• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.3
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.4
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• pp.499-503
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• 2009

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.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.451-454
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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 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.370-373
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• 2006

In this paper, we consider set-valued aggregation operators and investigate some properties of them. Moreover, we define interval-valued Choquet integral aggregation operators and discuss their characterizations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.71-75
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• 2009

The purpose of this paper is to prove a Jensen type inequality for Choquet integrals with respect to a non-additive measure which was introduced by Choquet [1] and Sugeno [20]; $$\Phi((C)\;{\int}\;fd{\mu})\;{\leq}\;(C)\;\int\;\Phi(f)d{\mu},$$ where f is Choquet integrable, ${\Phi}\;:\;[0,\;\infty)\;\rightarrow\;[0,\;\infty)$ is convex, $\Phi(\alpha)\;\leq\;\alpha$ for all $\alpha\;{\in}\;[0,\;{\infty})$ and ${\mu}_f(\alpha)\;{\leq}\;{\mu}_{\Phi(f)}(\alpha)$ for all ${\alpha}\;{\in}\;[0,\;{\infty})$. Furthermore, we give some examples assuring both satisfaction and dissatisfaction of Jensen type inequality for the Choquet integral.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.635-643
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• 1997

The purpose of this paper is to propose an interactive method, using fuzzy Choquet's integral, which is designed to find out the mostly preferred solutions for deterministic MADM problems with many attributes and alternatives. The basic idea of the paper is essentially the same as that of the one we have published before[1]; subgrouping of attributes and eliminating of inefficient solutions. But the difference between these two methods lies in the fact that the present method evaluates and eliminates alternatives using fuzzy Choquet's integral on the basis of decision-maker's judgements about the relative importance of subgroups of attributes, rather than using mathematical programming on the basis of pair-wise comparisons of alternatives. If such information is obtainable from the decision-maker, the method can be proved to be much easier to understand and more efficient to compute.

• 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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.2
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• pp.146-150
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• 2008

In this paper, we consider concepts of subsethood measure introduced by Fan et al. [2]. Based on this, we give various subsethood measure defined by Choquet integral with respect to a fuzzy measure on fuzzy sets which is often used in information fusion and data mining as a nonlinear aggregation tool and discuss some properties of them. Furthermore, we introduce simple examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.3
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• pp.196-199
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• 2005

Recently, many types of set-valued fuzzy integrals are studied by many authors. In this paper, we consider various types of convergence theorems of Choquet integrals of interval-valued function with respect to an autocontinuous fuzzy measure.