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Foundations of fuzzy reasoning
, 1976
"... 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 cl ..."
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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 ofpreeisifying 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. Thefuzzification of mathematical structures leads naturally to the concepts of fuzzy logics and inference, and consideration of implication suggests Lukasiewicz infinitevalued 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. 1.
Fuzzy Lie Groups
, 908
"... In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a C 1 fuzzy submanifold after reviewing C 1 −fuzzy manifold definition. In main section, we defined the Lie group and some its relative concepts such as fuzzy transformation gro ..."
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In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a C 1 fuzzy submanifold after reviewing C 1 −fuzzy manifold definition. In main section, we defined the Lie group and some its relative concepts such as fuzzy transformation group, fuzzy Ginvariant. Our aim is to prepare the suitable conditions for defining fuzzy differential invariant by constructing suitable objects. Keywords. fuzzy Lie group, fuzzy invariant, fuzzy Ginvariant, fuzzy transformation group. 1