CONVEXITY AND SEMICONTINUITY OF FUZZY MAPPINGS USING THE SUPPORT FUNCTION

Since Goetschel and Voxman (5) proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings deflned through the order. Since the order is only deflned for fuzzy numbers on R, it is natural to flnd a new order for normal fuzzy sets on 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 ""s" for normal fuzzy sets on R n with respect to the support function. We deflne the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semiconti- nuity and convexity of fuzzy mappings will be discussed..

[1]  Congxin Wu,et al.  Directional derivatives and subdifferential of convex fuzzy mappings and application in convex fuzzy programming , 2003, Fuzzy Sets Syst..

[2]  Peter E. Kloeden.  Compact supported endographs and fuzzy sets , 1980 .

[3]  Hong Yan,et al.  A class of convex fuzzy mappings , 2002, Fuzzy Sets Syst..

[4]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[5]  María Angeles Gil,et al.  Fuzzy random variables , 2001, Inf. Sci..

[6]  S. Nanda,et al.  Convex fuzzy mappings , 1992 .

[7]  Stanisław Heilpern,et al.  Fuzzy mappings and fixed point theorem , 1981 .

[8]  R. Goetschel,et al.  Elementary fuzzy calculus , 1986 .

[9]  Congxin Wu,et al.  Convexity and semicontinuity of fuzzy mappings , 2006, Comput. Math. Appl..

[10]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[11]  X. Yang.  A Note on Convexity of Upper Semi-Continuous Functions , 2001 .

[12]  M. Puri,et al.  The Concept of Normality for Fuzzy Random Variables , 1985 .

[13]  Nagata Furukawa.  Convexity and local Lipschitz continuity of fuzzy-valued mappings , 1998, Fuzzy Sets Syst..

[14]  Jiuping Xu,et al.  Nonconvex fuzzy mappings and the fuzzy pre-variational inequality , 2008, Fuzzy Sets Syst..

[15]  E. Stanley Lee,et al.  A note on convexity and semicontinuity of fuzzy mappings , 2008, Appl. Math. Lett..

[16]  Yu-Ru Syau,et al.  On convex and concave fuzzy mappings , 1999, Fuzzy Sets Syst..

[17]  R. Goetschel,et al.  Topological properties of fuzzy numbers , 1983 .