Fuzzy values in fuzzy logic (original) (raw)
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A presentation is provided of the basic notions and operations of a) the propositional calculus of a variant of fuzzy logic-canonical fuzzy logic, CFL-and in a more succinct and introductory way, of b) the theory of fuzzy sets according to that same logic. The propositional calculus of bivalent classical logic and classical set theory can be considered as particular cases of the corresponding theories of CFL if the numerical value of a specific parameter w is restricted to only two possibilities, 0 and 1.
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Fuzzy Description Logics are a family of logics which allow to deal with structured knowledge affected by vagueness. Although a relatively important amount of work has been carried out in the last years, current fuzzy DLs are open to be extend with several features worked out in the fuzzy logic literature. In this work, we extend fuzzy DLs with fuzzy truth values, allowing to state sentences such as "Tina is young is almost true".
An Overview of Fuzzy Quantifiers, Part 1: Interpretations
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Quanti cation is an important topic in fuzzy theory and its applications. An overview is presented for quanti cation in fuzzy theory. After This work has been supported by t h e I n ternational Projects of the Flemish Community Cooperation with P.R.China (No.9604) a brief review of quanti ers in rst order logic, two a p p r o a c hes of generalizing quantifers are given, the algebraic method and the substitution method. By distinguishing the fuzziness of predicates and quanti ers, various approaches to quanti cation in fuzzy logic can be organized. Quantiers in rst order logic can be generalized in crisp sense, and these generalized quanti ers can also be applied to fuzzy sets. Moreover, quanti ers themselves can be fuzzy, i.e., they can only be represented by a fuzzy set. These di erent kinds of quanti cations are identi ed. Quanti ers relate close to the concept of the cardinality of a fuzzy set, which is summarized before investigating fuzzy quanti cations. Di erent to classical logic, various semantics of propositions in fuzzy logic fall into di erent f r a m e w orks which are known as the possibility distribution based reasoning system and the many-valued fuzzy logics. Accordingly, n umerical and possibilistic interpretation explored in literature are reviewed conforming to these two frameworks.
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In the paper we introduce logical calculi for representation of propositions with modal operators indexed by fuzzy values. There calculi are called Heyting-valued modal logics. We introduce the concept of a Heyting-valued Kripke model and consider a semantics of Heyting-valued modal logics at the class of Heyting-valued Kripke models.
Yet another application of fuzzy logic
International Conference on Electronics, Communications, and Computers, 2010
Fuzzy logic has been mainly used for fuzzy control and other applications. Recently, it also has been studied as a symbolic logic with syntax and semantics. We know that fuzzy logic is a branch of many-valued logic based on the paradigm of inference under vagueness. In this paper, we consider a particular many valued logic to show a non-standard application