• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.1
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• pp.1-6
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• 2010

Ying[M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170(2006) 581-606] studied a framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using Sugeno integral. In this paper, we consider interval-valued fuzzy measures and interval quantifiers which are the generalized concepts of fuzzy measures and quantifiers, respectively. We also investigate logical properties of a first order language with interval quantifiers modeled by the Sugeno integral with respect to an interval-valued fuzzy measures.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.549-556
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• 2006

In this paper, we consider interval-valued Choquet integrals and fuzzy measures. Using these properties, we discuss some applications of them in multicriteria decision aid. In particular, we show how these interval-valued Choquet integrals can model behavioral analysis of aggregation in ulticriteria decision aid.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.175-178
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• 2007

We give a geometrical interpretation of the interval-valued fuzzy set. So, based on the geometrical background, we propose new distance measures between interval-valued fuzzy sets and compare these measures with distance measures proposed by Burillo and Bustince and Grzegorzewski, respectively. Furthermore, we extend three methods for measuring distances between interval-valued fuzzy sets to interval-valued intuitionistic fuzzy sets.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.224-229
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• 2010

In this paper, using fuzzy complex valued functions and fuzzy complex valued fuzzy measures ([11]) and interval-valued Choquet integrals ([2-6]), we define Choquet integral with respect to a fuzzy complex valued fuzzy measure of a fuzzy complex valued function and investigate some basic properties of them.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.171-183
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• 2008

In a previous work [18], the authors investigated autocontinuity, converse-autocontinuity, uniformly autocontinuity, uniformly converse-autocontinuity, and fuzzy multiplicativity of monotone set function defined by Choquet integral([3,4,13,14,15]) instead of fuzzy integral([16,17]). We consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. Then the interval-valued Choquet integral determines a new nonnegative monotone interval-valued set function which is a generalized concept of monotone set function defined by Choquet integral in [18]. These integrals, which can be regarded as interval-valued aggregation operators, have been used in [10,11,12,19,20]. In this paper, we investigate some characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral such as autocontinuity, converse-autocontinuity, uniform autocontinuity, uniform converse-autocontinuity, and fuzzy multiplicativity.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.143-146
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• 2005

In this paper, we define correlation coeeficients of interval-valued fuzzy numbers by utilizing Choquet integrals. Also we discuss some properties of them.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.66-70
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• 2007

Note that Choquet integral is a generalized concept of Lebesgue integral, because two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure. In this paper, we consider interval-valued Choquet integrals with respect to fuzzy measures(see [4,5,6,7]). Using these Choquet integrals, we define a mappings on the classes of Choquet integrable functions and give an example of a mapping defined by interval-valued Choquet integrals. And we will investigate some relations between m-convex mappings ${\phi}$ on the class of Choquet integrable functions and m-convex mappings $T_{\phi}$, defined by the class of closed set-valued Choquet integrals with respect to fuzzy measures.

• 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.

• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.227-234
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• 2007

At first, we consider nonnegative monotone interval-valued set functions and nonnegative measurable interval-valued functions. In this paper we investigate some properties and structural characteristics of the monotone interval-valued set function defined by an interval-valued Choquet integral.

• 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.