• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.443-451
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• 2005

The notion of grisly deductive systems of a BL-algebra is introduced. Conditions for a deductive system to be a grisly deductive system are given. Extension property for a grisly deductive system is established

• Honam Mathematical Journal
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• v.28 no.1
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• pp.45-56
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• 2006

We give characterizations of a deductive system of a BL-algebra, and discuss how to generate a deductive system by a set.

• 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.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.445-453
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• 2007

The notion of strong deductive system of a BL-algebra is introduced, and a characterization of a strong deductive system is given. A relation between a strong deductive system and a deductive system is given. It will be seen that every strong deductive system can be expressed as the union of special sets.

• Honam Mathematical Journal
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• v.40 no.3
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• pp.539-548
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• 2018

The notions of Smarandache (positive implicative, commutative, implicative) d-algebras, Smarandache subalgebras of Smarandache d-algebras and Smarandache BCK-ideals(d-ideals) of a Smarandache d-algebras are introduced. Examples are given, and several related properties are investigated.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.499-518
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• 1995

In this paper we consider more systematically the centralizer C(S) of the set $S = {f_a $\mid$ f_a : X \to X ; x \longmapsto x * a, a \in X}$ with respect to the semigroup End(X) of all endomorphisms of an implicative BCK-algebra X with the condition (S). We obtain a series of interesting results. The main results are stated as follows : (1) C(S) with repect to a binary operation * defined in a certain way forms a bounded implicative BCK-algebra with the condition (S). (2) X can be imbedded in C(S) such that X is an ideal of C(S)/ (3) If X is not bounded, it can be imbedded in a bounded subalgebra T of C(S) such that X is a maximal ideal of T. (4) If $X (\neq {0})$ is semisimple, C(S) is BCK-isomorphic to $\prod_{i \in I}{A_i}$ in which ${A_i}_{i \in I}$ is simple ideal family of X.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.707-720
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• 2008

Molodtsov [12] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to commutative ideals of BCK-algebras, The notions of commutative soft ideals and commutative idealistic soft BCK-algebras are introduced, and their basic properties are investigated. Examples to show that there is no relations between positive implicative idealistic soft BCK-algebras and commutative idealistic soft BCK-algebras are provided.

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.167-179
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• 2004

The notions of FSI-ideals and FSC-ideals in BCI-algebras are introduced. The characterization properties of FSI-ideals and FSC-ideals are obtained. We investigate the relations between FSI-ideals (resp. FSC-ideals) and other fuzzy ideals, between FSI-ideals (resp. FSC-ideals) and BCI-algebras, and show that a fuzzy subset of a BCI-algebra is an FSI-ideal if and only if it is both an FSC-ideal and a fuzzy BCI-positive implicative ideal.

• The Pure and Applied Mathematics
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• v.18 no.4
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• pp.293-304
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• 2011

The notions of an initial section and a special set in BH-algebras are defined and some of their properties are obtained. The notion of a complicated BH-algebra is introduced and some related properties are obtained. Finally, the notion of essences in BH-algebras are defined, and many properties are investigated.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.17-27
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• 2013

The notions of the extensions of bipolar fuzzy ideals, bipolar fuzzy prime ideals and bipolar fuzzy commutative ideals in BCK-algebras are introduced, and several properties are investigated.