• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.183-186
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• 2008

We consider fuzzy invex sets, fuzzy preinvex functions, fuzzy quasi-preinvex functions, and fuzzy logarithmic preinvex functions. Murofushi et al. have been studied Choquet integrals and their properties. In this paper, we study some characterizations in Choquet integrals as follows: fuzzy preinvexity, fuzzy quasi-preinvexity, and fuzzy logarithemic preinvexity, that mean some characterizations of functionals defined by Choquet integrals. Furthermore, we discuss Jensen's type inequality in Choquet integrals.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.127-128
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• 2008

In this paper, we consider define fuzzy invex sets and fuzzy preinvex functions on the class of Choquet integrable functions, and interval-valued fuzzy invex sets and interval-valued fuzzy preinvex functions on the class of interval-valued Choquet integrals. And also we prove some properties of them.