• 한국지능시스템학회논문지
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• 제22권5호
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• pp.646-655
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• 2012

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.

• 호남수학학술지
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• 제32권4호
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• pp.593-617
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• 2010

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

• 호남수학학술지
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• 제32권4호
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• pp.545-561
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• 2010

We introduce the concepts of interval-valued fuzzy sub-groups [resp. normal subgroups, rings and ideals] and investigate some of it's properties.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권3호
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• pp.231-244
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• 2013

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 $R_e$ on a group G, the interval-valued congruence class Re 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 $R{\subset}Q$, there exists a unique semigroup homomorphism g : S/R${\rightarrow}$S/G.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제14권2호
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• pp.154-161
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• 2014

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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제12권3호
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• pp.205-214
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• 2012

We study some properties of interval-valued fuzzy normal subgroups of a group. In particular, we obtain two characterizations of interval-valued fuzzy normal subgroups. Moreover, we introduce the concept of an interval-valued fuzzy coset and obtain several results which are analogous of some basic theorems of group theory.