• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.465-475
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• 2012

We characterize the fuzzy ideal generated by a fuzzy subset in a semigroup and the fuzzy interior ideal generated by a fuzzy subset in a semigroup. Our work generalizes the characterizations ([8]) of those fuzzy ideals generated by fuzzy subsets in semigroups with an identity element.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1071-1084
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• 2008

The notion of intuitionistic fuzzy filters in ordered semigroups is introduced and relation between intuitionistic fuzzy filters and intuitionistic fuzzy prime ideals is investegated. The notion of intuitionistic fuzzy bi-ideal subsets and intuitionistic fuzzy bi-filters are provided and relation between intuitionistic fuzzy bi-filters and intuitionistic fuzzy prime bi-ideal subsets is established. The concept of intuitionistic fuzzy right filters(1eft filters) is given and their relation with intuitionistic fuzzy prime right (left) ideals is discussed.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.749-755
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• 2008

In this paper, we introduce the relatively new notion of fuzzy ${\omega}^O$-open set. We prove that the collection of all fuzzy ${\omega}^O$-open subsets of a fuzzy topological space forms a fuzzy topology that is finer than the original one. Several characterizations and properties of this class are also given as well as connections to other well-known "fuzzy generalized open" subsets.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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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.

• The KIPS Transactions:PartB
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• v.8B no.5
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• pp.463-468
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• 2001

We propose a new similarity measure based on relative membership function (RMF). In this paper, the RMF is suggested to represent the relativity between fuzzy subsets easily. Since the shape of the RMF is determined according to the values of its parameters, we can easily represent the relativity between fuzzy subsets by adjusting only the values of its parameters. Hence, we can easily reflect the relativity among individuals or cultural differences when we represent the subjectivity by using the fuzzy subsets. In this case, these parameters may be regarded as feature points for determining the structure of fuzzy subset. In the sequel, the degree of similarity between fuzzy subsets can be quickly computed by using the parameters of the RMF. We use Euclidean distance to compute the degree of similarity between fuzzy subsets represented by the RMF. In the meantime, we present a new linguistic approximation method as an application area of the proposed similarity measure and show its numerical example.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1077-1108
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• 2019

The notions of intuitionistic fuzzy UP-subalgebras and intuitionistic fuzzy UP-ideals of UP-algebras were introduced by Kesorn et al. [13]. In this paper, we introduce the notions of intuitionistic fuzzy near UP-filters, intuitionistic fuzzy UP-filters, and intuitionistic fuzzy strong UP-ideals of UP-algebras, prove their generalizations, and investigate their basic properties. Furthermore, we discuss the relations between intuitionistic fuzzy near UP-filters (resp., intuitionistic fuzzy UP-filters, intuitionistic fuzzy strong UP-ideals) and their upper t-(strong) level subsets and lower t-(strong) level subsets in UP-algebras.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1995.10b
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• pp.331-334
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• 1995

We redefine the sup-min product of fuzzy subsets and discuss the redefined sup-min products of fuzzy subgroupoids, fuzzy submonoids and fuzzy subgroups. And we study lattice structures of the lattices of fuzzy subgroupoids, fuzzy submonoids and fuzzy subgroups.

• Journal of Digital Contents Society
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• v.9 no.1
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• pp.53-60
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• 2008

Based on similarities between fuzzy set theory and mathematical morphology, Grabish proposed a fuzzy morphology based on the Sugeno fuzzy integral. This paper proposes a fuzzy mathematical morphology based on the defuzzification of the fuzzy measure which corresponds to fuzzy integral. Its process makes a fuzzy set used as a measure of the inclusion of each fuzzy measure for subsets. To calculate such an integral a $\lambda$-fuzzy measure is defined which gives every subsets associated with the universe of discourse, a definite non-negative weight. Fast implementable definitions for erosion and dilation based on the fuzzy measure was given. An application for robust skeletonization of two-dimensional objects was presented. Simulation examples showed that the object reconstruction from their skeletal subsets that can be achieved by using the proposed was better than by using the binary mathematical morphology in most cases.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.409-420
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• 2006

In this paper we consider the set of all n + 1-tuples of real numbers, not necessarily all distinct, in the decreasing order from the unit interval under the usual ordering of real numbers, always including 1. Such n + 1-tuples inherently arise as the membership values of fuzzy subsets and are called keychains. An natural equivalence relation is introduced on this set and the equivalence classes of keychains are studied here. The number of such keychains is finite and the set of all keychains is a lattice under the coordinate-wise ordering. Thus keychains are subchains of a finite chain of real numbers in the unit interval. We study some of their properties and give some applications to counting fuzzy subsets of finite sets.