• Journal of Applied Reliability
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• v.14 no.2
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• pp.103-107
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• 2014

An algorithm to get network reliability, where each link has probability of fuzzy number, is proposed. Decomposition method and fuzzy numbers arithmetic are applied to the algorithm. Pivot link is chosen one by one from start node recursively at time of decomposition, and arithmetic of fuzzy complementary numbers is included at the same time. No criteria of pivot link selection and the recursive calculation make the algorithm simple.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• Journal of the Korean Data and Information Science Society
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• v.14 no.1
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• pp.93-101
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• 2003

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy quantities based on the extension principle suggested by Mare (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous t-norm which holds the distributivity under t-norm based fuzzy arithmetic operations.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.6
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• pp.754-758
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• 2003

The present paper establishes a strong law of large numbers for sums of tight fuzzy random variables as a generalization of SLLN for sums of independent and identically distributed fuzzy random variables.

• The Pure and Applied Mathematics
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• v.2 no.1
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• pp.9-16
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• 1995

D. Dubois and H. Prade introduced the notions of fuzzy numbers and defined its basic operations [3]. R. Goetschel, W. Voxman, A. Kaufmann, M. Gupta and G. Zhang [4,5,6,9] have done much work about fuzzy numbers. Let $\mathbb{R}$ the set of all real numbers and $F^{*}(\mathbb{R})$ all fuzzy subsets defined on $\mathbb{R}$. G. Zhang [8] defined the fuzzy number $\tilde{a}\;\in\;F^{*}(\mathbb{R})$ as follows : (omitted)

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.529-540
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• 2009

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.754-758
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• 2005

There have been several tipical methods being used tomeasure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. Recently, Wang and Chiu [FSS103(1999) 443-455] and Pedrycz [FSS 64(1994) 21-30] showed the relationship(addition, subtraction, multiplication) between the entropies of the resultant fuzzy number and the original fuzzy numbers of same type. In this paper, using Lebesgue-Stieltjes integral, we generalize results of Wang and Chiu [FSS 103(1999) 443-455] concerning entropy arithmetic operations without the condition of same types of fuzzy numbers. And using this results and trade-off relationship between information energy and entropy, we study more properties of information energy of fuzzy numbers.

• 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.