• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.535-545
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• 2007

In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.934-938
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• 2004

In this paper, we introduce the seminormed fuzzy co-integral as a complementary concept of seminormed fuzzy integral, and investigate its properties. Furthermore we propose an application of this new integral for decision making problems.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.455-459
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• 2007

Interval-valued fuzzy sets were suggested for the first time by Gorzafczany(1983) and Turksen(1986). Based on this, Zeng and Li(2006) introduced concepts of similarity measure and entropy on interval-valued fuzzy sets which are different from Bustince and Burillo(1996). In this paper, by using Choquet integral with respect to a fuzzy measure, we introduce distance measure and similarity measure defined by Choquet integral on interval-valued fuzzy sets and discuss some properties of them. Choquet integral is a generalization concept of Lebesgue inetgral, because the two definitions of Choquet integral and Lebesgue integral are equal if a fuzzy measure is a classical measure.

• Korean Journal of Mathematics
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• v.18 no.3
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• pp.229-241
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• 2010

In this paper, we introduce the Denjoy-Pettis integral of fuzzy mappings in Banach spaces and obtain some properties of the Denjoy-Pettis integral of fuzzy mappings and the convergence theorems for Denjoy-Pettis integrable fuzzy mappings.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.1
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• pp.27-37
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• 2000

In this paper, we will introduce the pan-dual generalized fuzzy integral of a commutative isotonic semigroup-valued functions, which is generalized of the (DG) fuzzy integral and investigate the fundamental properties of this kind of fuzzy integral.

• Journal of the Chungcheong Mathematical Society
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• v.11 no.1
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• pp.173-183
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• 1998

In this paper, we introduce the pan-generalized fuzzy integral of a commutative isotonic semigroup-valued function, which is generalization of the (G) fuzzy integral and investigate the fundamental properties of this kind of fuzzy integral.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.339-342
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• 2009

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.2
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• pp.279-291
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• 2010

In this paper, we introduce the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces in terms of the Kurzweil-Henstock-Pettis integral of set-valued mappings and obtain some properties of the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces and the convergence theorem for Kurzweil-Henstock-Pettis integrable fuzzy mappings.