✦ LIBER ✦

Fuzzy Weirstrass theorem and convex fuzzy mappings

✍ Scribed by Yu-Ru Syau; E. Stanley Lee

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 471 KB
Volume: 51
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2006.02.005

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✦ Synopsis

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.

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