• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.20-21
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• 2002

Recently, Lee[European J. Operational Research 129(2001) 682-688] calculated standard deviation of fuzzy numbers in order to obtain the membership function of the process capacity index (PCI) $C^{pk}$. In this note, we show that his result is not valid.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.29-32
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• 2002

We consider the question whether, for given fuzzy numbers, there are different Pairs of f-norm such that the resulting membership function within the extension principle under addition are identical. Some examples are given.

• Journal for History of Mathematics
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• v.33 no.5
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• pp.277-287
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• 2020

There are many results for Zadeh's max-min composition operators based on Zadeh's extension principle. We calculate Zadeh's max-min composition operators for two triangular fuzzy numbers defined on ℝ.

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.189-200
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• 2012

In this article we introduce the class of I-convergent double sequences of fuzzy real numbers. We have studied different properties like solidness, symmetricity, monotone, sequence algebra etc. We prove that the class of I-convergent double sequences of fuzzy real numbers is a complete metric spaces.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.365-369
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• 2006

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(1986). Based on this, Wang and Li extended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. Using interval-valued Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we studied some characterizations of interval-valued Choquet distance(2005). In this paper, we define Choquet distance measure for fuzzy number-valued fuzzy numbers and investigate some algebraic properties of them.

• 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.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.73-83
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• 2003

In this paper, we first obtain some characterizations of compact subsets of the space of level-wise continuous fuzzy numbers in R by the modulus of continuity. Using this, we establish the tightness for a sequence of level-wise continuous fuzzy random variables.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.371-381
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• 2004

In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1419-1430
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• 2010

Since Goetschel and Voxman [5] proposed a linear order on fuzzy numbers, several authors studied the concept of semicontinuity and convexity of fuzzy mappings defined through the order. Since the order is only defined for fuzzy numbers on $\mathbb{R}$, it is natural to find a new order for normal fuzzy sets on $\mathbb{R}^n$ in order to study the concept of semicontinuity and convexity of fuzzy mappings on normal fuzzy sets. In this paper, we introduce a new order "${\preceq}_s$ for normal fuzzy sets on $\mathbb{R}^n$ with respect to the support function. We define the semicontinuity and convexity of fuzzy mappings with this order. Some issues which are related with semicontinuity and convexity of fuzzy mappings will be discussed.