• International Journal of Fuzzy Logic and Intelligent Systems
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• 제8권3호
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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.

• Journal of Electrical Engineering and information Science
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• 제3권2호
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• pp.131-138
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• 1998

We derive a back-propagation learning algorithm of fuzzy neural networks using fuzzy operations, which preserves the shapes of fuzzy numbers, in order to utilize fuzzy if-then rules as well as numerical data in the learning of neural networks for classification problems and for fuzzy control problems. By introducing the shape preseving fuzzy operation into a neural network, the proposed network simplifies fuzzy arithmetic operations of fuzzy numbers with exact result in learning the network. And we illustrate our approach by computer simulations on numerical examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제3권2호
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• pp.173-177
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• 2003

In the first part an overview on fuzzy sets and fuzzy numbers is given. A detailed treatment of these notions is introduced in [1,2,3]. This sintetically presentation is useful in understanding and in developping the applications in context problems. In the second part, fuzzy context model is given as an application of fuzzy sets and the fuzzy equilibrium equation is solved [4,5].

• Communications for Statistical Applications and Methods
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• 제5권2호
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• pp.439-445
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• 1998

In this paper we introduce the definition for fuzzy random set by Puri and Ralescu(1985) and show strong laws of large numbers for fuzzy random sets on Banach spaces.

• 대한수학회논문집
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• 제23권2호
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• pp.179-185
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• 2008

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

• Korean Journal of Mathematics
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• 제16권4호
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• pp.573-581
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• 2008

We obtain an improvement of strong laws of large numbers for independent fuzzy random variables.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.311-320
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• 2023

In this article, a new penalty and different ranking algorithms are used to find the lowest transportation costs for the fuzzy transportation problem. This approach utilises different ranking techniques when dealing with triangular fuzzy numbers. Also, we find that the fuzzy transportation solution of the proposed method is the same as the Fuzzy Modified Distribution Method (FMODI) solution. Finally, examples are used to show how a problem is solved.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.215-220
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• 2002

In this paper, we establish weak laws of large numbers for weighted sums of convex-compactly uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.14-17
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• 2003

By Mazur's theorem, the convex hull of a relatively compact subset a Banach space is also relatively compact. But this is not true any more in the space of fuzzy numbers endowed with the Hausdorff-Skorohod metric. In this paper, we establish a necessary and sufficient condition for which the convex hull of K is also relatively compact when K is a relatively compact subset of the space F(R$\^$k/) of fuzzy numbers of R$\^$k/ endowed with the Hausdorff-Skorohod metric.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2001년도 추계학술발표회 논문집
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• pp.137-141
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• 2001

We can obtain SLLN's for fuzzy random variables with respect to the new metric $d_s$ on the space F(R) of fuzzy numbers in R. In this paper, we obtain a SLLN for convex tight random elements taking values in F(R).