• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.05a
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• pp.265-268
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• 2002

In this paper we introduce the concepts of type-2 fuzzy set-valued mappings and quasi-convex fuzzy mappings on L-L fuzzy numbers and discuss some properties of these mappings.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.53-56
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• 2000

In this paper, we define a concept of some set-theoretical operations of L-R type fuzzy numbers and discuss some properties of these concepts. Using these results, we discuss a concept of cardinality of type-two fuzzy sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.311-313
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• 2001

In this paper, we define type-2 fuzzy mappings on L-L fuzzy numbers and discuss some properties of these mappings.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.85-89
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• 2007

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.385-392
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• 2003

The sum Of L - R fuzzy numbers With Unbounded Supports based on Archimedean continuous f-norm T is considered. Results are more simple than those of the case for bounded supports.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.447-454
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• 1999

We study a general law of large numbers for array of mu-tually T related fuzzy numbers where T is an Archimedean t-norm and generalize earlier results of Fuller(1992), Triesch(1993) and Hong (1996).

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.2
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• pp.115-118
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• 2001

본 논문에서는 L-R 퍼지수의 집합-이론적 연산의 개념을 정의하고, 이들 개념의 성질들을 조사한다. 이들 연산들의 결과들을 이용하여 제2형 퍼지집합의 기수개념에 관하여 연구한다.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.41-51
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• 2017

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.242-246
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• 2010

It is well-known that the space $E^n$ of fuzzy numbers(i.e., normal, upper-semicontinuous, compact-supported and convex fuzzy subsets)in the n-dimensional Euclidean space $R^n$ is separable but not complete with respect to the $L_p$-metric. In this paper, we introduce the space $F_p(R^n)$ that is separable and complete with respect to the $L_p$-metric. This will be accomplished by assuming p-th mean bounded condition instead of compact-supported condition and by removing convex condition.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.3
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• pp.170-174
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• 2008

The measurement of performance of a process considering both the location and the dispersion of information about the process is referred to as the process capacity indices (PCIs) of interest, $C_{pk}$. This information is presented by the mean and standard deviation of the producing process. Linguistic variables are used to express the evaluation of the quality of a product. Consequently, $C_{pk}$ is defined with fuzzy numbers. Lee [Eur. J. Oper. Res. 129(2001) 683-688] constructed the definition of the $C_{pk}$ index estimation presented by fuzzy numbers and approximated its membership function using the "min" - norm based Zadeh's extension principle of fuzzy sets. However, Lee's result was shown to be invalid by Hong [Eur. J. Oper. Res. 158(2004) 529-532]. It is well known that $T_w$ (the weakest t-norm)-based addition and multiplication preserve the shape of L-R fuzzy numbers. In this paper, we allow that the fuzzy numbers are of L-R type. The object of the present study is to propose a new method to calculate the $C_{pk}$ index under $T_w-based$ fuzzy arithmetic operations.