• Proceedings of the Korea Contents Association Conference
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• 2003.11a
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• pp.338-342
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• 2003

The concept of a circularity function is used in defining fuzzy spheres The circularity function of a fuzzy sphere converses to one of crisp sphere as the fuzzy sphere shapes itself more and more like a crisp sphere.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.703-711
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• 2005

Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (${\alpha},\;{\beta}$)-fuzzy subalgebras where ${\alpha},\;{\beta}$ are any two of $\{\in,\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with $\;{\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ is introduced, and related properties are investigated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.385-388
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• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1041-1044
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• 2005

Recently, Zhang et al.(Fuzzy Sets and Systems 147(2004) 475-485) proved Fatou's lemma and Lebesgue dominated convergence theorem under some conditions of fuzzy measure. In this note, we show that these conditions of fuzzy measure is essential to prove Fatou's lemma and Lebesgue dominated convergence theorem by examples

• 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.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.291-302
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• 2006

In this paper, we give sufficient conditions for a.s. convergence of weighted sums of integrable fuzzy random variables. As a result, we obtain strong laws of large numbers for weighted sums of independent fuzzy random variables.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.177-182
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• 2004

In this paper, we establish some results on almost sure convergence for sums and weighted sums of uniformly integrable fuzzy random sets taking values in the space of upper-semicontinuous fuzzy sets in $R^{p}$.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.4
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• pp.557-562
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• 2007

This paper extends the work of Maji et al. (2001) to present the concept of interval-valued fuzzy soft sets and to present an algorithm for finding where the degree of membership are represented by interval values in [0, 1]. The proposed method is more flexible than the one presented in Maji et at. (2001) due to the fact that it allows the degrees of membership of object for parameters to be represented by interval-values rather than crisp real values between zero and one.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.2
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• pp.146-150
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• 2008

In this paper, we consider concepts of subsethood measure introduced by Fan et al. [2]. Based on this, we give various subsethood measure defined by Choquet integral with respect to a fuzzy measure on fuzzy sets which is often used in information fusion and data mining as a nonlinear aggregation tool and discuss some properties of them. Furthermore, we introduce simple examples.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.913-918
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• 2006

Chanas(2001) introduced the notion of interval approximation of a fuzzy number with the condition that the width of this interval is equal to the width of the expected interval. In this note, this condition is relaxed and the resulting formulae are derived for determining the approximation interval. This interval is compared with the expected interval and approximation interval of a fuzzy number as introduced by Chanas.