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Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 1, Pages 17-22
http://dx.doi.org/10.1155/S1048953399000027

Continuity of fuzzy multifunctions

Kuwait University, Department of Mathematics, P.O. Box 5969, Safat 13060, Kuwait

Received 1 October 1997; Revised 1 July 1998

Copyright © 1999 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We define the upper and lower inverse of a fuzzy multifunction and prove basic identities. Then by using these ideas we introduce the concept of hemicontinuity and obtain many interesting properties of lower and upper hemicontinuous fuzzy multifunctions. Using the notion of hemicontinuity, we also characterize closed and open fuzzy mappings.