• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-107
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• 2004

In this paper, we consider fuzzy number-valued functions and fuzzy number-valued Choquet integrals. And we also discuss positively homogeneous and monotonicity of Choquet integrals of fuzzy number-valued functions(simply, fuzzy number-valued Choquet integrals). Furthermore, we prove convergence theorems for fuzzy number-valued Choquet integrals.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.355-364
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• 2004

In this paper, we consider fuzzy integrals defined by max-measures and discuss some properties of these fuzzy integrals of measurable functions.

• 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 Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.7-7
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• 2003

We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1996.10a
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• pp.35-41
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• 1996

This paper presents a short introduction to fuzzy measures and fuzzy integrals for providing an useful understanding of articles related on fuzzy measure theory and its applications. A brief overview of the basic concepts of systems, models, uncertainty, fuzzy measures and fuzzy integrals is provided. And terminology and notation frequently used in the discussion on the topic are introduced.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.39-48
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• 2000

In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.2
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• pp.113-117
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• 2011

In this paper, we consider fuzzy complex valued fuzzy measures and Choquet integrals with respect to a fuzzy measure of real-valued measurable functions. In doing so, we investigate some basic properties and convergence theorems.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.3
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• pp.196-199
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• 2005

Recently, many types of set-valued fuzzy integrals are studied by many authors. In this paper, we consider various types of convergence theorems of Choquet integrals of interval-valued function with respect to an autocontinuous fuzzy measure.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.380-386
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• 1998

In this paper we introduce the concept of fuzzy integrals for set-valued mappings, which is an extension of fuzzy integrals for single-valued functions defined by Sugeno. And we give some properties including convergence theorems on fuzzy integrals for set-valued mappings.