• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.33-40
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• 2000

We prove some characterization of rings with chain conditions in terms of fuzzy quotient rings and fuzzy ideals. We also show that a ring R is left Artinian if and only of the set of values of every fuzzy ideal on R is upper well-ordered.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.551-562
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• 2007

This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

• Honam Mathematical Journal
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• v.34 no.2
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• pp.145-159
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• 2012

Several types of a bipolar fuzzy hyper BCK-ideal in a hyper BCK-algebra are introduced, and their relations are investigated.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.255-277
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• 2006

By means of the use of a triangular norm T, the notion of T-fuzzy hyperideals in hypernear-rings is stated, and basic properties are investigated. Moreover, the notion of Noetherian hypernear-rings is introduced, and its characterization is given. At last, the properties of quotient hypernear-rings and T-fuzzy characteristic hyper ideals are discussed.

• East Asian mathematical journal
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• v.9 no.2
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• pp.261-269
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• 1993

• Honam Mathematical Journal
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• v.16 no.1
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• pp.67-70
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• 1994

• Communications of the Korean Mathematical Society
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• v.9 no.1
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• pp.19-25
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• 1994

• East Asian mathematical journal
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• v.9 no.1
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• pp.105-111
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• 1993

• East Asian mathematical journal
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• v.27 no.1
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• pp.75-82
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• 2011

In this paper, we will introduce the concept of fuzzy mulitplication module. We will define a new operation called a product on th family of all fuzzy submodules of a fuzzy mulitplication module. We will define a fuzzy subset of the idealization ring R+M and find some relations with the product of fuzzy submodules and product of fuzzy ideals of the idealization ring R+M. Some properties of weakly fuzzy prime submoduels and fuzzy prime submodules which are de ned by T.K.Mukherjee M.K.Sen and D.Roy will be introduced. We will investigate some properties of fuzzy prime submodules of a fuzzy multiplication module.

• 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.