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CONVEXITY AND SEMICONTINUITY OF FUZZY MAPPINGS USING THE SUPPORT FUNCTION  

Hong, Dug-Hun (Department of Mathematics, Myongji University)
Moon, Eun-Ho L. (College of Basic Studies, Myongji University)
Kim, Jae-Duck (Department of Mathematics, Myongji University)
Publication Information
Journal of applied mathematics & informatics / v.28, no.5_6, 2010 , pp. 1419-1430 More about this Journal
Abstract
Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.
Keywords
Fuzzy sets; Ordering of fuzzy sets; Fuzzy mappings; Convexity; Semicontinuity; Continuity;
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