Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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CONVEXITY AND SEMICONTINUITY OF FUZZY MAPPINGS USING THE SUPPORT FUNCTION

  • Received : 2010.01.22
  • Accepted : 2010.05.31
  • Published : 2010.09.30
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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

References

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