Elsevier

Fuzzy Sets and Systems

Volume 219, 16 May 2013, Pages 113-125
Fuzzy Sets and Systems

On properties of convex fuzzy mappings

https://doi.org/10.1016/j.fss.2012.11.006Get rights and content

Abstract

The objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by Goetschel and Voxman. Firstly, a new kind of fuzzy mapping, termed semistrictly convex fuzzy mapping, is defined through this linear ordering. Note that semistrict convexity does not imply convexity. And the interrelationships among convex, strictly convex and semistrictly convex mappings are established under certain conditions. Furthermore, this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity. Finally, some further characteristic properties for semistrictly convex fuzzy mappings are derived.

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    This research was supported by the Chongqing Municipal Education Commission under Grant KJ120616, Chongqing Key Lab of Operations Research and System Engineering.

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