• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• 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.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.121-124
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• 2005

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, we define a distance measure on interval-valued fuzzy numbers using Choquet integral with respect to a classical measure and investigate their properties.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.579-584
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• 1998

In this work, we present a method to deal with the interval valued decision making systems. First, we propose a new type of equality measure based on the Ordered Weighted Averaging (OWA) operator. The proposed equality measure has a structure to render the extreme values of the measure by choosing a suitable weighting vector of the OWA operator. From this property, we derive a bidirectional fuzzy inference network which can be applied for the decisionmaking systems requiring the inverval valued decisions.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.477-486
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• 2007

This paper is the first in a series in which we consider bilinear integration with respect to measure-valued measure. We use the integration techniques to establish generalized Egorov theorem and Vitali theorem.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.224-229
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• 2010

In this paper, using fuzzy complex valued functions and fuzzy complex valued fuzzy measures ([11]) and interval-valued Choquet integrals ([2-6]), we define Choquet integral with respect to a fuzzy complex valued fuzzy measure of a fuzzy complex valued function and investigate some basic properties of them.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.61-68
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• 2006

In 2002, the author introduced the definition and its properties of an analogue of Wiener measure over paths. In this article, using these concepts, we will derive an operator-valued measure over paths and will investigate the properties for integral with respect to the measure. Specially, we will prove the Wiener integral formula for our integral and give some example of it.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.39-48
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• 2000

In this paper we define T-fuzzy integrals of set-valued mappings, which are extensions of fuzzy integrals of the single-valued functions defined by Sugeno. And we discuss their properties.