• Title/Summary/Keyword: (fuzzy) quasi-associative ideal

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FUZZIFICATIONS OF FOLDNESS OF QUASI-ASSOCIATIVE IDEALS IN BCI-ALGEBRAS

  • Jun, Young-Bae;Kim, Kyung-Ho
    • Journal of applied mathematics & informatics
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    • v.11 no.1_2
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    • pp.255-263
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    • 2003
  • Fuzzifications of n-fold quasi-associative ideals are considered. Conditions for a fuzzy ideal to be a fuzzy n-fold quasi-associative ideal are given. Using a collection of n-fold quasi-associative ideals, fuzzy n-fold quasi-associative ideals are constructed. Finally, the extension property for fuzzy n-fold quasi-associative ideals is established.

QUASI-ASSOCIATIVE IDEALS IN BCI-ALGEBRAS BASED ON BIPOLAR-VALUED FUZZY SETS

  • Jun, Young-Bae;Kim, Seon-Yu;Roh, Eun-Hwan
    • Honam Mathematical Journal
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    • v.31 no.1
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    • pp.125-136
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    • 2009
  • After the introduction of fuzzy sets by Zadeh, there have been a number of generaizations of this fundamental concept. The notion of bipolar-valued fuzzy sets introduced by Lee is one among them. In this paper, we apply the concept of a bipolar-valued fuzzy set to quasi-associative ideals in BCI-algebras. The notion of a bipolar fuzzy quasi-associative ideal of a BCI-algebra is introduced, and some related properties are investigated. Characterizations of a bipolar fuzzy quasi-associative ideal are given. Extension property for a bipolar fuzzy QA-ideal is established.

HESITANT FUZZY p-IDEALS AND QUASI-ASSOCIATIVE IDEALS IN BCI-ALGEBRAS

  • Jun, Young Bae;Roh, Eun Hwan;Ahn, Sun Shin
    • Honam Mathematical Journal
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    • v.44 no.2
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    • pp.148-164
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    • 2022
  • The main purpose of this paper is to apply the notion of hesitant fuzzy sets to an algebraic structure, so called a BCI-algebra. The primary goal of the study is to define hesitant fuzzy p-ideals and hesitant fuzzy quasi-associative ideals in BCI-algebras, and to investigate their properties and relations.

CONSTRUCTION OF QUOTIENT BCI(BCK)-ALGEBRA VIA A FUZZY IDEAL

  • Liu, Yong-Lin;Jie Meng
    • 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.