• 제목/요약/키워드: Implicative algebra

검색결과 52건 처리시간 0.021초

Weak positive implicative hyperBCK-ideal

  • Kim, Y.H.;Namkoong, Y.M.;T.E. Jeong
    • 한국지능시스템학회논문지
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    • 제13권2호
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    • pp.243-246
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    • 2003
  • In this paper we define a weak positive implicative hyperBCK-ideal of hyperBCK-algebra. Also we investigate that every positive implicative hyperBCK-algebra is a positive implicative hyperK-algebra and then we prove that every positive implicative hyperK-algebra is a weak positive implicative hyperk-algebra.

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

  • Liu, Yong-Lin;Jie Meng
    • Journal of applied mathematics & informatics
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    • 제10권1_2호
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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.

FUZZY IMPLICATIVE ALGEBRAS

  • Jun, Young-Bae;Kim, Hee-Sik
    • 대한수학회보
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    • 제36권1호
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    • pp.109-117
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    • 1999
  • We introduce the notion of a fuzzy topological implicative algebras and apply some of Foster's results [2] to homomorphic images and inverse images of fuzzy topological implicative algebras.

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(WEAK) IMPLICATIVE HYPER K-IDEALS

  • Saeid, A.Borumand;Borzooei, R.A.;Zahedi, M.M.
    • 대한수학회보
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    • 제40권1호
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    • pp.123-137
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    • 2003
  • In this note first we define the notions of weak implicative and implicative hyper K-ideals of a hyper K-algebra H. Then we state and prove some theorems which determine the relationship between these notions and (weak) hyper K-ideals. Also we give some relations between these notions and all types of positive implicative hyper K-ideals. Finally we classify the implicative hyper K-ideals of a hyper K-algebra of order 3.

WEAK IMPLICATIVE FILTERS OF BE-ALGEBRAS

  • RAO, M. SAMBASIVA
    • Journal of applied mathematics & informatics
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    • 제35권5_6호
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    • pp.513-528
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    • 2017
  • The concept of weak implicative filters is introduced in BE-algebras. Some characterizations of weak implicative filters are derived in terms of filters of a BE-algebra. Fuzzification is applied to the class of weak implicative filters. Some properties of fuzzy weak implicative filters are studied with respect to fuzzy relations and homomorphisms. The notion of triangular normed fuzzy weak implicative filters is introduced in BE-algebras and their properties are studied.

Implicative filters of lattice implication algebras

  • Jun, Young-Bae
    • 대한수학회보
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    • 제34권2호
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    • pp.193-198
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    • 1997
  • In order to research the logical system whose propositional value is given in a lattice, Y. Xu [4] proposed the concept of lattice implication algebras, and discussed their some properties in [3] and [4]. Y. Xu and K. Qin [5] introduced the notions of filter and implicative filter in a lattice implication algebra, and investigated their properties. In this paper, in the first place, we give an equivalent condition of a filter, and provide some equivalent conditions that a filter is an implicative filter in a lattice implication algebra. By using these results, we construct an extension property for implicative filter.

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INT-SOFT POSITIVE IMPLICATIVE FILTERS IN BE-ALGEBRAS

  • PARK, JUNG HEE;KIM, YOUNG HEE
    • Journal of applied mathematics & informatics
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    • 제33권3_4호
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    • pp.459-467
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    • 2015
  • The notion of int-soft implicative filters of a BE-algebra is introduced, and related properties are investigated. The problem of clas- sifying int-soft positive implicative by their γ-inclusive filter is solved. We provide conditions for a soft set to be an int-soft filter. We make a new int-soft implicative filter from old one.

Positive implicative and associative filters of lattice implication algebras

  • Jun, Young-Bae;Yang Xu;Keyun Qin
    • 대한수학회보
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    • 제35권1호
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    • pp.53-61
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    • 1998
  • We introduce the concepts of a positive implicative filter and an associative filter in a lattice implication algebra. We prove that (i) every positive implicative filter is an implicative filter, and (ii) every associative filter is a filter. We provide equivalent conditions for both a positive implicative filter and an associative filter.

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ON FUZZY IMPLICATIVE FILTERS OF LATTICE IMPLICATION ALGEBRAS

  • Zhu, Yiquan;Zhang, Qun;Roh, Eun-Hwan
    • 대한수학회논문집
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    • 제18권4호
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    • pp.621-628
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    • 2003
  • We investigate some related properties of fuzzy filters and fuzzy implicative filters in lattice implication algebras. We find a characterization of fuzzy filters and fuzzy implicative filters, and we discuss a relation between fuzzy filters and fuzzy implicative filters in lattice implication algebras. Also we give an extension theorem of fuzzy implicative filters.