• 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.

• 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.

• 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.

• Honam Mathematical Journal
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• v.28 no.1
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• pp.1-22
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• 2006

First, we obtain some results of intuitionistic fuzzy congruences on a regular semigroups contained in ($XH,\;XH^c$). Secondly, we introduce the concept of intuitionistic fuzzy idempotent separating congruences on a semigroup and investigate some of it's properties.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.167-187
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• 2006

We introduce the concepts of intuitionistic fuzzy submodules and intuitionistic fuzzy weak congruences on an R-module (Near-ring module). And we obtain the correspondence between intuitionistic fuzzy weak congruences and intuitionistic fuzzy submodules of an R-module. Also, we define intuitionistic fuzzy quotient R-module of an R-module over an intuitionistic fuzzy submodule and obtain the correspondence between intuitionistic fuzzy weak congruences on an R-module and intuitionistic fuzzy weak congruences on intuitionistic fuzzy quotient R-module over an intuitionistic fuzzy submodule of an R-module.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.372-377
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• 2004

We introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a lattice, and discuss the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruence on a distributive lattice. Also we prove that for a generalized Boolean algebra, the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences. Finally, we consider the products of intuitionistic fuzzy ideals and obtain a necessary and sufficient condition for an intuitionistic fuzzy ideals on the direct sum of lattices to be representable on a direct sum of intuitionistic fuzzy ideals on each lattice.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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• pp.100-111
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• 2007

We introduce the concept of intuitionistic fuzzy G-equivalence relations (congruence), and we obtain some results. Furthermore, we prove that $IFC_G(K)$ is isomorphic to $IFN^*(K)$ for any group K. Also, we prove that($IFC_{G,({\lambda},{\mu})}/{\sim},\;*$) and ($IFNG_{({\lambda},{\mu})}(K),\;{\circ}$) are isomorphic.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.357-366
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• 2006

We introduce the notion of intuitionistic fuzzy (t, s)-congruences on a lattice and study some of its properties. Moreover, we obtain some properties of intuitionistic fuzzy congruences on the direct product of two lattices. Finally, we prove that the set of all intuitionistic fuzzy congruences on a lattice forms a distributive lattice.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.465-486
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• 2005

We study the relationship between intuitionistic fuzzy ideals and intuitionistic fuzzy congruences on a distributive lattice. And we prove that the lattice of intuitionistic fuzzy ideals is isomorphic to the lattice of intuitionistic fuzzy congruences on a generalized Boolean algebra.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.315-325
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• 2006

The notion of intuitionistic fuzzy finite switchboard state machines and (strong) homomorphisms of intuitionistic fuzzy finite state machines are introduced, and related properties are investigated. After we give a congruence relation on the set of all words of elements of X of finite length, the quotient structure is discussed. We show that the family of equivalence classes is a finite semigroup with identity.