• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.365-369
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• 2006

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. Using interval-valued Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we studied some characterizations of interval-valued Choquet distance(2005). In this paper, we define Choquet distance measure for fuzzy number-valued fuzzy numbers and investigate some algebraic properties of them.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.5
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• pp.603-608
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• 2009

In this paper, a similarity measure between interval-valued vague sets is proposed. In the interval-valued vague sets representation, the upper bound and the lower bound of a vague set are represented as intervals of interval-valued fuzzy set respectively. Proposed method combines the concept of geometric distance and the center-of-gravity point of interval-valued vague set to evaluate the degree of similarity between interval-valued vague sets. We also prove three properties of the proposed similarity measure. It provides a useful way to measure the degree of similarity between interval-valued vague sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.187-190
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• 2007

In this paper, we introduce concepts of entropy and similarity measure of interval-valued intuitionistic fuzzy sets (IVIFSs), discuss their relationship between similarity measure and entropy of IVIFSs, show that similarity measure and entropy of IVIFSs can be transformed by each other based on their axiomatic definitions and give some formulas to calculate entropy and similarity measure of IVIFSs.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.5
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• pp.550-555
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• 2006

Internal-valued fuzzy sets were suggested for the first time by Gorzalczang(1983). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy numbers with Riemann integral. By using interval-valued Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we studied some characterizations of interval-valued Choquet distance(2005). In this paper, we define Choquet distance measure for fuzzy number-valued fuzzy numbers and investigate some properties of them.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.1-3
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• 2001

In this paper, we define the convergence in measure and convergence in distribution for set-valued Choquet integrals. Using there definitions, we discuss convergence theorems for set-valued Choquet integrals.

• 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.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.349-363
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• 2001

The analytic in mass operator-valued Feynman integral is related to integration with respect to unbounded set functions formed from the semigroup obtained by analytic continuation of the heat semigroup and the spectral measure of multiplication by characteristics functions.

• East Asian mathematical journal
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• v.17 no.2
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• pp.253-264
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• 2001

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.7
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• pp.789-793
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• 2005

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(19a6). Based on this, Wang and Li offended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, using Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we define a Choquet distance measure for interval-valued fuzzy numbers and investigate its properties.

• 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.