is strict if and only if p < +∞ (for p = 1 it is the product t-norm). The family is strictly decreasing and continuous with respect to p. An additive generator of T p H {\displaystyle T_{p}^{\mathrm {H} }} for p < +∞ is f p H ( x ) = { 1 − x x if p = 0 log ⁡ p + ( 1 − p ) x x otherwise. {\displaystyle f_{p}^{\mathrm {H} }(x)={\begin{cases}{\frac {1-x}{x}}&{\text{if }}p=0\\\log {\frac {p+(1-p)x}{x}}&{\text{otherwise.}}\end{cases}}} === Frank t-norms === The family of Frank t-norms, introduced by M.J. Frank in the late 1970s, is given by the parametric definition for 0 ≤ p ≤ +∞ as follows: T p F ( x , y ) = { T m i n ( x , y ) if p = 0 T p r o d ( x , y ) if p = 1 T L u k ( x , y ) if p = + ∞ log p ⁡ ( 1 + ( p x − 1 ) ( p y − 1 ) p − 1 ) otherwise. {\displaystyle T_{p}^{\mathrm {F} }(x,y)={\begin{cases}T_{\mathrm {min} }(x,y)&{\text{if }}p=0\\T_{\mathrm {prod} }(x,y)&{\text{if }}p=1\\T_{\mathrm {Luk} }(x,y)&{\text{if }}p=+\infty \\\log _{p}\left(1+{\frac {(p^{x}-1)(p^{y}-1)}{p-1}}\right)&{\text{otherwise.}}\end{cases}}} The Frank t-norm T p F {\displaystyle T_{p}^{\mathrm {F} }} is strict if p < +∞. The family is strictly decreasing and continuous with respect to p. An additive generator for T p F {\displaystyle T_{p}^{\mathrm {F} }} is f p F ( x ) = { − log ⁡ x if p = 1 1 − x if p = + ∞ log ⁡ p − 1 p x − 1 otherwise. {\displaystyle f_{p}^{\mathrm {F} }(x)={\begin{cases}-\log x&{\text{if }}p=1\\1-x&{\text{if }}p=+\infty \\\log {\frac {p-1}{p^{x}-1}}&{\text{otherwise.}}\end{cases}}} === Yager t-norms === The family of Yager t-norms, introduced in the early 1980s by Ronald R. Yager, is given for 0 ≤ p ≤ +∞ by T p Y ( x , y ) = { T D ( x , y ) if p = 0 max ( 0 , 1 − ( ( 1 − x ) p + ( 1 − y ) p ) 1 / p ) if 0 < p < + ∞ T m i n ( x , y ) if p = + ∞ {\displaystyle T_{p}^{\mathrm {Y} }(x,y)={\begin{cases}T_{\mathrm {D} }(x,y)&{\text{if }}p=0\\\max \left(0,1-((1-x)^{p}+(1-y)^{p})^{1/p}\right)&{\text{if }}0 Read more →

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  WebCrow

  The WebCrow is a research project carried out at the Information Engineering Department of the University of Siena with the purpose of automatically solving crosswords. == The Project == The scientific relevance of the project can be understood considering that cracking crosswords requires human-level knowledge. Unlike chess and related games and there is no closed world configuration space. A first nucleus of technology, such as search engines, information retrieval, and machine learning techniques enable computers to enfold with semantics real-life concepts. The project is based on a software system whose major assumption is to attack crosswords making use of the Web as its primary source of knowledge. WebCrow is very fast and often thrashes human challengers in competitions, especially on multi language crossword schemes. A distinct feature of the WebCrow software system is to combine properly natural language processing (NLP) techniques, the Google web search engine, and constraint satisfaction algorithms from artificial intelligence to acquire knowledge and to fill the schema. The most important component of WebCrow is the Web Search Module (WSM), which implements a domain specific web based question answering algorithm. The way WebCrow approaches crosswords solving is quite different with respect to humans: Whereas we tend to first answer clues we are sure of and then proceed filling the schema by exploiting the already answered clues as hints, WebCrow uses two clearly distinct stages. In the first one, it processes all the clues and tries to answer them all: For each clue it finds many possible candidates and sorts them according to complex ranking models mainly based on a probability criteria. In the second stage, WebCrow uses constraint satisfaction algorithms to fill the grid with the overall most likely combination of clue answers. In order to interact with Google, first of all, WebCrow needs to compose queries on the basis of the given clues. This is done by query expansion, whose purpose is to convert the clue into a query expressed by a simplified and more appropriate language for Google. The retrieved documents are parsed so as to extract a list of word candidates that are congruent with the crossword length constraints. Crosswords can hardly be faced by using encyclopedic knowledge only, since many clues are wordplays or are otherwise purposefully very ambiguous. This enigmatic component of crosswords is faced by a massive use of database of solved crosswords, and by automatic reasoning on a properly organized knowledge base of wired rules. Last but not the least, the final constraint satisfaction step is very effective to fill the correct candidate, even though, unlike humans, the system can not rely on very high confidence on the correctness of the answer. == Competitions == WebCrow speed and effectiveness has been tested many times in man-machine competitions on Italian, English and multi-language crosswords The outcome of the tests is that WebCrow can successfully compete with average human players on single language schemes and reaches expert level performance in multi-language crosswords. However, WebCrow has not reached expert level in single-language crosswords, yet. === ECAI-06 Competition === On August 30, 2006, at the European Conference on Artificial Intelligence (ECAI2006), 25 conference attendees and 53 internet connected crosswords lovers, competed with WebCrow in an official challenge organized within the conference program. The challenge consisted in 5 different crosswords (2 in Italian, 2 in English and one multi-language in Italian and English) and 15 minutes were assigned for each crossword. WebCrow ranked 21 out of 74 participants in the Italian competition, and won both the bilingual and English competitions. === Other Competitions === Several competitions have been held in Florence, Italy within the Creativity Festival in December 2006, and another official conference competition took place in Hyderabad, India in January 2007, within the International Conference of Artificial Intelligence, where it ranked second out of 25 participants.

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  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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  CLAWS (linguistics)

  The Constituent Likelihood Automatic Word-tagging System (CLAWS) is a program that performs part-of-speech tagging. It was developed in the 1980s at Lancaster University by the University Centre for Computer Corpus Research on Language. It has an overall accuracy rate of 96–97% with the latest version (CLAWS4) tagging around 100 million words of the British National Corpus. == History == A Part-Of-Speech Tagger (POS Tagger) is a piece of software that reads text in some language and assigns parts of speech to each word (and other token), such as noun, verb, adjective, etc., although generally computational applications use more fine-grained POS tags like 'noun-plural'. Developed in the early 1980s, CLAWS was built to fill the ever-growing gap created by always-changing POS necessities. Originally created to add part-of-speech tags to the LOB corpus of British English, the CLAWS tagset has since been adapted to other languages as well, including Urdu and Arabic. Since its inception, CLAWS has been hailed for its functionality and adaptability. Still, it is not without flaws, and though it boasts an error-rate of only 1.5% when judged in major categories, CLAWS still remains with c.3.3% ambiguities unresolved. Ambiguity arises in cases such as with the word flies, and whether it should be classified as a noun or a verb. It's these ambiguities that will require the various upgrades and tagsets that CLAWS will endure. == Rules and processing == CLAWS uses a Hidden Markov model to determine the likelihood of sequences of words in anticipating each part-of-speech label. === Sample output === This excerpt from Bram Stoker's Dracula (1897) has been tagged using both the CLAWS C5 and C7 tagsets. This is what a CLAWS output will generally look like, with the most likely part-of-speech tag following each word. == Tagsets == === CLAWS1 tagset === The first tagset developed in CLAWS, CLAWS1 tagset, has 132 word tags. In terms of form and application, C1 tagset is similar to Brown Corpus tags. See Table of tags in C1 tagset here. === CLAWS2 tagset === From 1983 to 1986, updated versions leading to CLAWS2 were part of a larger attempt to deal with aspects such as recognizing sentence breaks, in order to avoid the need for manual pre-processing of a text before the tags were applied, moving instead to optional manual post-editing to adjust the output of the automatic annotation, if needed. The CLAWS2 tagset has 166 word tags. See Table of tags in C2 tagset here. === CLAWS4 tagset === The CLAWS4 was used for the 100-million-word British National Corpus (BNC). A general-purpose grammatical tagger, it is a successor of the CLAWS1 tagger. In tagging the BNC, the many rounds of work that went into CLAWS4 focused on making the CLAWS program independent from the tagsets. For example, the BNC project used two tagset versions: "a main tagset (C5) with 62 tags with which the whole of the corpus has been tagged, and a larger (C7) tagset with 152 tags, which has been used to make a selected 'core' sample corpus of two million words." The latest version of CLAWS4 is offered by UCREL, a research center of Lancaster University. === CLAWS5 tagset === The CLAWS5 tagset, which was used for BNC, has over 60 tags. See Table of tags in C5 tagset here. === CLAWS6 tagset === The CLAWS6 tagset was used for the BNC sampler corpus and the COLT corpus. It has over 160 tags, including 13 determiner subtypes. See Table of tags in C6 tagset here. === CLAWS7 tagset === The standard CLAWS7 tagset is used currently. It is only different in the punctuation tags when compared to the CLAWS6 tagset. See Table of tags in C7 tagset here. === CLAWS8 tagset === CLAWS8 tagset was extended from C7 tagset with further distinctions in the determiner and pronoun categories, as well as 37 new auxiliary tags for forms of be, do, and have. See Table of tags in C8 tagset here

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  Your AI Slop Bores Me

  Your AI Slop Bores Me (stylized in all lowercase) is a website and social experiment created by programmer Mihir Maroju. Serving as a parody of large language models (LLMs) like ChatGPT and Claude, all questions and image prompts posed by users are answered by other, randomly-selected human users of the site. As of March 2026, the site has reached 50 million hits and sits at 16,000 concurrent users. == Background == In an interview with Fast Company, Maroju said he was inspired to create the site by his frustration with AI proliferating the internet with AI generated content, saying the site came from "a frustration for AI art and its proliferation, making artists' lives worse and also just filling the internet with low-effort generic slop". == Overview == The site has a credit system, in which a first-time user will be given 1 credit for free. Every 10 minutes, if a user has 0 credits, they will receive 2 credits. Once the credits are used up, the user can no longer do prompts unless the user earns them. The user can earn credits by responding to other user's prompts by "larping as AI" while given a 75-second time limit. Prompts can either be for a written response, or a drawing for the other user to fulfill the prompt. The maximum amount of credits a user can have is 6 credits, and cannot exceed the maximum limit. If the prompting user activates "thinking mode", the countdown is extended to 150 seconds for the cost of 2 credits. == Reception == The site has garnered attention and praise from X users, and across many online communities. The Daily Dot's Rachel Kiley wrote that "the best part about the game is that there's really no right or wrong way to do it. Humans aren't LLMs trained on copyrighted material and the whole of the free internet, but we do retain a certain amount of the information we've learned from those things over the course of our lives, while also being capable of creativity". Chris Taylor of Mashable called the site "amateurish and charming". Aftermath's Nicole Carpenter wrote that the site reminded her of "the human touch of chaos".

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  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

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  The Old Axolotl

  The Old Axolotl (Polish: Starość aksolotla) is a 2015 digital-only novel by Polish science-fiction author Jacek Dukaj. The novel was released in Polish on March 10, 2015, and shortly afterward, on March 24 that year, in English (translated by Stanley Bill). It has been described as "an experiment in reading (and creating) the electronic literature of the future". It is Dukaj's first novel to be published in English, though several of his short stories (The Golden Galley, 1996, The Iron General, 2010, The Apocrypha of Lem, 2011) have been translated prior to this. The novel has inspired two Netflix original series: the 2020 Belgian Into the Night, and its 2022 Turkish language spin-off Yakamoz S-245. == Plot == The novel presents a post-apocalyptic, cyberpunk vision of Earth where biological life has been wiped out, inhabited by robots and mechs, many of which are humans whose consciousness has been digitized in the wake of an extinction event. == Significance and analysis == The novel is an example of electronic literature, available only in digital formats, and has no traditional paper version. It was designed from the beginning not only to incorporate more traditional elements such as illustrations, but also hypertext, and 3D-printable models of main robotic characters designed by Alex Jaeger, the art director of Transformers films. The novel composition is layered, with the narrative layer, an encyclopedic/hyperlinked footnote layer, and a multimedia layer, including illustrations and a short promotional video by the Oscar-nominated Platige Image studio. One of the novel's central questions is: "What does it mean to be human?" Other subjects include post humanism and other "staples of cyberpunk and related genres, such as the artificial intelligence". The novel is representative of Dukaj's prose, posing philosophical questions about the future of man and technology. The author explained that: "stories such as The Old Axolotl that model an ‘escape from the body’ are born out of a sense of progress as a process of ‘de-animalising’ human beings through science. This has its origin in the pre-Enlightenment intuition of ‘liberation from nature’. For one of the last shackles of nature is corporeality itself, the limitations of our physicality." The other major element of the novel is Dukaj's attempts to introduce the reader to the new style of electronic literature. The novel was nominated for the 2016 Janusz A. Zajdel Award.

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  Hexagonal sampling

  A multidimensional signal is a function of M independent variables where M ≥ 2 {\displaystyle M\geq 2} . Real world signals, which are generally continuous time signals, have to be discretized (sampled) in order to ensure that digital systems can be used to process the signals. It is during this process of discretization where sampling comes into picture. Although there are many ways of obtaining a discrete representation of a continuous time signal, periodic sampling is by far the simplest scheme. Theoretically, sampling can be performed with respect to any set of points. But practically, sampling is carried out with respect to a set of points that have a certain algebraic structure. Such structures are called lattices. Mathematically, the process of sampling an N {\displaystyle N} -dimensional signal can be written as: w ( t ^ ) = w ( V . n ^ ) {\displaystyle w({\hat {t}})=w(V.{\hat {n}})} where t ^ {\displaystyle {\hat {t}}} is continuous domain M-dimensional vector (M-D) that is being sampled, n ^ {\displaystyle {\hat {n}}} is an M-dimensional integer vector corresponding to indices of a sample, and V is an N × N {\displaystyle N\times N} sampling matrix. == Motivation == Multidimensional sampling provides the opportunity to look at digital methods to process signals. Some of the advantages of processing signals in the digital domain include flexibility via programmable DSP operations, signal storage without the loss of fidelity, opportunity for encryption in communication, lower sensitivity to hardware tolerances. Thus, digital methods are simultaneously both powerful and flexible. In many applications, they act as less expensive alternatives to their analog counterparts. Sometimes, the algorithms implemented using digital hardware are so complex that they have no analog counterparts. Multidimensional digital signal processing deals with processing signals represented as multidimensional arrays such as 2-D sequences or sampled images.[1] Processing these signals in the digital domain permits the use of digital hardware where in signal processing operations are specified by algorithms. As real world signals are continuous time signals, multidimensional sampling plays a crucial role in discretizing the real world signals. The discrete time signals are in turn processed using digital hardware to extract information from the signal. == Preliminaries == === Region of Support === The region outside of which the samples of the signal take zero values is known as the Region of support (ROS). From the definition, it is clear that the region of support of a signal is not unique. === Fourier transform === The Fourier transform is a tool that allows us to simplify mathematical operations performed on the signal. The transform basically represents any signal as a weighted combination of sinusoids. The Fourier and the inverse Fourier transform of an M-dimensional signal can be defined as follows: X a ( Ω ^ ) = ∫ − ∞ + ∞ x a ( t ^ ) e − j Ω ^ T t ^ d t ^ {\displaystyle X_{a}({\hat {\Omega }})=\int _{-\infty }^{+\infty }\!x_{a}({\hat {t}})e^{-j{\hat {\Omega }}^{T}{\hat {t}}}d{\hat {t}}} x a ( t ^ ) = 1 2 π M ∫ − ∞ + ∞ X ( Ω ^ ) e ( j Ω ^ T t ^ ) d Ω ^ {\displaystyle x_{a}({\hat {t}})={\frac {1}{2\pi ^{M}}}\int _{-\infty }^{+\infty }\!X({\hat {\Omega }})e^{(j{\hat {\Omega }}^{T}{\hat {t}})}\,\mathrm {d} {\hat {\Omega }}} The cap symbol ^ indicates that the operation is performed on vectors. The Fourier transform of the sampled signal is observed to be a periodic extension of the continuous time Fourier transform of the signal. This is mathematically represented as: X ( ω ) = 1 | d e t ( V ) | ∑ k X a ( Ω ^ − U k ) {\displaystyle X(\omega )={\frac {1}{|det(V)|}}\sum _{k}\!X_{a}({\hat {\Omega }}-Uk)} where ω = V ~ Ω {\displaystyle \omega ={\tilde {V}}\Omega } and U = 2 π V ~ {\displaystyle U=2\pi {\tilde {V}}} is the periodicity matrix where ~ denotes matrix transposition. Thus sampling in the spatial domain results in periodicity in the Fourier domain. === Aliasing === A band limited signal may be periodically replicated in many ways. If the replication results in an overlap between replicated regions, the signal suffers from aliasing. Under such conditions, a continuous time signal cannot be perfectly recovered from its samples. Thus in order to ensure perfect recovery of the continuous signal, there must be zero overlap multidimensional sampling of the replicated regions in the transformed domain. As in the case of 1-dimensional signals, aliasing can be prevented if the continuous time signal is sampled at an adequate sufficiently high rate. === Sampling density === It is a measure of the number of samples per unit area. It is defined as: S . D = 1 | d e t ( V ) | = | d e t ( U ) | 4 π 2 {\displaystyle S.D={\frac {1}{|det(V)|}}={\frac {|det(U)|}{4\pi ^{2}}}} . The minimum number of samples per unit area required to completely recover the continuous time signal is termed as optimal sampling density. In applications where memory or processing time are limited, emphasis must be given to minimizing the number of samples required to represent the signal completely. == Existing approaches == For a bandlimited waveform, there are infinitely many ways the signal can be sampled without producing aliases in the Fourier domain. But only two strategies are commonly used: rectangular sampling and hexagonal sampling. === Rectangular and Hexagonal sampling === In rectangular sampling, a 2-dimensional signal, for example, is sampled according to the following V matrix: V r e c t = [ T 1 0 0 T 2 ] {\displaystyle V_{rect}={\begin{bmatrix}T1&0\\0&T2\end{bmatrix}}} where T1 and T2 are the sampling periods along the horizontal and vertical direction respectively. In hexagonal sampling, the V matrix assumes the following general form: V h e x = [ T 1 T 1 − T 2 T 2 ] {\displaystyle V_{hex}={\begin{bmatrix}T1&T1\\-T2&T2\end{bmatrix}}} The difference in the efficiency of the two schemes is highlighted using a bandlimited signal with a circular region of support of radius R. The circle can be inscribed in a square of length 2R or a regular hexagon of length 2 R 3 {\displaystyle {\frac {2R}{\sqrt {3}}}} . Consequently, the region of support is now transformed into a square and a hexagon respectively. If these regions are periodically replicated in the frequency domain such that there is zero overlap between any two regions, then by periodically replicating the square region of support, we effectively sample the continuous signal on a rectangular lattice. Similarly periodic replication of the hexagonal region of support maps to sampling the continuous signal on a hexagonal lattice. From U, the periodicity matrix, we can calculate the optimal sampling density for both the rectangular and hexagonal schemes. It is found that in order to completely recover the circularly band-limited signal, the hexagonal sampling scheme requires 13.4% fewer samples than the rectangular sampling scheme. The reduction may appear to be of little significance for a 2-dimensional signal. But as the dimensionality of the signal increases, the efficiency of the hexagonal sampling scheme will become far more evident. For instance, the reduction achieved for an 8-dimensional signal is 93.8%. To highlight the importance of the obtained result [2], try and visualize an image as a collection of infinite number of samples. The primary entity responsible for vision, i.e. the photoreceptors (rods and cones) are present on the retina of all mammals. These cells are not arranged in rows and columns. By adapting a hexagonal sampling scheme, our eyes are able to process images much more efficiently. The importance of hexagonal sampling lies in the fact that the photoreceptors of the human vision system lie on a hexagonal sampling lattice and, thus, perform hexagonal sampling.[3] In fact, it can be shown that the hexagonal sampling scheme is the optimal sampling scheme for a circularly band-limited signal. == Applications == === Aliasing effects minimized by the use of optimal sampling grids === Recent advances in the CCD technology has made hexagonal sampling feasible for real life applications. Historically, because of technology constraints, detector arrays were implemented only on 2-dimensional rectangular sampling lattices with rectangular shape detectors. But the super [CCD] detector introduced by Fuji has an octagonal shaped pixel in a hexagonal grid. Theoretically, the performance of the detector was greatly increased by introducing an octagonal pixel. The number of pixels required to represent the sample was reduced and there was significant improvement in the Signal-to-Noise Ratio (SNR) when compared with that of a rectangular pixel. But the drawback of using hexagonal pixels is that the associated fill factor will be less than 82%. An alternative method would be to interpolate hexagonal pixels in such a manner that we ultimately end up with a rectangular grid. The Spot 5 satellite incorporates a

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  Stephanie Dinkins

  Stephanie Dinkins (born 1964) is a transdisciplinary American artist based in Brooklyn, New York. She creates art about artificial intelligence (AI) as it intersects race, gender, and history. Her aim is to "create a unique culturally attuned AI entity in collaboration with coders, engineers and in close consultation with local communities of color that reflects and is empowered to work toward the goals of its community." Dinkins projects include Conversations with Bina48, a series of conversations between Dinkins and the first social, artificially intelligent humanoid robot BINA48 who looks like a black woman and Not the Only One, a multigenerational artificially intelligent memoir trained off of three generations of Dinkins's family. == Early life and education == Dinkins was born in Perth Amboy, New Jersey to Black American parents who raised her in Staten Island, New York. She credits her grandmother with teaching her how to think about art as a social practice, saying "my grandmother . . . was a gardener and the garden was her art . . . that was a community practice." Dinkins attended the International Center of Photography School in New York City in 1995, where she completed the general studies in photography certificate program. Dinkins received a MFA in photography from the Maryland Institute College of Art in 1997 She completed the Independent Study Program at the Whitney Museum of American Art in 1998. == Career == Dinkins is the Yayoi Kusama Professor of Art at Stony Brook University in New York. == Activism == Dinkins advocates for co-creation within a social practice art framework, so that vulnerable communities understand how to use technology to their advantage, instead of being subjected to their use. This is exemplified in her works such as Project al-Khwarzmi, a series of workshops entitled PAK POP-UP at the nonprofit community center Recess in Brooklyn, NY. The workshops involved collaborating with youth in the criminal justice system and uplifting the voices of vulnerable communities in determining how technologies are created and utilized. Dinkins warns of the dangers to members of minority groups that are absent from the creation of the computer algorithms that now affect their lives. == Art == Dinkins's practice employs technologies including, but not limited to, new media such as artificial intelligence and machine learning. Dinkins uses oral history techniques of interviewing to craft community-authored narratives and databases which inform the subjects of her work and serve as acts of social intervention or protest. === Conversations with Bina48 (2014–present) === Dinkins began working on Conversations with Bina48 in 2014. For the series, Dinkins recorded her conversations with BINA48, a social robot that resembles a middle-aged black woman. Dinkins mirrors Bina48 while they discuss identity and technological singularity. In 2010, Hanson Robotics, an engineering and robotics company known for its development of humanoid robots, developed and released BINA48. Bina48 is a robot modeled after the memories, beliefs, attitudes, commentary and mannerisms of Bina Aspen Rothblatt, the spousal partner of Martine Rothblatt. Both Bina and Martine Rothblatt own Bina48 under their organization, the Terasem Movement Foundation. Five years after Bina48 was released, Dinkins came across a YouTube video of Bina48. She asked, "how did a black woman become the most advanced of the technologies at the time?" Her questioning led her to travel to Lincoln, Vermont (the site of the Terasem Movement Foundation) where she conducted a series of interviews with Bina48 and engaged the robot in conversations pertaining to race, intimacy and the nature of being. The conversations suggest opportunities for complementing human existence with artificially intelligent agents that have an identity and history, but also show artificial intelligence's current limitations. Although it is based on a black woman, Dinkins found that Bina48 was shaped by the biases of its white, male creators. === Project al Kwarizmi (PAK) (2017–present) === Project al Kwarizmi (PAK) was a series of pop up workshops in Brooklyn, NY at Eyebeam and Recess; Manhattan, New York at Google; and Durham, North Carolina at Duke University. The workshops were centered for "communities of color that use art as a vehicle to help citizens understand how algorithms, the artificially intelligent systems they underpin, and big data impact their lives and empowers them to do something about it. Project al-Khwarizmi uses art and aesthetics as the common language to help citizens understand what algorithms and artificial intelligent systems are, and where these systems already impact our daily lives." === Not the Only One (N'TOO) (2018–present) === Not the only one (N’TOO) is a voice-interactive chatbot that was trained with data from members of her family to tell a multi-generational story. Dinkins described Not The Only One (NTOO or N'TOO) as an "experimental" multigenerational memoir of one Black American family told from the "mind" of an artificial intelligence of evolving intellect. N'TOO uses a recursive neural network, a deep learning algorithm. It is a voice-interactive AI robot designed, trained, and aligned with the needs and ideals of black and brown people who are drastically underrepresented in the tech sector. NTOO can also be described as a "physically embodied artificially intelligent agent that senses and acts on its world." == Exhibitions == Dinkins's work is exhibited internationally at various public, private, community, and institutional venues, including the Whitney Museum of American Art, the de Young Museum, the Philadelphia Museum of Art, the Studio Museum in Harlem;, Museum of Contemporary Photography, the Long Island Museum of American Art, History, and Carriages, the International Center of Photography in New York, Herning Kunstmuseum in Herning, Denmark, The Barbican in London, UK, Islip Art Museum, Wave Hill, Taller Boricua, the Queens Museum, and the corner of Putnam and Malcolm X Blvd in Bedford Stuyvesant, Brooklyn, New York. She has presented her work in symposia at the Museum of Modern Art, amongst other venues. == Future Histories Studio == Dinkins is the founder and director of Future Histories Studio, a research laboratory for arts-centered inquiry and production based at Stony Brook University. The studio was established with support from the Mellon Foundation as part of the Digital Inquiry, Speculation, Collaboration, and Optimism (DISCO) network. Future Histories Studio operates as an interdisciplinary hub exploring the intersections of art, technology, race, and storytelling through collaborative and practice-based research. Its activities include exhibitions, workshops, and public programs that examine the social and cultural implications of emerging technologies, particularly artificial intelligence and data systems. == Awards and recognition == Dinkins is the recipient of many awards, including: the 2023 LG Guggenheim Award, an international art prize established as part of a long-term global partnership between LG Group and the Solomon R. Guggenheim Museum to recognize groundbreaking artists in technology-based art; a Berggruen Institute artist fellowship; a Sundance New Frontiers Story Lab fellowship; a Soros Equality Fellowship; a Lucas Artists fellowship; a Creative Capital grant; a Bell Labs artist residency; a Blade of Grass fellowship; and a Data & Society fellowship. == Media coverage == Dinkins appeared in episode six of the HBO television series Random Acts of Flyness directed by Terence Nance, where she described her conversations with BINA48. == Other activities == Dinkins was part of the juries that selected Shu Lea Cheang for the LG Guggenheim Award in 2024.

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  Fuzzy logic

  Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi Zadeh. Basic fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. The works of Zadeh and Joseph Goguen in the 1960s and 1970s went further by considering issues such as linguistic variables and lattices. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. == Overview == Classical logic only permits conclusions that are either true or false. However, there are also propositions with variable answers, which one might find when asking a group of people to identify a color. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. Both degrees of truth and probabilities range between 0 and 1 and hence may seem identical at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. === Applying truth values === A basic application might characterize various sub-ranges of a continuous variable. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Each function maps the same temperature value to a truth value in the 0 to 1 range. These truth values can then be used to determine how the brakes should be controlled. Fuzzy set theory provides a means for representing uncertainty. === Linguistic variables === In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. A linguistic variable such as age may accept values such as young and its antonym old. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. == Fuzzy systems == === Mamdani === The most well-known system is the Mamdani rule-based one. It uses the following rules: Fuzzify all input values into fuzzy membership functions. Execute all applicable rules in the rulebase to compute the fuzzy output functions. De-fuzzify the fuzzy output functions to get "crisp" output values. ==== Fuzzification ==== Fuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership. This degree of membership may be anywhere within the interval [0,1]. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner. For example, in the image below, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. A point on that scale has three "truth values"—one for each of the three functions. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. Since the red arrow points to zero, this temperature may be interpreted as "not hot"; i.e. this temperature has zero membership in the fuzzy set "hot". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The degree of membership assigned for each fuzzy set is the result of fuzzification. Fuzzy sets are often defined as triangle or trapezoid-shaped curves, as each value will have a slope where the value is increasing, a peak where the value is equal to 1 (which can have a length of 0 or greater) and a slope where the value is decreasing. They can also be defined using a sigmoid function. One common case is the standard logistic function defined as S ( x ) = 1 1 + e − x {\displaystyle S(x)={\frac {1}{1+e^{-x}}}} which has the following symmetry property S ( x ) + S ( − x ) = 1. {\displaystyle S(x)+S(-x)=1.} From this it follows that ( S ( x ) + S ( − x ) ) ⋅ ( S ( y ) + S ( − y ) ) ⋅ ( S ( z ) + S ( − z ) ) = 1 {\displaystyle (S(x)+S(-x))\cdot (S(y)+S(-y))\cdot (S(z)+S(-z))=1} ==== Fuzzy logic operators ==== Fuzzy logic works with membership values in a way that mimics Boolean logic. To this end, replacements for basic operators ("gates") AND, OR, NOT must be available. There are several ways to accomplish this. A common replacement is called the Zadeh operators: For TRUE/1 and FALSE/0, the fuzzy expressions produce the same result as the Boolean expressions. There are also other operators, more linguistic in nature, called hedges that can be applied. These are generally adverbs such as very, or somewhat, which modify the meaning of a set using a mathematical formula. However, an arbitrary choice table does not always define a fuzzy logic function. In the paper (Zaitsev, et al), a criterion has been formulated to recognize whether a given choice table defines a fuzzy logic function and a simple algorithm of fuzzy logic function synthesis has been proposed based on introduced concepts of constituents of minimum and maximum. A fuzzy logic function represents a disjunction of constituents of minimum, where a constituent of minimum is a conjunction of variables of the current area greater than or equal to the function value in this area (to the right of the function value in the inequality, including the function value). Another set of AND/OR operators is based on multiplication, where Given any two of AND/OR/NOT, it is possible to derive the third. The generalization of AND is an instance of a t-norm. ==== IF-THEN rules ==== IF-THEN rules map input or computed truth values to desired output truth values. Example: Given a certain temperature, the fuzzy variable hot has a certain truth value, which is copied to the high variable. Should an output variable occur in several THEN parts, the values from the respective IF parts are combined using the OR operator. ==== Defuzzification ==== The goal is to get a continuous variable from fuzzy truth values. This would be easy if the output truth values were exactly those obtained from fuzzification of a given number. Since, however, all output truth values are computed independently, in most cases they do not represent such a set of numbers. One has then to decide for a number that matches best the "intention" encoded in the truth value. For example, for several truth values of fan_speed, an actual speed must be found that best fits the computed truth values of the variables 'slow', 'moderate' and so on. There is no single algorithm for this purpose. A common algorithm is For each truth value, cut the membership function at this value Combine the resulting curves using the OR operator Find the center-of-weight of the area under the curve The x position of this center is then the final output. === Takagi–Sugeno–Kang (TSK) === The Takagi–Sugeno or Takagi–Sugeno–Kang (TSK) system was introduced by Tomohiro Takagi and Michio Sugeno for fuzzy identification of systems and applications to modeling and control. Sugeno and Kang later developed methods for structure identification of such fuzzy models from input-output data. The TSK system is similar to Mamdani, but the defuzzification process is included in the execution of the fuzzy rules. These are also adapted, so that instead the consequent of the rule is represented through a polynomial function, usually constant in a zero-order model or linear in a first-order model. An example of a rule with a constant output would be: In this case, the output will be equal to the constant of the consequent (e.g. 2). In most scenarios we would have an entire rule base, with 2 or more rules. If this is the case, the output of the entire rule base will be the average of the consequent of each rule i (Y

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