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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01 Jan 1972TL;DR: In this paper, it was shown that under certain conditions a precise control goal can be attained with fuzzy observation and control as long as the observations become sufficiently precise when the goal is approached.
Abstract: A fuzzy mapping from X to Y is a fuzzy set on X × Y. The concept is extended to fuzzy mappings of fuzzy sets on X to Y, fuzzy function and its inverse, fuzzy parametric functions, fuzzy observation, and control. Set theoretical relations are obtained for fuzzy mappings, fuzzy functions, and fuzzy parametric functions. It is shown that under certain conditions a precise control goal can be attained with fuzzy observation and control as long as the observations become sufficiently precise when the goal is approached.
741 citations
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TL;DR: The distance between two points in a fuzzy metric space is a non-negative, upper semicontinuous, normal and convex fuzzy number.
738 citations
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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
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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
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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