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Fuzzy Weirstrass theorem and convex fuzzy mappings |
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| Authors: | Yu-Ru Syau E Stanley Lee |
| Affiliation: | 1Department of Information Management National Formosa University Huwei, Yunlin 63201, Taiwan 2Department of Industrial and Manufacturing Systems Engineering Kansas State University Manhattan, KS 66506, U.S.A. |
| 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. |
| Keywords: | Fuzzy numbers Convexity Continuity Convex fuzzy mappings Linear ordering Fuzzy Weirstrass theorem Fuzzy optimization |
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