Interval-valued Fuzzy Normal Subgroups

Jang, Su Yeon; Hur, Kyeong; Lim, Pyung Ki

doi:10.5391/ijfis.2012.12.3.205

Cited by 7 publications

(8 citation statements)

References 12 publications

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“…The present paper is a sequel to [4]. We obtain a number of further analogs of the properties of groups, thereby enriching the theory of interval-valued fuzzy groups and, in particular, corroborating the concept of interval-valued fuzzy normal subgroups and interval-valued fuzzy cosets introduced in [4,5].…”

Section: Introductionsupporting

confidence: 57%

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Interval-Valued Fuzzy Cosets

Lee¹,

Hur²,

Lim³

2012

Journal of Korean Institute of Intelligent Systems

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First, we prove a number of results about interval-valued fuzzy groups involving the notions of interval-valued fuzzy cosets and interval-valued fuzzy normal subgroups which are analogs of important results from group theory. Also, we introduce analogs of some group-theoretic concepts such as characteristic subgroup, normalizer and abelian groups.Secondly, we prove that if A is an interval-valued fuzzy subgroup of a group G such that the index of A is the smallest prime dividing the order of G, then A is an interval-valued fuzzy normal subgroup. Finally, we show that there is a one-to-one correspondence the interval-valued fuzzy cosets of an interval-valued fuzzy subgroup A of a group G and the cosets of a certain subgroup H of G.

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Section: Introductionsupporting

confidence: 57%

“…After that time, Mondal and Samanta [8], and choi et al [3] applied it to topology. Also, several researchers [1,2,[4][5][6][7] applied one to algebra.…”

Section: Introductionmentioning

confidence: 99%

Interval-Valued Fuzzy Cosets

Lee¹,

Hur²,

Lim³

2012

Journal of Korean Institute of Intelligent Systems

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“…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%

“…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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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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“…Kang [16], Kang and Hur [17] applied the notion of interval-valued fuzzy sets to algebra. Jang et al [18] investigated interval-valued fuzzy normal subgroups.…”

Section: Introductionmentioning

confidence: 99%

Interval-Valued Fuzzy Congruences on a Semigroup

Lee¹,

Hur

Lim³

2013

International Journal of Fuzzy Logic and Intelligent Systems

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We introduce the concept of interval-valued fuzzy congruences on a semigroup S and we obtain some important results: First, for any interval-valued fuzzy congruence R on a group G, the interval-valued congruence class R e is an interval-valued fuzzy normal subgroup of G. Second, for any interval-valued fuzzy congruence R on a groupoid S, we show that a binary operation * an S/R is well-defined and also we obtain some results related to additional conditions for S. Also we improve that for any two interval-valued fuzzy congruences R and Q on a semigroup S such that R ⊂ Q, there exists a unique semigroup homomorphism g : S/R → S/G.

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Interval-valued Fuzzy Normal Subgroups

Cited by 7 publications

References 12 publications

Interval-Valued Fuzzy Cosets

Interval-Valued Fuzzy Cosets

Lattices of Interval-Valued Fuzzy Subgroups

Interval-Valued Fuzzy Congruences on a Semigroup

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