• 제목/요약/키워드: interval-valued set functions

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

  • Jang, Lee-Chae
    • 호남수학학술지
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    • 제30권1호
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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.

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

  • Jang, Lee-Chae
    • 대한수학회논문집
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    • 제22권2호
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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.

구간치 쇼케이적분에 의해 정의된 단조 구간치 집합함수의 구조적 성질에 관한 연구 (Structural characterizations of monotone interval-valued set functions defined by the interval-valued Choquet integral)

  • 장이채
    • 한국지능시스템학회논문지
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    • 제18권3호
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    • pp.311-315
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    • 2008
  • We introduce nonnegative interval-valued set functions and nonnegative measurable interval-valued Junctions. 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 [17]. We also obtained absolutely continuity of them in [9]. In this paper, we investigate some characterizations of the monotone interval-valued set function defined by the interval-valued Choquet integral, and such as subadditivity, superadditivity, null-additivity, converse-null-additivity.

Some Characterizations of the Choquet Integral with Respect to a Monotone Interval-Valued Set Function

  • Jang, Lee-Chae
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제13권1호
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    • pp.83-90
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    • 2013
  • Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.

단조집합함수에 의해 정의된 구간치 쇼케이적분에 대한 르베그형태 정리에 관한 연구 (On Lebesgue-type theorems for interval-valued Choquet integrals with respect to a monotone set function.)

  • 장이채;김태균
    • 한국지능시스템학회:학술대회논문집
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    • 한국지능시스템학회 2007년도 추계학술대회 학술발표 논문집
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    • pp.195-198
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    • 2007
  • In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval-valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

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단조집합함수에 의해 정의된 구간치 쇼케이적분에 대한 르베그형태 정리에 관한 연구 (On Lebesgue-type theorems for interval-valued Choquet integrals with respect to a monotone set function)

  • 장이채;김태균
    • 한국지능시스템학회논문지
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    • 제17권6호
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    • pp.749-753
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    • 2007
  • In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

On fuzzy preinvex mappings associated with interval-valued Choquet integrals

  • Lee, Chae-Jang;Kim, Hyun-Mee
    • 한국지능시스템학회:학술대회논문집
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    • 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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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.

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컴팩트 집합치 쇼케이 적분에 관한 연구 (On compact set-valued Choquet integrals)

  • 김현미;장이채
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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    • pp.170-173
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    • 2005
  • We note that Jang et at. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions, instead of interval valued we investigate characterization of compact set-valued Choquet integrals.

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On fuzzy number-valued Choquet integrals

  • 장이채;김태균
    • 한국전산응용수학회:학술대회논문집
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    • 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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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.

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INTERVAL-VALUED CHOQUET INTEGRALS AND THEIR APPLICATIONS

  • Jang, Lee-Chae
    • Journal of applied mathematics & informatics
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    • 제16권1_2호
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    • pp.429-443
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    • 2004
  • In this paper, using Zhang, Guo and Liu's comments in [17], we define interval-valued functionals and investigate their properties. Furthermore, we discuss some applications of interval-valued Choquet expectations.