Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: The fuzzy pattern matching procedure is improved by introducing weights assessing the relative importance of atoms in the pattern by using weighted versions of the minimum and maximum operations of fuzzy set theory.
328 citations
01 Nov 1976-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: The problem of borderline cases in set theory and the two classical approaches of precisifying them out, or admitting them as a third case, are discussed, leading to Zadeh's suggestion of continuous degrees of set membership.
Abstract: This paper gives an overview of the theory of fuzzy sets and fuzzy reasoning as proposed and developed by Lotfi Zadeh. In particular it reviews the philosophical and logical antecedents and foundations for this theory and its applications. The problem of borderline cases in set theory and the two classical approaches of precisifying them out, or admitting them as a third case, are discussed, leading to Zadeh's suggestion of continuous degrees of set membership. The extension of basic set operations to such fuzzy sets, and the relationship to other multivalued logics for set theory, are then outlined. The fuzzification of mathematical structures leads naturally to the concepts of fuzzy logics and inference, and consideration of implication suggests Łukasiewicz infinite-valued logic as a base logic for fuzzy reasoning. The paradoxes of the barber, and of sorites, are then analysed to illustrate fuzzy reasoning in action and lead naturally to Zadeh's theory of linguistic hedges and truth. Finally, the logical, modeltheoretic and psychological derivations of numeric values in fuzzy reasoning are discussed, and the rationale behind interest in fuzzy reasoning is summarized.
327 citations
TL;DR: It is demonstrated that two points of view can be considered to extend classical linear constraints: either tolerance constraints, or approximate (in)equality constraints can be obtained.
326 citations
TL;DR: A survey on methods for solving fuzzy linear programs, first LP models with soft constraints, then LP problems in which coefficients of constraints and/or of the objective function may be fuzzy are outlined.
326 citations
TL;DR: This paper proposes two parameters, value and ambiguity, for fuzzy number representation and uses them to obtain canonical representations and to deal with fuzzy numbers in decision-making problems.
325 citations