• Title/Summary/Keyword: (Implicative) ideal

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SOME RESULTS ON FUZZY IDEAL EXTENSIONS OF BCK-ALGEBRAS

  • Jeong, Won-Kyun
    • East Asian mathematical journal
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    • v.26 no.3
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    • pp.379-387
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    • 2010
  • In this paper, we prove that the extension ideal of a fuzzy characteristic ideal of a positive implicative BCK-algebra is a fuzzy characteristic ideal. We introduce the notion of the extension of intuitionistic fuzzy ideal of BCK-algebras and some properties of fuzzy intuitionistic ideal extensions of BCK-algebra are investigated.

SMARANDACHE d-ALGEBRAS

  • Kim, Young Hee;Kim, Young Hie;Ahn, Sun Shin
    • 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.

FSI-IDEALS AND FSC-IDEALS OF BCI-ALGEBRAS

  • Liu, Yong-Lin;Liu, San-Yang;Meng, Jie
    • 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.

C(S) extensions of S-I-BCK-algebras

  • Zhaomu Chen;Yisheng Huang;Roh, Eun-Hwan
    • 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.

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SOFT SET THEORY APPLIED TO COMMUTATIVE IDEALS IN BCK-ALGEBRAS

  • Jun, Young-Bae;Lee, Kyoung-Ja;Park, Chul-Hwan
    • 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.

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BCK-ALGEBRAS INDUCED BY EXTENDED POGROUPOIDS

  • Ahn, Sun Shin;Kim, Hee Sik
    • Journal of the Chungcheong Mathematical Society
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    • v.11 no.1
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    • pp.53-58
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    • 1998
  • In this paper we study (positive) implicativeness of $BCK^{\star}(X^{\star})$, and investigate some properties of ideals in $BCK^{\star}(X)$.

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ON KERNELS AND ANNIHILATORS OF LEFT-REGULAR MAPPINGS IN d-ALGEBRAS

  • Ahn, Sun-Shin;So, Keum-Sook
    • Honam Mathematical Journal
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    • v.30 no.4
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    • pp.645-658
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    • 2008
  • In this paper, left-regular maps on d-algebras are defined. These mappings show behaviors reminiscent of homomorphisms on d-algebras which have been studied elsewhere. In particular for these mappings kernels, annihilators and co-annihilators are defined and some of their properties are investigated, especially in the setting of positive implicative d-algebras.