A class of convex fuzzy mappings
type: Item
instance of: scholarly article
title: A class of convex fuzzy mappings
zbMATH Open document ID: 1028.46112
DOI: 10.1016/S0165-0114(01)00157-9
author: Hong Yan
author: Jiuping Xu
published in: Fuzzy Sets and Systems
publication date: 2002-09-30T00:00:00Z
review text: Fuzzy functions are examined from diverse points of view [cf. \textit{M. Sasaki}, Fuzzy Sets Syst. 55, 295-301 (1993; Zbl 0795.04006); \textit{M. Demirci}, J. Math. Anal. Appl. 252, 495-517 (2000; Zbl 0973.03071)]. One of these directions is the convexity of fuzzy mappings [cf. \textit{S. Nanda} and \textit{K. Kar}, Fuzzy Sets Syst. 48, 129-132 (1992; Zbl 0760.90093); \textit{N. Furukawa}, Fuzzy Sets Syst. 93, 113-119 (1998; Zbl 0931.26015)]. This paper deals with continuity and convexity of fuzzy mappings defined in normed vector spaces and with fuzzy number values. The authors characterize convexity and quasi-convexity of fuzzy mappings using their level sets and epigraphs. Boundedness and local extrema of convex mappings are also examined.
reviewed by: Józef Drewniak
Mathematics Subject Classification ID: 46S40
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 26E50
zbMATH DE Number: 1809977
zbMATH Keywords: fuzzy mapping
zbMATH Keywords: fuzzy number
zbMATH Keywords: convex mapping
zbMATH Keywords: quasi-convexity
zbMATH Keywords: continuity
zbMATH Keywords: boundedness
zbMATH Keywords: local extremum
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1809977