Interval-Valued Fuzzy Subgroups

Lee, Jeong Gon; Hur, Kyeong; Lim, Pyung Ki

doi:10.5831/hmj.2013.35.4.565

Cited by 2 publications

(4 citation statements)

References 11 publications

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“…Lee et al [11] studied interval-valued fuzzy subgroup in the sense of a lattice. Cheong and Hur [5], Lee et al [10], Jang et al [6], Kang and Hur [8] investigated interval-valued fuzzy ideals/(generalized) bi-ideals, subgroup and ring, respectively.…”

Section: Resultsmentioning

confidence: 99%

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Lattices of Interval-Valued Fuzzy Subgroups

Lee¹,

Hur²,

Lim³

2014

International Journal of Fuzzy Logic and Intelligent Systems

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We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy version of a well-known result from classical lattice theory. Finally, we employ a lattice diagram to exhibit the interrelationship among these sublattices.

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Section: Resultsmentioning

confidence: 99%

“…Subsequently, a number of researchers applied interval-valued fuzzy sets to algebra [5][6][7][8][9][10][11], and Lee et al [12] furthered the investigation of interval-valued fuzzy subgroups in the sense of a lattice.…”

Section: Introductionmentioning

confidence: 99%

Lattices of Interval-Valued Fuzzy Subgroups

Lee¹,

Hur²,

Lim³

2014

International Journal of Fuzzy Logic and Intelligent Systems

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“…Hence Z M is a subgroup of Z . Moreover, by applying theorem (30) and using the normality of M for any element…”

Section: -Intrtval Valued Fuzzification Of Lagrange's Theorem Of mentioning

confidence: 99%

“…The author [29] introduced the concept of IVF coset in 2011. In 2013, Lee et al [30] proved that an IVFSG cannot be visualized as the union of two suitable IVFSGs. Liu and Luo [31] gave useful methods to construct entropy of IVFS in 2015.…”

Section: Introductionmentioning

confidence: 99%

On Γ-Interval Valued Fuzzification of Lagrange’s Theorem of Γ-Interval Valued Fuzzy Subgroups

et al. 2020

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In this paper, we present the idea of interval valued fuzzy subgroup defined over a certain t-conorm (-IVFSG) and prove that every IVFSG is-IVFSG. We use this ideology to define the concepts of-IVF cosets,-IVFNSG and formulate their various important algebraic characteristics. We also propose the study of the notion of level subgroups of-IVFSG and investigate the condition under which a-IVFS is-IVFSG. Moreover, we extend the study of this phenomenon to introduce the concept of quotient group of a group Z relative to the-IVFNSG and acquire a correspondence between each-IVF(N)SG of a group Z and-IVF(N)SG of its quotient group. Furthermore, we define the index of-IVFSG and establish the-interval valued fuzzification of Lagrange's theorem of any-IVFSG of a finite group Z .

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Interval-Valued Fuzzy Subgroups

Cited by 2 publications

References 11 publications

Lattices of Interval-Valued Fuzzy Subgroups

Lattices of Interval-Valued Fuzzy Subgroups

On Γ-Interval Valued Fuzzification of Lagrange’s Theorem of Γ-Interval Valued Fuzzy Subgroups

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