• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.537-545
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• 2010

The notions of (weak) hyper MV-deductive systems and (weak) implicative hyper MV-deductive systems are introduced, and several properties are investigated. Relations among hyper MV-deductive systems, weak hyper MV-deductive systems, implicative hyper MV-deductive systems and weak implicative hyper MV-deductive systems are discussed. A characterization of a hyper MV-deductive system is provided. A condition for a weak hyper MV-deductive system to be a weak implicative hyper MV-deductive system is given.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.499-505
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• 1997

This paper is a continuation of [3]. We prove that if A is quasi-associative (resp. an implicative) ideal of a BCI-algebra X then the k-nil radical of A is a quasi-associative (resp. an implicative) ideal of X. We also construct the quotient algebra $X/[Z;k]$ of a BCI-algebra X by the k-nhil radical [A;k], and show that if A and B are closed ideals of BCI-algebras X and Y respectively, then

• Journal of applied mathematics & informatics
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• v.34 no.5_6
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• pp.527-536
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• 2016

In this paper, we introduce the notions about int-soft mighty filters, int-soft n-fold mighty filters, and int-soft n-fold positive implicative filters of BE-algebras. We investigate their properties and provide conditions which have connecting relationship among int-soft filters, int-soft mighty filters, and int-soft positive implicative filters. Also, characterizations of int-soft n-fold mighty filters and int-soft n-fold positive implicative filters are provided in BE-algebras.

• 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.28 no.4
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• pp.709-721
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• 2013

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

• 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

• Honam Mathematical Journal
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• v.27 no.4
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• pp.561-570
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• 2005

In this paper, we introduce the notion of positive implicative subtraction algebras and study some relations between R(L)-maps and positive implicativity in subtraction algebras.

• Honam Mathematical Journal
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• v.27 no.2
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• pp.141-162
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• 2005

In this paper, by considering the notion of hyperK-algebras of order 3 (which satisfies the simple or normal condition), we state and prove some theorems which determine the relationships between (weak) hyperK-ideals and positive implicative hyperK-ideals of type $1,{\ldots},8$.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.323-333
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• 2009

We introduce the concepts of a fuzzifying filter and a fuzzifying implicative filter in lattice implication algebras.

• Journal of the Chungcheong Mathematical Society
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• v.13 no.2
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• pp.53-59
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• 2001

In this paper, we introduce the notion of positive implicative BH-algebras and study some relations between R - (L-) maps and positive implicativity in BH-algebras.