• Title/Summary/Keyword: Pseudo-BCK-algebra

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FUZZY PSEUDO-IDEALS OF PSEUDO-BCK ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun
    • Journal of applied mathematics & informatics
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    • v.12 no.1_2
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    • pp.243-250
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    • 2003
  • The fuzzification of (Positive implicative) pseudo-ideals in a pseudo-BCK algebra is discussed, and several properties are investigated. Characterizations of a fuzzy pseudo-ideal are displayed.

PSEUDO-BCI ALGEBRAS

  • Dudek, Wieslaw A.;Jun, Young-Bae
    • East Asian mathematical journal
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    • v.24 no.2
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    • pp.187-190
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    • 2008
  • As a generalization of BCI-algebras, the notion of pseudo-BCI algebras is introduced, and some of their properties are investigated. Characterizations of pseudo-BCI algebras are established. Some conditions for a pseudo-BCI algebra to be a pseudo-BCK algebra are given.

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BCK/BCI-ALGEBRAS WITH PSEUDO-VALUATIONS

  • Doh, Myung-Im;Kang, Min-Su
    • Honam Mathematical Journal
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    • v.32 no.2
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    • pp.217-226
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    • 2010
  • Using the Bu$\c{s}$neag's model ([1, 2, 3]), the notion of pseudo-valuations (valuations) on a ${\mathbf{BCK/BCI}}$-algebra is introduced, and a pseudo-metric is induced by a pseudo-valuation on ${\mathbf{BCK/BCI}}$-algebras. Based on the notion of (pseudo) valuation, we show that the binary operation in ${\mathbf{BCK/BCI}}$-algebras is uniformly continuous.

Fuzzy Prime Ideals of Pseudo- ŁBCK-algebras

  • Dymek, Grzegorz;Walendziak, Andrzej
    • Kyungpook Mathematical Journal
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    • v.55 no.1
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    • pp.51-62
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    • 2015
  • Pseudo-ŁBCK-algebras are commutative pseudo-BCK-algebras with relative cancellation property. In the paper, we introduce fuzzy prime ideals in pseudo-ŁBCK-algebras and investigate some of their properties. We also give various characterizations of prime ideals and fuzzy prime ideals. Moreover, we present conditions for a pseudo-ŁBCKalgebra to be a pseudo-ŁBCK-chain.

Quasi-Valuation Maps on BCK/BCI-Algebras

  • SONG, SEOK-ZUN;ROH, EUN HWAN;JUN, YOUNG BAE
    • Kyungpook Mathematical Journal
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    • v.55 no.4
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    • pp.859-870
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    • 2015
  • The notion of quasi-valuation maps based on a subalgebra and an ideal in BCK/BCI-algebras is introduced, and then several properties are investigated. Relations between a quasi-valuation map based on a subalgebra and a quasi-valuation map based on an ideal is established. In a BCI-algebra, a condition for a quasi-valuation map based on an ideal to be a quasi-valuation map based on a subalgebra is provided, and conditions for a real-valued function on a BCK/BCI-algebra to be a quasi-valuation map based on an ideal are discussed. Using the notion of a quasi-valuation map based on an ideal, (pseudo) metric spaces are constructed, and we show that the binary operation * in BCK-algebras is uniformly continuous.

PSEUDO P-CLOSURE WITH RESPECT TO IDEALS IN PSEUDO BCI-ALGEBRAS

  • MOUSSAEI, HOSSEIN;HARIZAVI, HABIB
    • Journal of applied mathematics & informatics
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    • v.38 no.1_2
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    • pp.65-77
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    • 2020
  • In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by ApcI, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that Apc{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which ApcI = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.

ON MINIMALITY IN PSEUDO-BCI-ALGEBRAS

  • Kim, Young-Hee;So, Keum-Sook
    • Communications of the Korean Mathematical Society
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    • v.27 no.1
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    • pp.7-13
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    • 2012
  • In this paper we consider pseudo-BCK/BCI-algebras. In particular, we consider properties of minimal elements ($x{\leq}a$ implies x = a) in terms of the binary relation $\leq$ which is reflexive and anti-symmetric along with several more complicated conditions. Some of the properties of minimal elements obtained bear resemblance to properties of B-algebras in case the algebraic operations $\ast$ and $\circ$ are identical, including the property $0{\circ}(0{\ast}a)$ = a. The condition $0{\ast}(0{\circ}x)=0{\circ}(0{\ast}x)=x$ all $x{\in}X$ defines the class of p-semisimple pseudo-BCK/BCI-algebras($0{\leq}x$ implies x = 0) as an interesting subclass whose further properties are also investigated below.