• Title/Summary/Keyword: interval-valued fuzzy measures

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A note on Linguistic quantifiers modeled by Sugeno integral with respect to an interval-valued fuzzy measures (구간치 퍼지측도와 관련된 수게노적분에 의해 모델화된 언어 정량자에 관한 연구)

  • Jang, Lee-Chae;Kim, Tae-Kyun;Kim, Hyun-Mee
    • 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.

THE APPLICATION OF INTERVAL-VALUED CHOQUET INTEGRALS IN MULTI CRITERIA DECISION AID

  • Jang, Lee-Chae
    • 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.

Distances between Interval-valued Intuitionistic Fuzzy Sets (구간 값 직관적 퍼지집합들 사이의 거리)

  • Park, Jin-Han;Lim, Ki-Moon;Lee, Bu-Young;Son, Mi-Jung
    • 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.

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On Choquet Integrals with Respect to a Fuzzy Complex Valued Fuzzy Measure of Fuzzy Complex Valued Functions

  • Jang, Lee-Chae;Kim, Hyun-Mee
    • 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.

THE AUTOCONTINUITY OF MONOTONE INTERVAL-VALUED SET FUNCTIONS DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

  • Jang, Lee-Chae
    • 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.

Some characterizations of a mapping defined by interval-valued Choquet integrals

  • Jang, Lee-Chae;Kim, Hyun-Mee
    • 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.

A note on the Choquet distance measures for fuzzy number-valued fuzzy numbers (퍼지수치 퍼지수 상의 쇼케이 거리측도에 관한 성질)

  • Jang Lee-Chae;Kim Won-Joo
    • 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.

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A NOTE ON THE MONOTONE INTERVAL-VALUED SET FUNCTION DEFINED BY THE INTERVAL-VALUED CHOQUET INTEGRAL

  • Jang, Lee-Chae
    • 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.

Some properties of Choquet distance measures for interval-valued fuzzy numbers (구간치 퍼지수 상의 쇼케이 거리측도에 관한 성질)

  • Jang, Lee-Chae;Kim, Won-Joo
    • 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.