• Honam Mathematical Journal
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• v.30 no.1
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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.

• 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.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.4
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• pp.323-326
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• 2002

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

• 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.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1041-1044
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• 2005

Recently, Zhang et al.(Fuzzy Sets and Systems 147(2004) 475-485) proved Fatou's lemma and Lebesgue dominated convergence theorem under some conditions of fuzzy measure. In this note, we show that these conditions of fuzzy measure is essential to prove Fatou's lemma and Lebesgue dominated convergence theorem by examples