• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-470
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• 2006

As a continuation of [4], characterizations of fuzzy implicative ideals are given. An extension property for fuzzy implicative ideals is established. We prove that the family of fuzzy implicative ideals is a completely distributive lattice. Using level subsets of a BCk-algebra X with respect to a fuzzy set $\={A}$ in X, we construct a fuzzy implicative ideal of X containing $\={A}$.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.177-189
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• 2005

We obtain characterizations of T-fuzzy (implicative) filters and some properties of T-product of fuzzy (implicative) filters in lattice implication algebras. We also establish the extension property for T-fuzzy implicative filters.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.369-383
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• 2007

This paper is devoted to the foldness theory of implicative ideals in BCK-algebras. We use the fuzzy point concept to give some characterizations of fuzzy n-fold implicative ideals and establish some relationships with various n-fold ideals. We also construct some algorithms for studying the foldness of implicative ideals in BCK-algebras.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.505-512
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• 2008

The notion of positive implicative Smarandache BCC-ideals is introduced, and related properties are investigated. Relations between Smarandache BCC-ideals and positive implicative Smarandache BCC-ideals are discussed. The extension property of a positive implicative Smarandache BCC-ideals is given.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.535-559
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• 2022

The notions of cubic intuitionistic fuzzy set to filters and implicative filters of BE-algebras are introduced. Relations between cubic intuitionistic fuzzy filters with cubic intuitionistic fuzzy implicative filters of BE-algebras are investigated. The homomorphic image and inverse image of cubic intuitionistic fuzzy filters are studied and some related properties are investigated. Also, the product of cubic intuitionistic fuzzy subalgebras (implicative filters) of BE-algebras are investigated.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.475-489
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• 2006

After the introduction of fuzzy sets by Zadeh [8], there have been a number of generalizations of fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. An intuitionistic fuzzy set is also called a bifuzzy set according to [5]. In this paper, we apply the concept of a bifuzzy set to (implicative) ideals in pseudo MV-algebras. The notion of a bifuzzy (implicative) ideal of a pseudo MV-algebra is introduced, and some related properties are investigated. Conditions for a bifuzzy set to be a bifuzzy ideal are given, and characterizations of a bifuzzy (implicative) ideal are provided. Using a family of ideals, bifuzzy ideals are established.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.669-687
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• 2012

As a generalization of the concept of a fuzzy implicative filter which is introduced by Liu and Li [3], the notion of (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filters is introduced, and related properties are investigated. The relationship between (${\in}$, ${\in}{\vee}q_k$)-fuzzy filters and (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filters is established. Conditions for an (${\in}$, ${\in}{\vee}q_k$)-fuzzy filter to be an (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filter are considered. Characterizations of an (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filter are provided, and the implication-based fuzzy implicative filters of an $R_0$-algebra is discussed.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.377-402
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• 2007

After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to implicative ideals in BCK-algebras. The notion of an intuitionistic fuzzy implicative ideal of a BCK-algebra is introduced, and some related properties are investigated. An extension property for intuitionistic fuzzy implicative ideals is established. Characterizations of an intuitionistic fuzzy implicative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy implicative ideal are given. Using a collection of implicative ideals, intuitionistic fuzzy implicative ideals are established.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.303-303
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• 2019

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1489-1500
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• 2011

The notions of $\mathcal{N}$-subalgebra, (positive implicative) $\mathcal{N}$-ideals of d-algebras are introduced, and related properties are investigated. Characterizations of an $\mathcal{N}$-subalgebra and a (positive implicative) $\mathcal{N}$-ideals of d-algebras are given. Relations between an $\mathcal{N}$-subalgebra, an $\mathcal{N}$-ideal and a positive implicative N-ideal of d-algebras are discussed.