Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Choquet integrals and interval-valued necessity measures

쇼케이 적분과 구간치 필요측도

  • Jang, Lee-Chae (Dept of Mathematics and Computer Science, Konkuk University) ;
  • Kim, Tae-Kyun (Division of General Education, Kwangwoon University)
  • Received : 2009.04.06
  • Accepted : 2009.06.04
  • Published : 2009.08.25
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Abstract

Y. R$\acute{e}$ball$\acute{e}$ [11] discussed the representation of necessity measure through the Choquet integral criterian. He also consider a decision maker who ranks necessity measures related with Choquet integral representation. In this paper, we consider a decision maker have an "ambiguity"(say, interval-valued) necessity measure according to their Choquet's expected utility. Furthermore, we prove two theorems which are weak Choquet integral representation of preferences with a monotone set function for interval-valued necessity measures and strong Choquet integral representation of preferences with an interval-valued utility function for necessity measures.

Y. R$\acute{e}$ball$\acute{e}$ [11]교수는 쇼케이적분 기준에 의한 필요측도의 표현에 관해 조사한다. 또한 쇼케이적분 표현관 관련된 필요측도의 순위를 결정 연장을 생각한다. 이 논문에서, 우리는 결정연장이 쇼케이 기대효용에 따른 애매한(구간치로 명명함) 필요측도를 가지는 경우를 생각한다. 더욱이, 구간치 필요측도에 대한 단조 집합치 함수를 갖는 기호에 대한 약 쇼케이적분표현과 필요측도에 대한 구간치 효용함수를 갖는 기호에 대한 강 쇼케이적분 표현에 대한 두 가지 정리를 증명한다.

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References

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