• 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 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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.3
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• pp.333-341
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• 2018

In this paper we introduce the concept of equi-integrability of sequence of the fuzzy number-valued AP-Henstock-Stieltjes integrable functions. Under this concept, we prove two convergence theorems for sequences of the fuzzy number-valued AP-Henstock-Stieltjes integrable functions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.95-107
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• 2004

In this paper, we consider fuzzy number-valued functions and fuzzy number-valued Choquet integrals. And we also discuss positively homogeneous and monotonicity of Choquet integrals of fuzzy number-valued functions(simply, fuzzy number-valued Choquet integrals). Furthermore, we prove convergence theorems for fuzzy number-valued Choquet integrals.

• 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.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.307-315
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• 2017

In this paper, we aim to compare the differentials with the regularity of the hypercomplex valued functions in Clifford analysis. For three kinds of conjugation of the bicomplex numbers, we define the differentials of the bicomplex number functions by the naive approach. And we investigate some relations of the corresponding Cauchy-Riemann system and the conditions of the differentiable functions in the bicomplex number system.

• Journal of Korean Medical Ki-Gong Academy
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• v.20 no.1
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• pp.148-162
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• 2020

Objective : The purpose of this study is not only to examine the negative functions of alcohol, but also to examine the positive functions and look at it with a balanced perspective. Methods : We investigated the number of times the word "酒"(alcohol) appears in 《Hwangjenaegyeong》 and 《Gyeongakjeonseo》. The meaning of alcohol was divided into seven categories. The number of positive and negative functions of alcohol was counted and the ratio was calculated. Results : 1. In the 《Hwangjenaegyeong》, the word alcohol appears 23 times, of which 9 times has positive functions, 10 times has negative functions, and the remaining 4 times does not correspond anywhere. The ratio of positive functions is 39.13% and negative functions 43.48%. 2. In the 《Gyeongakjeonseo》, the word alcohol appears 1,487 times, of which 1,140 times (76.66%) has positive functions, and 327 times (21.99%) has negative functions. Conclusions : 1. In 《Hwangjenaegyeong》, the number of comments about positive and negative functions of alcohol is similar. 2. 《Gyeongakjeonseo》 has commented a lot about the positive functions of alcohol. However, it has more mentions to negative functions of alcohol except for those related to herbs and prescriptions (48 to 64 chapter). 3. It is somewhat unreasonable to judge the emphasis on the positive and negative function of alcohol according to the number of references to alcohol in oriental medicine classics. But in these books, we can find a balanced approach between the two sides, not a one-sided biased view. 4. From a curative point of view, it is desirable to know and to use the positive and negative functions of alcohol, and drink alcohol as appropriate control.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.685-692
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• 2016

The aim of this paper is to investigate the differentials of the hypercomplex valued functions in Clifford analysis. Like as the differentials defined by the naïve approach in one complex variable analysis, we define the differentials of functions with values in ternary number functions by same ways. And we survey the properties of each differential with respect to a non-commutativity of the skew field.

• ETRI Journal
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• v.15 no.2
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• pp.35-51
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• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.3
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• pp.357-363
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• 1986

In the design of PLA's of VLSI, as the number of subsets of functions from which common preme implicants must be determined increases, the execution time increases by a factor of O(2\ulcorner. When the number of functions N is a large number, this poses a serious problem in minumization of multiple-output logic functions. In this paper a new algorithm that minimizes multiple-output logic functions is proposed. The algorithm requires less number of Fortran statements, less execution time, and less memory area than existing methods. The bases of this algorithm are explained and verified, and the sequential operation for preparation of the program is discussed.