• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.22-24
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• 2002

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 Mares (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous f-norm which holds the distributivity under f-norm based fuzzy arithmetic operations.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.153-161
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• 2001

In this paper, a strong law of large numbers for sums of stationary and ergodic fuzzy random variables is obtained.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.49-57
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• 2003

In this paper, we give some sufficient conditions for convergence of geometric mean for T-related fuzzy numbers where T is an Archimedean t-norm under some mild restrictions. These results generalize earlier results of Hong and Lee [Fuzzy Sets and Systems 116 (2000) 263-267].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.143-146
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• 2005

In this paper, we define correlation coeeficients of interval-valued fuzzy numbers by utilizing Choquet integrals. Also we discuss some properties of them.

• Korean Journal of Mathematics
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• v.4 no.2
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• pp.117-124
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• 1996

In this paper we define a new fuzzy metric $\tilde{\theta}$ of fuzzy number sequences, and prove that the space of convergent sequences of fuzzy numbers is a fuzzy complete metric space in the fuzzy metric $\tilde{\theta}$.

• Journal of Internet Computing and Services
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• v.8 no.3
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• pp.99-107
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• 2007

In general, the reliabilities of the fuzzy system are represented and analyzed by real numbers between zero and one, fuzzy numbers, intervals of confidence, interval-valued fuzzy sets, vague sets, etc. This paper addresses the method to analyze the reliability of the fuzzy system for the weighted components with the weights reflected on the importance of weighted components in an system. The reliabilities and the weights of the weighted components in a fuzzy numbers and considers the weights of the weighted components in a fuzzy system, therefore, its execution is faster and more flexible than the conventional methods.

• Journal of the Korean Institute of Intelligent Systems
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• v.25 no.2
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• pp.197-202
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• 2015

A triangular fuzzy number is one of the most popular fuzzy numbers. Many results for the extended algebraic operations between two triangular fuzzy numbers are well-known. We generalize the triangular fuzzy numbers on $\mathbb{R}$ to $\mathbb{R}^2$. By defining parametric operations between two regions valued ${\alpha}$-cuts, we get the parametric operations for two triangular fuzzy numbers defined on $\mathbb{R}^2$.

• Journal of the Korean Data and Information Science Society
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• v.17 no.2
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• pp.657-659
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• 2006

This note gives a counterexample showing that a main theorem of Aytal and Pehliven's (Information Sciences 176 (2006) 734-744) result on statically monotonic and bounded sequences of fuzzy numbers is not valid.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.224-229
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• 2010

In this paper, using fuzzy complex valued functions and fuzzy complex valued fuzzy measures ([11]) and interval-valued Choquet integrals ([2-6]), we define Choquet integral with respect to a fuzzy complex valued fuzzy measure of a fuzzy complex valued function and investigate some basic properties of them.