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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 Iranian Azerbaijani mathematician Lotfi Zadeh. Fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-valued Logic
Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued, nine-valued, the finite-valued (finitely-many valued) with more than three values, and the infinite-valued (infinitely-many-valued), such as fuzzy logic and probability logic. History It is wrong that the first known classical logician who did not fully accept the law of excluded middle was Aristotle (who, ironically, is also generally considered to be the first classical logician and the "father of wo-valuedlogic"). In fact, Aristotle did not contest the univ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th Ed, (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', (Vol 1), 3rd Ed, (1968), Wiley, . The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (computer Programming)
In computer programming, operators are constructs defined within programming languages which behave generally like functions, but which differ syntactically or semantically. Common simple examples include arithmetic (e.g. addition with ), comparison (e.g. " greater than" with >), and logical operations (e.g. AND, also written && in some languages). More involved examples include assignment (usually = or :=), field access in a record or object (usually .), and the scope resolution operator (often :: or .). Languages usually define a set of built-in operators, and in some cases allow users to add new meanings to existing operators or even define completely new operators. Syntax Syntactically operators usually contrast to functions. In most languages, functions may be seen as a special form of prefix operator with fixed precedence level and associativity, often with compulsory parentheses e.g. Func(a) (or (Func a) in Lisp). Most languages support programmer-define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Function
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with equation f(x) = \frac, where For values of x in the domain of real numbers from -\infty to +\infty, the S-curve shown on the right is obtained, with the graph of f approaching L as x approaches +\infty and approaching zero as x approaches -\infty. The logistic function finds applications in a range of fields, including biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, statistics, and artificial neural networks. A generalization of the logistic function is the hyperbolastic function of type I. The standard logistic function, where L=1,k=1,x_0=0, is sometimes simply called ''the sigmoid''. It is also sometimes called the ''expit'', being the inverse of the logit. History The logistic function was introduced in a series of three papers by Pierre François Verhuls ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sigmoid Function
A sigmoid function is a mathematical function having a characteristic "S"-shaped curve or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: :S(x) = \frac = \frac=1-S(-x). Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of artificial neural networks, the term "sigmoid function" is used as an alias for the logistic function. Special cases of the sigmoid function include the Gompertz curve (used in modeling systems that saturate at large values of x) and the ogee curve (used in the spillway of some dams). Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Set
In mathematics, fuzzy sets (a.k.a. uncertain sets) are sets whose elements have degrees of membership. Fuzzy sets were introduced independently by Lotfi A. Zadeh in 1965 as an extension of the classical notion of set. At the same time, defined a more general kind of structure called an ''L''-relation, which he studied in an abstract algebraic context. Fuzzy relations, which are now used throughout fuzzy mathematics and have applications in areas such as linguistics , decision-making , and clustering , are special cases of ''L''-relations when ''L'' is the unit interval , 1 In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition—an element either belongs or does not belong to the set. By contrast, fuzzy set theory permits the gradual assessment of the membership of elements in a set; this is described with the aid of a membership function valued in the real unit interval , 1 Fuzzy sets general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Logic Temperature En
Fuzzy or Fuzzies may refer to: Music * Fuzzy (band), a 1990s Boston indie pop band * Fuzzy (composer) (born 1939), Danish composer Jens Vilhelm Pedersen * ''Fuzzy'' (album), 1993 debut album by the Los Angeles rock group Grant Lee Buffalo * "Fuzzy", a song from the 2009 ''Collective Soul'' album by Collective Soul * "Fuzzy", a song by Poppy from '' Poppy.Computer'' Nickname * Faustina Agolley (born 1984), Australian television presenter, host of the Australian television show ''Video Hits'' * Fuzzy Haskins (born 1941), American singer and guitarist with the doo-wop group Parliament-Funkadelic * Fuzzy Hufft (1901−1973), American baseball player * Fuzzy Knight (1901−1976), American actor * Andrew Levane (1920−2012), American National Basketball Association player and coach * Robert Alfred Theobald (1884−1957), United States Navy rear admiral * Fuzzy Thurston (1933-2014), American National Football League player * Fuzzy Vandivier (1903−1983), American high school and co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ebrahim Mamdani
Ebrahim (Abe) H. Mamdani (1 June 1942Magdalena, Luis (2010"Abe Mamdani, in Memoriam"''Elsevier'', accessed 15 February 2022 – 22 January 2010) was a mathematician, computer scientist, electrical engineer and artificial intelligence researcher. He worked at the Imperial College London. Life Abe Mamdani was born in Tanzania in June 1942. He was educated in India and in 1966 he went to the UK. He obtained his PhD at Queen Mary College, University of London. After that he joined its Electrical Engineering Department In 1975 he introduced a new method of fuzzy inference systems, which was called 'Mamdani-Type Fuzzy Inference'. Mamdani-Type Fuzzy Inference have elements like human instincts, working under the rules of linguistics, and has a fuzzy algorithm that provides an approximation to enter mathematical analysis. In July 1995, he moved from Queen Mary College to Imperial College London. Awards and honors Abe Mamdani was an Emeritus Professor at Imperial College London ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hedge (linguistics)
In the linguistic sub-fields of applied linguistics and pragmatics, a hedge is a word or phrase used in a sentence to express ambiguity, probability, caution, or indecisiveness about the remainder of the sentence, rather than full accuracy, certainty, confidence, or decisiveness. Hedges can also allow speakers and writers to introduce (or occasionally even eliminate) ambiguity in meaning and typicality as a category member. Hedging in category membership is used in reference to the prototype theory, to signify the extent to which items are typical or atypical members of different categories. Hedges might be used in writing, to downplay a harsh critique or a generalization, or in speaking, to lessen the impact of an utterance due to politeness constraints between a speaker and addressee. Typically, hedges are adjectives or adverbs, but can also consist of clauses such as one use of tag questions. In some cases, a hedge could be regarded as a form of euphemism. Linguists consider hed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adverbs
An adverb is a word or an expression that generally modifies a verb, adjective, another adverb, determiner, clause, preposition, or sentence. Adverbs typically express manner, place, time, frequency, degree, level of certainty, etc., answering questions such as ''how'', ''in what way'', ''when'', ''where'', ''to what extent''. This is called the adverbial function and may be performed by single words (adverbs) or by multi-word adverbial phrases and adverbial clauses. Adverbs are traditionally regarded as one of the parts of speech. Modern linguists note that the term "adverb" has come to be used as a kind of "catch-all" category, used to classify words with various types of syntactic behavior, not necessarily having much in common except that they do not fit into any of the other available categories (noun, adjective, preposition, etc.) Functions The English word ''adverb'' derives (through French) from Latin ''adverbium'', from ''ad-'' ("to"), ''verbum'' ("word", "verb"), and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adjectives
In linguistics, an adjective (abbreviated ) is a word that generally modifies a noun or noun phrase or describes its referent. Its semantic role is to change information given by the noun. Traditionally, adjectives were considered one of the main parts of speech of the English language, although historically they were classed together with nouns. Nowadays, certain words that usually had been classified as adjectives, including ''the'', ''this'', ''my'', etc., typically are classed separately, as determiners. Here are some examples: * That's a funny idea. ( attributive) * That idea is funny. ( predicative) * * The good, the bad, and the funny. ( substantive) Etymology ''Adjective'' comes from Latin ', a calque of grc, ἐπίθετον ὄνομα, epítheton ónoma, additional noun (whence also English '' epithet''). In the grammatical tradition of Latin and Greek, because adjectives were inflected for gender, number, and case like nouns (a process called declension), the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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