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Membership function
About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.
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TL;DR: This paper develops an approach to group decision making based on intuitionistic preference relations and an approach based on incomplete intuitionism preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionism fuzzy weighted arithmetic averagingoperator are used to aggregate intuitionistic preferences.
781 citations
TL;DR: This paper uses two quantifier guided choice degrees of alternatives, a dominance degree used to quantify the dominance that one alternative has over all the others, in a fuzzy majority sense, and a non dominance degree, that generalises Orlovski's non dominated alternative concept.
761 citations
TL;DR: A method to deal with multiple-alternative decision problems under uncertainty by considering each of these variables as fuzzy quantities, characterized by appropriate membership functions of fuzzy sets induced by mappings is proposed.
737 citations
Book•
01 May 1994
TL;DR: Fuzzy Sets Spaces of Subsets of Rn Compact Convex Subsetsof Rn Set Valued Mappings Crisp Generalizations The Space En Metrics on En Compactness Criteria Generalizations Fuzzy Set Valuing Mappings of Real Variables.
Abstract: Fuzzy Sets Spaces of Subsets of Rn Compact Convex Subsets of Rn Set Valued Mappings Crisp Generalizations The Space En Metrics on En Compactness Criteria Generalizations Fuzzy Set Valued Mappings of Real Variables Fuzzy Random Variables Computational Methods Fuzzy Differential Equations Optimization Under Uncertainty Fuzzy Iterations and Image Processing.
731 citations
TL;DR: This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊓, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzies form a distributive lattice under ⊢ and ⊡.
Abstract: The concept of fuzzy sets of type 2 has been defined by L. A. Zadeh as an extension of ordinary fuzzy sets. The fuzzy set of type 2 can be characterized by a fuzzy membership function the grade (or fuzzy grade) of which is a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1]. This paper investigates the algebraic structures of fuzzy grades under the operations of join ⊔, meet ⊔, and negation ┐ which are defined by using the extension principle, and shows that convex fuzzy grades form a commutative semiring and normal convex fuzzy grades form a distributive lattice under ⊔ and ⊓. Moreover, the algebraic properties of fuzzy grades under the operations and which are slightly different from ⊔ and ⊓, respectively, are briefly discussed.
725 citations