• East Asian mathematical journal
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• v.24 no.4
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• pp.329-338
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• 2008

The aim of this paper is to introduce a new generalization of fuzzy faintly continuous functions called fuzzy faintly pre-continuous functions and also we have introduced and studied weakly fuzzy pre-continuous functions. Several characterizations of fuzzy faintly pre-continuous functions are given and some interesting properties of the above functions are discussed.

• Korean Journal of Mathematics
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• v.4 no.1
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• pp.77-82
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• 1996

We introduce the concepts of fuzzy $s$-continuous functions. And we investigate several properties of the fuzzy $s$-continuous function. In particular, we study the relation between fuzzy continuous functions and fuzzy $s$-continuous functions.

• East Asian mathematical journal
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• v.26 no.1
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• pp.1-8
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• 2010

In this paper the concepts of somewhat fuzzy almost $\alpha$-irresolute functions and strongly somewhat fuzzy $\beta$-open functions are introduced and studied. Besides giving characterizations of these functions, some interesting properties of these functions are also given.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.183-186
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• 2008

We consider fuzzy invex sets, fuzzy preinvex functions, fuzzy quasi-preinvex functions, and fuzzy logarithmic preinvex functions. Murofushi et al. have been studied Choquet integrals and their properties. In this paper, we study some characterizations in Choquet integrals as follows: fuzzy preinvexity, fuzzy quasi-preinvexity, and fuzzy logarithemic preinvexity, that mean some characterizations of functionals defined by Choquet integrals. Furthermore, we discuss Jensen's type inequality in Choquet integrals.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.135-140
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• 1996

We introduce the concepts of fuzzy $s$-open functions, and $s$-closed functions. And we investigate several properties of such functions. In particular, we study the relation between fuzzy $s$-continuous maps and fuzzy $s$-open maps( $s$-closed maps).

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.164-168
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• 2005

As a generalization of the notions of fuzzy $\alpha-irresolute$, fuzzy preirresolute, fuzzy irresolute and fuzzy $\beta-irresolute$ functions, we introduce the notion of fuzzy $\beta\alpha-continuous$ functions and investigate the relationships between fuzzy $\beta\alpha-continuous$ functions and fuzzy separation axioms.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.221-233
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• 2004

In this paper we introduce the concept of the McShane-Stieltjes integrals of interval-valued functions and fuzzy-number-valued functions and investigate some of their properties.

• Proceedings of the KIEE Conference
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• 1993.07a
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• pp.489-491
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• 1993

Many optimization problem or multiple attribute, multiple alternative decision making problem may have fuzzy evaluation factors. In this case, fuzzy number operation technique is needed to evaluate and compare object functions which become fuzzy sets. Generally, fuzzy number operations can be defined by extension principle of fuzzy set theory, but it is tedious to do fuzzy number operations by using extension principle when the membership functions are defined by complex functions. Many fast methods which approximate the membership functions such as triangle, trapezoidal, or L-R type functions are proposed. In this paper, a fast fuzzy number operation method is proposed which do not simplify the membership functions of fuzzy numbers.

• East Asian mathematical journal
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• v.23 no.1
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• pp.83-101
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• 2007

In this paper the concept of somewhat pairwise fuzzy continuous functions and somewhat pairwise fuzzy open functions are introduced. Some interesting properties of these functions are investigated besides giving some characterizations of these functions.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.7-7
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• 2003

We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.