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http://dx.doi.org/10.5391/JKIIS.2009.19.4.499

Choquet integrals and interval-valued necessity measures  

Jang, Lee-Chae (Dept of Mathematics and Computer Science, Konkuk University)
Kim, Tae-Kyun (Division of General Education, Kwangwoon University)
Publication Information
Journal of the Korean Institute of Intelligent Systems / v.19, no.4, 2009 , pp. 499-503 More about this Journal
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.
Keywords
non-additive measures; necessity measures; interval-valued necessity measures; Choquet integrals;
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