Fuzzy Weirstrass theorem and convex fuzzy mappings

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 map...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 51; no. 12; pp. 1741 - 1750
Main Authors Syau, Yu-Ru, Lee, E. Stanley
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.06.2006
Subjects
Continuity
Convex fuzzy mappings
Convexity
Fuzzy numbers
Fuzzy optimization
Fuzzy Weirstrass theorem
Linear ordering
Linear ordering
Fuzzy numbers
Continuity
Convexity
Fuzzy optimization
Fuzzy Weirstrass theorem
Convex fuzzy mappings
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2006.02.005