• 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.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.227-237
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• 2009

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued Denjoy-Pettis integrable mappings.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.381-393
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• 2012

In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.83-90
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• 2013

Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.

• 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.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.439-454
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• 2013

In this paper, we introduce the Birkho integral of fuzzy mappings in Banach spaces in terms of the Birkhoff integral of set-valued mappings and investigate some properties of the Birkho integrals of set-valued mappings and fuzzy mappings in Banach spaces.

• 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.

• Communications of the Korean Mathematical Society
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• v.25 no.1
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• pp.37-49
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• 2010

In this paper we introduce the integration of scalar valued functions with respect to a generalized fuzzy number measure which we call the generalized fuzzy number valued Bartle integral. We first establish some properties of the generalized fuzzy number measures and then study the generalized fuzzy number valued Bartle integrals.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.257-270
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• 2009

In this paper we introduce the Henstock integral of fuzzy mappings in Banach spaces as a generalization of the Henstock integral of set-valued mappings and investigate some properties of it.

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.315-326
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• 2009

In this paper, we introduce Debreu integral of fuzzy mappings in Banach spaces in terms of the Debreu integral of set-valued mappings, investigate properties of Debreu integral of fuzzy mappings in Banach spaces and obtain the convergence theorem for Debreu integral of fuzzy mappings in Banach spaces.