• Korean Journal of Mathematics
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• v.14 no.2
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.771-779
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• 2005

We introduce two concepts of intuitionistic fuzzy Rees congruence on a semigroup and intuitionistic fuzzy Rees con-gruence semigroup. As an important result, we prove that for a intuitionistic fuzzy Rees congruence semigroup S, the set of all intuitionistic fuzzy ideals of S and the set of all intuitionistic fuzzy congruences on S are lattice isomorphic. Moreover, we show that a homomorphic image of an intuitionistic fuzzy Rees congruence semigroup is an intuitionistic fuzzy Rees congruence semigroup.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.343-356
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• 2010

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, discuss some of its basic properties, and characterize the G-fuzzy congruence generated by a fuzzy relation on a semigroup. We also give certain lattice theoretic properties of G-fuzzy congruences on semigroups.

• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.461-468
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• 2008

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.4
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• pp.321-330
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• 2006

We introduce the concept of intuitionistic fuzzy weak congruence on a semiring and obtain the relation between intuitionistic fuzzy weak congruence and intuitionistic fuzzy ideal of a semiring. Also we define and investigate intuitionistic fuzzy quotient semiring of a semiring over an intuitionistic fuzzy ideal or over an intuitionistic fuzzy weak congruence.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.683-691
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• 2014

We redefine a fuzzy congruence, discuss some properties of the fuzzy congruences, find the fuzzy congruence generated by a fuzzy relation on a semigroup, and give some lattice theoretic properties of the fuzzy congruences on semigroups.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.385-392
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• 2003

Using a fuzzy filter, a new congruence relation induced by the fuzzy filter is given in lattice implication algebras, and some of their properties are investigated.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.53-58
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• 2009

We unite the two con concepts - normality We unite the two con concepts - normality and congruence - in an intuitionistic fuzzy subgroup setting. In particular, we prove that every intuitionistic fuzzy congruence determines an intuitionistic fuzzy subgroup. Conversely, given an intuitionistic fuzzy normal subgroup, we can associate an intuitionistic fuzzy congruence. The association between intuitionistic fuzzy normal sbgroups and intuitionistic fuzzy congruences is bijective and unigue. This leads to a new concept of cosets and a corresponding concept of guotient.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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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.

• Korean Journal of Mathematics
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• v.25 no.4
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• pp.563-577
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• 2017

We define a weak fuzzy equivalence relation and a weak fuzzy congruence and develop some properties of the weak fuzzy equivalence relations and the weak fuzzy congruences on semigroups.