• 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.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.489-503
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• 2007

In this paper, we define signed interval-valued Choquet integrals which have numerous applications in mathematical economics, informatiom theory, expected utility theory, and risk analysis on interval-valued random variables, for examples: interval-valued random payments and interval-valued random profiles, etc. And we discuss axiomatic characterizations of them. Furthermore, we fine some condition that comonotonic additivity of symmetric Choquet integrals on interval-valued random payments is satisfied and give two examples related the main theorem.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.131-132
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• 2008

In this paper, we consider interval probability as a unifying concept for uncertainty and Choquet integrals with resect to a capacity functional. By using interval probability, we will define an interval-valued capacity functional and Choquet integrals with respect to an interval-valued capacity functional. Furthermore, we investigate Choquet Choquet weak convergence of interval-valued capacity functionals of random sets.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.139-147
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• 2003

In this paper, we consider Choquet integrals of interval number-valued functions(simply, interval number-valued Choquet integrals). Then, we prove a convergence theorem for interval number-valued Choquet integrals with respect to an autocontinuous fuzzy measure.

• 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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• 2004.10a
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• pp.331-334
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• 2004

In this paper, we define signed interval-valued Choquet integrals and shows the signed interval-valued Choquet integrals can model violations of separability and monotonicity Furthermore, we discuss some applications to intertemporal preference, asset pricing, and welfare evauations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.209-212
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• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}_1,\;{\mu}_2$ such that it is represented by interval-valued choquet integral on interval-valued risks.