Fuzzy Weirstrass theorem and convex fuzzy mappings

Authors:
Yu-Ru Syau;E. Stanley Lee
Affiliations:
Department of Information Management National Formosa University Huwei, Yunlin 63201, Taiwan;Department of Industrial and Manufacturing Systems Engineering Kansas State University Manhattan, KS 66506, U.S.A.
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 6
Cited 3

Elementary fuzzy calculus

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Convex fuzzy mappings

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Convexity and local Lipschitz continuity of fuzzy-valued mappings

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On convex and concave fuzzy mappings

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A class of convex fuzzy mappings

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Convex fuzzy mapping and operations of convex fuzzy mappings

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Continuity and semicontinuity of fuzzy mappings

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A Characterization of Convex Fuzzy Mappings

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On properties of convex fuzzy mappings

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Abstract

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.