• Title/Summary/Keyword: fuzzy subsets

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INTUITIONISTIC FUZZY FILTERS OF ORDERED SEMIGROUPS

  • Shabir, M.;Khan, A.
    • 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.

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FUZZY ωO-OPEN SETS

  • Al-Hawary, Talal
    • 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.

On compact convex subsets of fuzzy number space (퍼지 수 공간의 컴팩트 볼륵 집합에 관한 연구)

  • Kim, Yun-Kyong
    • 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.

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A New Similarity Measure based on RMF and It s Application to Linguistic Approximation (상대적 소수 함수에 기반을 둔 새로운 유사성 측도와 언어 근사에의 응용)

  • Choe, Dae-Yeong
    • 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.

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A NOVEL APPROACH TO INTUITIONISTIC FUZZY SETS IN UP-ALGEBRAS

  • Thongngam, Nattaporn;Iampan, Aiyared
    • 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.

LATTICES OF FUZZY SUBGROUPOIDS, FUZZY SUBMONOIDS AND FUZZY SUBGROUPS

  • Kim, Jae-Gyeom
    • 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.

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The Skeletonization of 2-Dimensional Image for Fuzzy Mathematical Morphology using Defuzzification (비퍼지화를 이용한 퍼지 수학적 형태학의 2차원 영상의 골격화)

  • Park, In-Kue;Lee, Wan-Bum
    • 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.

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LATTICE OF KEYCHAINS

  • MURALI V.
    • 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.