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Fuzzy Rule
Fuzzy rules are used within fuzzy logic systems to infer an output based on input variables. Modus ponens and modus tollens are the most important rules of inference. A modus ponens rule is in the form :Premise: ''x is A'' :Implication: ''IF x is A THEN y is B'' :Consequent: ''y is B'' In crisp logic, the premise ''x is A'' can only be true or false. However, in a fuzzy rule, the premise ''x is A'' and the consequent ''y is B'' can be true to a degree, instead of entirely true or entirely false. This is achieved by representing the linguistic variables ''A'' and ''B'' using fuzzy sets. In a fuzzy rule, modus ponens is extended to ''generalised modus ponens:.'' :Premise: ''x is A''* :Implication: ''IF x is A THEN y is B'' :Consequent: ''y is B''* The key difference is that the premise ''x is A'' can be only partially true. As a result, the consequent ''y is B'' is also partially true. Truth is represented as a real number between 0 and 1, where 0 is false and 1 is true. Comparis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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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 algebra, 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 A. Zadeh, Lotfi Zadeh. Fuzzy logic had, however, been studied since the 1920s, as Łukasiewicz logic, infinite-valued logic—notably by Jan Łukasiewicz, Łukasiewicz and Alfred Tarski, Tarski. 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, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Modus Ponens
In propositional logic, (; MP), also known as (), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P'' implies ''Q.'' ''P'' is true. Therefore, ''Q'' must also be true." ''Modus ponens'' is a mixed hypothetical syllogism and is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of ''modus ponens''. The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. Explanation The form of a ''modus ponens'' argument is a mixed hypothetical syllogism, with two premises and a con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Modus Tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "mode that by denying denies") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens'' is a mixed hypothetical syllogism that takes the form of "If ''P'', then ''Q''. Not ''Q''. Therefore, not ''P''." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from ''P implies Q'' to ''the negation of Q implies the negation of P'' is a valid argument. The history of the inference rule ''modus tollens'' goes back to antiquity. The first to explicitly describe the argument form ''modus tollens'' was Theophrastus. ''Modus tollens'' is closely related to ''modus ponens''. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. Explanation The form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Linguistic Variable
In artificial intelligence, fuzzy logic operations research, and related fields, a linguistic value is a natural language A natural language or ordinary language is a language that occurs naturally in a human community by a process of use, repetition, and change. It can take different forms, typically either a spoken language or a sign language. Natural languages ... term which is derived using quantitative or qualitative reasoning such as with probability and statistics or fuzzy sets and systems. Variables that take linguistic values are called linguistic variables. Joseph Goguen ''Fuzzy Sets And The Social Nature of Truth'' in Advances in Fuzzy Sets and Systems, North Holland, 1979. § 2.3 ''Linguistic Truth Values''. Examples of linguistic variables and values For example, "age" may be a linguistic variable if its values are not numerical, e.g. very young, quite young, not young, old, not very old etc. These values could be derived from the numeric values for age. As anot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |