• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.51-62
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• 2002

The present paper gives a new construction of a quotient BCI(BCK)-algebra X/${\mu}$ by a fuzzy ideal ${\mu}$ in X and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if ${\mu}$ is a fuzzy ideal (closed fuzzy ideal) of X, then X/${\mu}$ is a commutative (resp. positive implicative, implicative) BCK(BCI)-algebra if and only if It is a fuzzy commutative (resp. positive implicative, implicative) ideal of X Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra of X We show that if the period of every element in a BCI-algebra X is finite, then any fuzzy ideal of X is closed. Especiatly, in a well (resp. finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.2
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• pp.213-226
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• 2017

The concept of fuzzy transitive filters is introduced in BE-algebras. Some sufficient conditions are established for every fuzzy filter of a BE-algebra to become a fuzzy transitive filter. Some properties of fuzzy transitive filters are studied with respect to fuzzy relations and cartesian products.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.251-259
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• 2002

The fuzzification of an ideal in a Lie algebra is considered. Using a level subset of a fuzzy subset of a Lie algebra, we give a characterization of a fuzzy ideal, and using a family of ideals of a Lie algebra, we establish a fuzzy ideal. With relation to the ascending chain of ideals, a characterization for the set of values of any fuzzy ideal to be a well-ordered subset of the closed unit interval [0,1] is stated.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.443-458
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• 2022

In this paper, we apply the concept of intuitionistic Q-fuzzy set to PMS-algebras. We study the concept of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras and investigate some related properties of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras. We provide the relationship between an intuitionistic Q-fuzzy PMS-subalgebra and an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. We establish a condition for an intuitionistic Q-fuzzy set in a PMS-algebra to be an intuitionistic Q-fuzzy PMS-ideal of a PMS-algebra. Characterizations of intuitionistic Q-fuzzy PMS-ideals of PMS-algebras in terms of their level sets are given.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.395-404
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• 2020

Based on a sub-BCK-algebra K of a BCI-algebra X, the notions of fuzzy (K, ε)-subalgebras, fuzzy (K, ε)-ideals and fuzzy commutative (K, ε)-ideals are introduced, and their relations/properties are investigated. Conditions for a fuzzy subalgebra/ideal to be a fuzzy (K, ε)-subalgebra/ideal are provided.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1049-1057
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• 2011

In this paper, we fuzzify the concept of BE-algebras, investigate some of their properties. We give a characterization of fuzzy BE-algebras, and discuss a characterization of fuzzy BE-algebras in terms of level subalgebras of fuzzy BE-algebras.

• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.513-528
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• 2017

The concept of weak implicative filters is introduced in BE-algebras. Some characterizations of weak implicative filters are derived in terms of filters of a BE-algebra. Fuzzification is applied to the class of weak implicative filters. Some properties of fuzzy weak implicative filters are studied with respect to fuzzy relations and homomorphisms. The notion of triangular normed fuzzy weak implicative filters is introduced in BE-algebras and their properties are studied.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.795-807
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• 2009

The concepts of fuzzy pseudo ideals (resp. fuzzy pseudo p-ideals, associative fuzzy pseudo ideals, fuzzy pseudo q-ideals and fuzzy pseudo a-ideals) in a pseudo BCI-algebra are introduced, and related properties are investigated. Conditions for a fuzzy pseudo ideal to be a fuzzy pseudo p-ideal (resp. fuzzy pseudo q-ideal) are provided. A characterization and properties of an associative fuzzy pseudo ideal are given.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.522-525
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• 1998

Although each de Morgan algebra has not always fixed points(centers), it has always fixed cores, the natural extention of fixed points. Fixed cores, of they do not degenerate to fixed points, are Boolean algebras, It is also shown the necessary and sufficient condition a algebra to be a Kleene algebra(fuzzy algebra) is that it has just one fixed core.

• Kyungpook Mathematical Journal
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• v.55 no.1
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• pp.51-62
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• 2015

Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.