The ugly duckling theorem is an argument showing that classification is not really possible without some sort of bias. More particularly, it assumes finitely many properties combinable by logical connectives, and finitely many objects; it asserts that any two different objects share the same number of (extensional) properties. The theorem is named after Hans Christian Andersen's 1843 story "The Ugly Duckling", because it shows that a duckling is just as similar to a swan as two swans are to each other. It was derived by Satosi Watanabe in 1969. == Mathematical formula == Suppose there are n things in the universe, and one wants to put them into classes or categories. One has no preconceived ideas or biases about what sorts of categories are "natural" or "normal" and what are not. So one has to consider all the possible classes that could be, all the possible ways of making a set out of the n objects. There are 2 n {\displaystyle 2^{n}} such ways, the size of the power set of n objects. One can use that to measure the similarity between two objects, and one would see how many sets they have in common. However, one cannot. Any two objects have exactly the same number of classes in common if we can form any possible class, namely 2 n − 1 {\displaystyle 2^{n-1}} (half the total number of classes there are). To see this is so, one may imagine each class is represented by an n-bit string (or binary encoded integer), with a zero for each element not in the class and a one for each element in the class. As one finds, there are 2 n {\displaystyle 2^{n}} such strings. As all possible choices of zeros and ones are there, any two bit-positions will agree exactly half the time. One may pick two elements and reorder the bits so they are the first two, and imagine the numbers sorted lexicographically. The first 2 n / 2 {\displaystyle 2^{n}/2} numbers will have bit #1 set to zero, and the second 2 n / 2 {\displaystyle 2^{n}/2} will have it set to one. Within each of those blocks, the top 2 n / 4 {\displaystyle 2^{n}/4} will have bit #2 set to zero and the other 2 n / 4 {\displaystyle 2^{n}/4} will have it as one, so they agree on two blocks of 2 n / 4 {\displaystyle 2^{n}/4} or on half of all the cases, no matter which two elements one picks. So if we have no preconceived bias about which categories are better, everything is then equally similar (or equally dissimilar). The number of predicates simultaneously satisfied by two non-identical elements is constant over all such pairs. Thus, some kind of inductive bias is needed to make judgements to prefer certain categories over others. === Boolean functions === Let x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\dots ,x_{n}} be a set of vectors of k {\displaystyle k} booleans each. The ugly duckling is the vector which is least like the others. Given the booleans, this can be computed using Hamming distance. However, the choice of boolean features to consider could have been somewhat arbitrary. Perhaps there were features derivable from the original features that were important for identifying the ugly duckling. The set of booleans in the vector can be extended with new features computed as boolean functions of the k {\displaystyle k} original features. The only canonical way to do this is to extend it with all possible Boolean functions. The resulting completed vectors have 2 k {\displaystyle 2^{k}} features. The ugly duckling theorem states that there is no ugly duckling because any two completed vectors will either be equal or differ in exactly half of the features. Proof. Let x and y be two vectors. If they are the same, then their completed vectors must also be the same because any Boolean function of x will agree with the same Boolean function of y. If x and y are different, then there exists a coordinate i {\displaystyle i} where the i {\displaystyle i} -th coordinate of x {\displaystyle x} differs from the i {\displaystyle i} -th coordinate of y {\displaystyle y} . Now the completed features contain every Boolean function on k {\displaystyle k} Boolean variables, with each one exactly once. Viewing these Boolean functions as polynomials in k {\displaystyle k} variables over GF(2), segregate the functions into pairs ( f , g ) {\displaystyle (f,g)} where f {\displaystyle f} contains the i {\displaystyle i} -th coordinate as a linear term and g {\displaystyle g} is f {\displaystyle f} without that linear term. Now, for every such pair ( f , g ) {\displaystyle (f,g)} , x {\displaystyle x} and y {\displaystyle y} will agree on exactly one of the two functions. If they agree on one, they must disagree on the other and vice versa. (This proof is believed to be due to Watanabe.) == Discussion == A possible way around the ugly duckling theorem would be to introduce a constraint on how similarity is measured by limiting the properties involved in classification, for instance, between A and B. However Medin et al. (1993) point out that this does not actually resolve the arbitrariness or bias problem since in what respects A is similar to B: "varies with the stimulus context and task, so that there is no unique answer, to the question of how similar is one object to another". For example, "a barberpole and a zebra would be more similar than a horse and a zebra if the feature striped had sufficient weight. Of course, if these feature weights were fixed, then these similarity relations would be constrained". Yet the property "striped" as a weight 'fix' or constraint is arbitrary itself, meaning: "unless one can specify such criteria, then the claim that categorization is based on attribute matching is almost entirely vacuous". Stamos (2003) remarked that some judgments of overall similarity are non-arbitrary in the sense they are useful: "Presumably, people's perceptual and conceptual processes have evolved that information that matters to human needs and goals can be roughly approximated by a similarity heuristic... If you are in the jungle and you see a tiger but you decide not to stereotype (perhaps because you believe that similarity is a false friend), then you will probably be eaten. In other words, in the biological world stereotyping based on veridical judgments of overall similarity statistically results in greater survival and reproductive success." Unless some properties are considered more salient, or 'weighted' more important than others, everything will appear equally similar, hence Watanabe (1986) wrote: "any objects, in so far as they are distinguishable, are equally similar". In a weaker setting that assumes infinitely many properties, Murphy and Medin (1985) give an example of two putative classified things, plums and lawnmowers: "Suppose that one is to list the attributes that plums and lawnmowers have in common in order to judge their similarity. It is easy to see that the list could be infinite: Both weigh less than 10,000 kg (and less than 10,001 kg), both did not exist 10,000,000 years ago (and 10,000,001 years ago), both cannot hear well, both can be dropped, both take up space, and so on. Likewise, the list of differences could be infinite… any two entities can be arbitrarily similar or dissimilar by changing the criterion of what counts as a relevant attribute." According to Woodward, the ugly duckling theorem is related to Schaffer's Conservation Law for Generalization Performance, which states that all algorithms for learning of boolean functions from input/output examples have the same overall generalization performance as random guessing. The latter result is generalized by Woodward to functions on countably infinite domains.
Open-source software security
Open-source software security is the measure of assurance or guarantee in the freedom from danger and risk inherent to an open-source software system. == Implementation debate == === Benefits === Proprietary software forces the user to accept the level of security that the software vendor is willing to deliver and to accept the rate that patches and updates are released. It is assumed that any compiler that is used creates code that can be trusted, but it has been demonstrated by Ken Thompson that a compiler can be subverted using a compiler backdoor to create faulty executables that are unwittingly produced by a well-intentioned developer. With access to the source code for the compiler, the developer has at least the ability to discover if there is any mal-intention. Kerckhoffs' principle is based on the idea that an enemy can steal a secure military system and not be able to compromise the information. His ideas were the basis for many modern security practices, and followed that security through obscurity is a bad practice. === Drawbacks === Simply making source code available does not guarantee review. An example of this occurring is when Marcus Ranum, an expert on security system design and implementation, released his first public firewall toolkit. At one time, there were over 2,000 sites using his toolkit, but only 10 people gave him any feedback or patches. Having a large amount of eyes reviewing code can "lull a user into a false sense of security". Having many users look at source code does not guarantee that security flaws will be found and fixed. == Metrics and models == There are a variety of models and metrics to measure the security of a system. These are a few methods that can be used to measure the security of software systems. === Number of days between vulnerabilities === It is argued that a system is most vulnerable after a potential vulnerability is discovered, but before a patch is created. By measuring the number of days between the vulnerability and when the vulnerability is fixed, a basis can be determined on the security of the system. There are a few caveats to such an approach: not every vulnerability is equally bad, and fixing a lot of bugs quickly might not be better than only finding a few and taking a little bit longer to fix them, taking into account the operating system, or the effectiveness of the fix. === Poisson process === The Poisson process can be used to measure the rates at which different people find security flaws between open and closed source software. The process can be broken down by the number of volunteers Nv and paid reviewers Np. The rates at which volunteers find a flaw is measured by λv and the rate that paid reviewers find a flaw is measured by λp. The expected time that a volunteer group is expected to find a flaw is 1/(Nv λv) and the expected time that a paid group is expected to find a flaw is 1/(Np λp). === Morningstar model === By comparing a large variety of open source and closed source projects a star system could be used to analyze the security of the project similar to how Morningstar, Inc. rates mutual funds. With a large enough data set, statistics could be used to measure the overall effectiveness of one group over the other. An example of such as system is as follows: 1 Star: Many security vulnerabilities. 2 Stars: Reliability issues. 3 Stars: Follows best security practices. 4 Stars: Documented secure development process. 5 Stars: Passed independent security review. === Coverity scan === Coverity in collaboration with Stanford University has established a new baseline for open-source quality and security. The development is being completed through a contract with the Department of Homeland Security. They are utilizing innovations in automated defect detection to identify critical types of bugs found in software. The level of quality and security is measured in rungs. Rungs do not have a definitive meaning, and can change as Coverity releases new tools. Rungs are based on the progress of fixing issues found by the Coverity Analysis results and the degree of collaboration with Coverity. They start with Rung 0 and currently go up to Rung 2. Rung 0 The project has been analyzed by Coverity's Scan infrastructure, but no representatives from the open-source software have come forward for the results. Rung 1 At rung 1, there is collaboration between Coverity and the development team. The software is analyzed with a subset of the scanning features to prevent the development team from being overwhelmed. Rung 2 There are 11 projects that have been analyzed and upgraded to the status of Rung 2 by reaching zero defects in the first year of the scan. These projects include: AMANDA, ntp, OpenPAM, OpenVPN, Overdose, Perl, PHP, Postfix, Python, Samba, and Tcl.
Micah Xavier Johnson
Micah Xavier Johnson (July 2, 1991 – July 8, 2016) was an American Army reserve Afghan war veteran, black nationalist, and mass murderer who perpetrated the 2016 shooting of Dallas police officers during a Black Lives Matter protest. He ambushed and killed five officers and wounded eleven others in Downtown, Dallas, Texas. He was killed by police during a standoff after expressing anger over police killings of black men. The shootings were the second-deadliest targeted attack on law enforcement officers in U.S. history, surpassed only by the September 11 attacks. == Early life == Micah Xavier Johnson was born in Magee, Mississippi, on July 2, 1991, and he was raised in Mesquite, Texas. When he was four years old, his parents divorced. At 17, Johnson enrolled at John Horn High School, where he joined the Junior Reserve Officers' Training Corps, as reported by the Mesquite Independent school district. He faced academic challenges, graduating in 2009 with a 1.98 GPA and ranking 430th out of 453 students in his class. In Spring 2011, Johnson registered for four courses at Richland college but did not complete any. Evidence suggests his enrollment at Richland gave him access to El Centro College, due to his pre-planned and coordinated movements throughout Building B during his standoff with police in 2016. == Military service == === Enlistment and early service === Micah Xavier Johnson enlisted in the U.S. Army Reserve in March 2009 at the age of 18, shortly after graduating high school in Mesquite, Texas. His initial service was primarily stateside, where he trained as a carpentry and masonry specialist (military occupational specialty 51B). This role involved engineering tasks such as construction and repair in support of military operations. During his reserve tenure, Johnson served part-time while living at home, and he was described by family and friends as initially idealistic about the military, even aspiring to become a police officer. === Deployment to Afghanistan === In September 2013, Johnson was activated for full-time duty and deployed to Afghanistan as part of the 420th Engineer Brigade, a unit based in Seagoville, Texas. His tour began in November 2013 and lasted approximately eight months, ending in July 2014. During this period, he performed non-combat engineering duties, though the stresses of serving in a combat zone were noted by those close to him. Associates from his service later suggested he experienced significant psychological strain, including the loss of friends and general disillusionment with military life, which contrasted with his pre-deployment enthusiasm. His mother later reflected that "the military was not what Micah thought it would be." === Sexual harassment allegation and early return === About six months into his deployment, in May 2014, Johnson faced a serious accusation of sexual harassment from a higher-ranking female soldier. She filed for a military protective order against him, prompting an investigation. As a result, his chain of command recommended an "other than honorable" discharge—the second (more severe is a dishonorable discharge, which does not require a court martial) most severe administrative separation short of a court-martial—and he was sent back to the United States ahead of schedule. Despite this, Johnson was not court-martialed, and the case did not lead to criminal charges. A military lawyer who represented him described the handling as unusual, noting that "someone really screwed up" in allowing him to avoid harsher consequences. === Post-deployment and discharge === Upon returning stateside in August 2014, Johnson resumed reserve duties with his engineering brigade until April 2015. He was honorably discharged at the rank of private first class (E-3), a relatively low junior enlisted rank after six years of service, which military sources attributed partly to the unresolved harassment allegation impacting his promotions and evaluations. Friends and family observed a marked change in his demeanor post-deployment: he became more reclusive, resentful toward the government, and withdrawn, with some speculating that the Afghanistan experience and the scandal contributed to a "small breakdown." In July 2016, following the Dallas shooting, the U.S. Army launched an internal review of his service record, including the harassment claims, to assess whether all misconduct allegations had been fully investigated. == Shootings == On July 7, 2016, a peaceful Black Lives Matter protest marched through downtown Dallas, Texas, drawing about 800 demonstrators. The event responded to the recent police killings of Alton Sterling in Baton Rouge, Louisiana, on July 5, and Philando Castile in Falcon Heights, Minnesota, on July 6—both black men shot during encounters captured on video. Around 100 officers monitored the march, which passed near El Centro College without incident until gunfire erupted around 8:45 p.m. Johnson arrived in a dark SUV, armed with an SKS semi-automatic rifle, a handgun, extra ammunition, and ballistic vests. He parked near the protest's end, chatted briefly with two officers, then opened fire on police from an elevated position on Lamar Street (now Botham Jean Boulevard). He shot from behind barriers, through windows, and while moving, targeting white officers specifically. The ambush killed five officers and wounded seven more, plus two civilians. Gunfire scattered protesters in panic as Johnson used military-style tactics, like quick position changes, to prolong the assault. === Standoff and Johnson's end === Johnson fled into El Centro College's Building C, then Building B, navigating pre-planned routes with familiarity from prior enrollment at nearby Richland College. He barricaded in a parking garage, wounding more officers in close-range fights. During two-hour negotiations, he taunted police via phone—laughing, singing, asking kill counts, and claiming planted bombs (none found). He admitted solo action, rage at White officers, and no group ties. At 2:30 a.m. on July 8, SWAT ended the standoff by detonating a bomb via remote-controlled robot in the garage, killing Johnson. This marked the first U.S. police use of such a tactic. === Victims and investigation findings === The slain officers were: Brent Thompson (Transit Authority, 36), Patrick Zamarripa (Dallas PD, 33), Michael Krol (Dallas PD, 40), Lorne Ahrens (Dallas PD, 48), and Michael Smith (Dallas PD, 55). Wounded officers included Sheik Smith, John Mitchell, and others; civilians She Tamara El-Sobky and Hillary Castro. Searches of Johnson's home revealed bomb-making materials, rifles, vests, and notes on tactics, suggesting plans for a larger attack. He had practiced explosions and honed skills post-discharge, including marksmanship. === Aftermath and impact === Dallas mourned with vigils and memorials, while national protests against police violence continued amid grief. President Barack Obama, the first African American president of the United States, called Johnson a "demented individual" and formed a task force on race and policing. The incident fueled debates on gun control, race relations, and veteran mental health—Johnson had sought VA treatment for stress and anxiety but showed no prior violent signs to friends. El Centro College canceled all classes on July 8. Police barricaded the perimeter and began canvassing the crime scene. The explosion that killed Johnson also destroyed the school's servers, further delaying reopening. The school partially reopened on July 20, with staff returning that day and students on the following day. Buildings A, B, and C remained closed pending the FBI investigation. == Motive == An investigation into his online activities uncovered his interest in black nationalist groups. The Southern Poverty Law Center (SPLC), and news outlets reported that Johnson "liked" the Facebook pages of black nationalist organizations such as the New Black Panther Party (NBPP), Nation of Islam, and Black Riders Liberation Party, three groups which are listed by the SPLC as hate groups. On Facebook, Johnson posted an angry and "disjointed" post against White people on July 2, several days before the attack. NBPP head Quanell X said after the shooting that Johnson had been a member of the NBPP's Houston chapter for about six months, several years before. Quanell X added that Johnson had been "asked to leave" the group for violating the organization's "chain of command" and espousing dangerous rhetoric, such as asking the NBPP why they had not purchased more weapons and ammunition, and expressing his desire to harm black church preachers because he believed they were more interested in money than God. Following the shooting, a national NBPP leader distanced the group from Johnson, saying that he "was not a member of" the party. Further investigation into his digital footprint showed that Johnson visited the sites of Marxist Leninist groups associated with "Revolutionary Black Nationalism",
Tilly Norwood
Tilly Norwood is a character created using generative artificial intelligence in 2025 by Xicoia, the AI division of Particle6 Group, a production company founded by Eline Van der Velden. "AI Commissioner", the first project to feature the Norwood character, was criticised by reviewers for The Guardian, PC Gamer, and The A.V. Club. A press release that talent agencies expressed interest in representing the character attracted strong criticism from Hollywood actors and firms, prompting allegations of personality rights violations and arguments over the impact of the character on production costs in the media industry. == History == Norwood was created by Xicoia, which was founded in February 2025 as the artificial intelligence (AI) division of Particle6, a production company founded by Dutch actress and producer Eline Van der Velden in 2015. Van der Velden had previously starred in a satirical comedy series for BBC Three based around her character Miss Holland, whom she created in 2012 as a parody of beauty standards. She stated that the process of creating Norwood took "a long time" and compared the process to that of writers creating characters. An Instagram account under Norwood's name, with posts dating back to 6 May 2025, had gained 50,000 followers by October 3, and featured AI-generated modelling shots, selfies, and epic film scenes. Van der Velden stated in July 2025 that she intended Norwood to be the next Scarlett Johansson or Natalie Portman and later said that audiences were more interested in a film's story than whether its actors were real. Particle6 has claimed that using Norwood could cut production costs by 90%. On 30 July 2025, a comedy sketch named "AI Commissioner" was released, featuring Norwood as an "actress" along with other AI-generated characters. It was created with ten AI software tools, with a script generated by ChatGPT. Stuart Heritage of The Guardian described it as technically competent but "relentlessly unfunny to watch", with "sloppily written, woodenly delivered dialogue", and that Norwood's teeth kept "blurring into a single white block." Joshua Wolens of PC Gamer wrote that Norwood's exaggerated mouth movements gave the impression "that her skeleton was about to leave her body", while William Hughes of The A.V. Club wrote that the sketch's attempt at mimicking human body and mouth movements produced "such a hideous uncanny valley effect" that it gave them "a full-on case of the screaming fantods". By October 2, the sketch had been viewed more than 700,000 times on YouTube. Xicoia was officially announced on 27 September 2025, at the Zurich Summit, part of the Zurich Film Festival; there, van der Velden unveiled Norwood and later joined a panel with Verena Puhm, head of Luma AI's Studio Dream Lab LA. They suggested that media companies were quietly embracing AI and that public announcements of AI-generated works were imminent. Van der Velden claimed that studios had dropped their objections by May after being opposed in February, and that multiple talent agencies were considering representing Norwood. The latter claim drew heightened attention to the character and was printed as fact by Deadline under the headline "Talent Agents Circle AI Actress Tilly Norwood." The report caused controversy, with Vulture describing the reaction to it as "Hollywood [lurching] into a fresh wave of existential panic" while being critical of Deadline's reporting, writing that "when Deadline called it a 'revelation' and published the supposed interest as fact without verification, [it] metastasized into a full-fledged cyberpunk news cycle", and that "by Tuesday, it had grown like wildfire." By September 2025, AI-generated videos had been released depicting Norwood on a red carpet, crying on the sofa of The Graham Norton Show, and starring in mock trailers for sci-fi, fantasy, horror, and action films. Later that month, actresses Melissa Barrera, Kiersey Clemons, and Natasha Lyonne suggested boycotting any agency who signed Norwood, while Mara Wilson asked why none of the "hundreds of living young women whose faces were composited together" to create Norwood could be hired instead. Also around this time, Emily Blunt described Norwood as "really, really scary", and Sophie Turner, Toni Collette, Ralph Ineson, and Ariel Winter also expressed disapproval, while Lukas Gage, Odessa A'zion, and Trace Lysette joked about having supposedly worked with Norwood and finding her incompetent and unpleasant to work with, with Gage claiming that "She was a nightmare to work with!" and "She couldn't hit her mark and she was late!" and Lysette adding "She cut me in line at lunch one day and didn't even say excuse me. She won't get far." Jenelle Riley, Nicholas Alexander Chavez, and the American union SAG-AFTRA stated that they do not consider Norwood an actress. The Gersh Agency and WME both announced that they would not sign Norwood. Whoopi Goldberg and Charlie Fink expressed scepticism that AI could replace jobs. Esquire UK reported that a post on Deadline's Instagram account about Norwood also sparked "varying levels of disgust and outrage" in its comments section from Adelaide Kane, Eiza González, Katie Cassidy, Jewel Staite, Lucy Hale, Stephen Sean Ford, and others, singling out González's comment, saying "Shame on whoever is trying to normalize this. Horrific and terrifying." Actor Bronson Pinchot expressed concern that Norwood could take his job. The British union Equity and the Canadian union ACTRA also condemned Norwood. Following this criticism, Van der Velden released a statement claiming Norwood was "not a replacement for a human being, but a creative work." She also denied that a £120,000 grant from the British Film Institute to fund Particle6 had been used to create Norwood, stating that Norwood had been a self-funded project solely for Xicoia. In late October, businessman Kevin O'Leary, while advocating for the use of AI to replace background actors, stated that they could be replaced with "100 Norwell Tillies" without being able to tell the difference. Ryan Reynolds and a real woman named Natalie "Tilly" Norwood also starred in an advertisement for Mint Mobile's internet service provider Minternet that mocked the character of Norwood. In November 2025, Van der Velden stated in an interview with Deadline that she planned to create 40 further "very diverse" characters alongside Norwood in order to expand the character's "whole universe". Also that month, actress Jameela Jamil criticized the idea of Norwood as "deeply disturbing" for being "a teenage-looking girl who can't say no to a type of sex scene" or "advocate for herself". Van der Velden announced later that month that Particle6 would be producing the History Channel's Streets of the Past, a Dutch documentary series which would be hosted by reality television personality Corjan Mol and would use AI to recreate historical scenes. In March 2026, a music video titled "Take The Lead" featuring Norwood was released on YouTube. It addressed the backlash of Norwood's creation by opening with the lyrics: "When they talk about me, they don't see/ The human spark, the creativity," and, "I'm just a tool, but I've got life." It also featured a disclaimer that says: "made by 18 real humans — from production designers to costume designers to prompters, editors and an actor." The vocals were generated by Suno. == Commentary == Charles Pulliam-Moore of The Verge argued that Norwood's introduction was a stunt to normalize "AI actors" despite Norwood essentially being a digital puppet. Straight Arrow News compared Tilly Norwood to Aki Ross, a CGI character from 2001 that was similarly intended to become a "digital star" and appear in multiple films, while Nicholas Schrivens, writing for The Conversation, likened Norwood to the posthumous use of footage of Carrie Fisher as Princess Leia for Star Wars: The Rise of Skywalker in 2019 and the Los Angeles Times likened Norwood to Hatsune Miku. Scrivens also wrote that "no AI creation has achieved the media cut-through that Tilly has". Moises Mendez II of Out dismissed this as "vapid bullshit", writing, "Nobody wants AI actresses." Scottish actress Briony Monroe alleged that Norwood had been modeled after her likeness and mannerisms, and stated that she was consulting Equity regarding the matter. Musician Stella Hennen said in a viral TikTok video, which was uploaded in October 2025 and featured a side-by-side comparison between herself and Norwood, that Norwood was her "doppleganger". On April 14, 2026, Marie Claire published an article titled "Is Tilly Norwood the Most Dangerous 'Actress' in Hollywood?", though it noted that AI-generated characters are "still not very good at, well, acting," "audiences have not been kind to AI-led productions," and "Norwood's 'performances' have already faced negative reviews as well". The University of Southern California's Entertainment Technology Center's AI media director Yves Bergquist dismissed th
Fuzzy number
A fuzzy number is a generalization of a regular real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. This weight is called the membership function. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. Just like fuzzy logic is an extension of Boolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers. Calculations with fuzzy numbers allow the incorporation of uncertainty on parameters, properties, geometry, initial conditions, etc. The arithmetic calculations on fuzzy numbers are implemented using fuzzy arithmetic operations, which can be done by two different approaches: (1) interval arithmetic approach; and (2) the extension principle approach. A fuzzy number is equal to a fuzzy interval. The degree of fuzziness is determined by the a-cut which is also called the fuzzy spread.
Terminology model
A terminology model is a refinement of a concept system. Within a terminology model the concepts (object types) of a specific problem or subject area are defined by subject-matter experts in terms of concept (object type) definitions and definitions of subordinated concepts or characteristics (properties). Besides object types, the terminology model allows defining hierarchical classifications, definitions for object type and property behavior and definition of casual relations. The terminology model is a means for subject-matter experts to express their knowledge about the subject in subject-specific terms. Since the terminology model is structured rather similar to an object-oriented database schema, is can be transformed without loss of information into an object-oriented database schema. Thus, the terminology model is a method for problem analysis on the one side and a mean of defining database schema on the other side. Several terminology models have been developed and published in the field of statistics: Terminology model for classifications Terminology model for statistical variables Reference model for statistical metadata
Minne Atairu
Minne Atairu is a Nigerian interdisciplinary artist, a recipient of the 2021 Global South Award Lumen Prize for Art and Technology. She generates synthetic Benin Bronzes through recombination of historical fragments, sculptures, texts, images, and sounds. == Early life and education == Atairu was born in Benin, Nigeria. She holds a bachelor's degree in art history from the University of Maiduguri in Maiduguri, Nigeria; a master's degree in museum studies from the George Washington University in Washington, D.C.; and a doctorate in art education from Teachers College, Columbia University in New York City. Her academic research integrates artificial intelligence, art/museum education and hip-hop based education. == Works == Atairu's artmaking involves using artificial intelligence (AI; such as StyleGAN, GPT-3) to make artwork. She uses tools such as Midjourney and Blender software to develop her works. === Mami Wata === Her first work is a Yoruba goddess called Mami Wata where she used Midjourney in generating the images. === To the Hand === For her 2023 installation To the Hand at The Shed arts center, she worked with Blender to convert text into 3D-printed sculptures made of corn starch or sugarcane infused with bronze. The rings of ground terra-cotta that surround the sculpture represent the walls and deep moats of Benin. == Publications == Atairu, Minne (February 1, 2024). "Reimagining Benin Bronzes using generative adversarial networks". AI & Society. 39 (1): 91–102. doi:10.1007/s00146-023-01761-7. ISSN 1435-5655.