• Journal of applied mathematics & informatics
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• 제2권2호
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• pp.83-95
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• 1995

Given a closed subset of the family $S^{*}(\alpha)$ of functions starlike of order $\alpha$, a continuous Frechet differentiable functional J, is constructed with this collection as the solution set to the extremal problem ReJ(f) over $S^{*}(\alpha)$. The support points of $S^{*}(\alpha)$ is completely characterized and shown to coincide with the extreme points of its convex hulls. Given any finite collection of support points of $S^{*}(\alpha)$ a continuous linear functional J, is constructed with this collection as the solution set to the extremal problem ReJ(f) over $S^{*}(\alpha)$.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.221-236
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• 2014

This paper introduces semiopen and semiclosed soft sets in soft topological spaces and then these are used to generalize the notions of interior and closure. Further, we study the properties of semiopen soft sets, semiclosed soft sets, semi interior and semi closure of soft set in soft topological spaces. Various forms of soft functions, like semicontinuous, irresolute, semiopen and semiclosed soft functions are introduced and characterized including those of soft semicompactness, soft semiconnectedness. Besides, soft semiseparation axioms are also introduced and studied.

• 충청수학회지
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• 제6권1호
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• pp.25-43
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• 1993

This paper introduces a numerical method approximating the minimum norm solution to the first kind integral equation Kf = g with its kernel satisfying a certain property, where g belongs to the range space of K. Most of the existing expansion methods suffer from choosing a set of basis functions, whereas this method automatically provides an optimal set of basis functions approximating the minimum norm solution of Kf = g. Perturbation results and numerical experiments are also provided to analyze this method.

• 대한수학회논문집
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• 제23권2호
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• pp.251-256
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• 2008

In this paper, we introduce the concept of the semi-preconvex set on preconvexity spaces. We study some properties for the semi-preconvex set. Also we introduce the concepts of the sc-convex function and $s^*c$-convex function. Finally, we characterize sc-convex functions, $s^*$-convex functions and semi-preconvex sets by using the co-convexity hull and the convexity hull.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.367-367
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• 2000

In this paper, an Adaptive neuro-fuzzy Inference system(ANFIS) using fuzzy min-max network(FMMN) is proposed. Fuzzy min-max network classifier that utilizes fuzzy sets as pattern classes is described. Each fuzzy set is an aggregation of fuzzy set hyperboxes. Here, the proposed method transforms the hyperboxes into gaussian membership functions, where the transformed membership functions are inserted for generating fuzzy rules of ANFIS. Finally, we applied the proposed method to the classification problem of iris data and obtained a better performance than previous works.

• 대한수학회보
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• 제30권1호
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• pp.91-97
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• 1993

In this article, we consider the case that S is a topologically complete subspace of $R^{k}$ , and that .GAMMA. is a set of monotone functions on S into S. It is obtained the sugficient condition for the existence of a unique invariant probability to which $P^{(n}$/(x,dy) converges exponentially fast in a metric stronger than the Kolmogorov's distance. This extends the earlier results of Bhattacharya and Lee (1988) who considered the case .GAMMA. a set of nondecreasing functions.tions.

• 대한수학회논문집
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• 제26권2호
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• pp.305-320
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• 2011

The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of $\v{S}$ostak's I-fuzzy topological spaces are discussed. The projection maps are defined as fuzzy proper functions and their properties are proved.

• 대한수학회논문집
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• 제30권4호
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• pp.493-504
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• 2015

The aim of this paper is to present some properties of sT-continuous functions. Moreover, we obtain a characterization and preserving theorems of semi-compact, S-closed and s-closed spaces.

• 충청수학회지
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• 제4권1호
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• pp.55-59
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• 1991

We consider perturbation problems and Lagrangians for convex set function optimization problems. In particular, we prove that the Lagrangian $L({\Omega},y)$ is a convex set function in ${\Omega}$ for each y if the perturbation function is convex.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제4권1호
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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.