• Title, Summary, Keyword: (implicative) filter

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ON POSITIVE IMPLICATIVE FILTERS IN BE-ALGEBRAS

  • Kim, Young Hee;Park, Jung Hee
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.3
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    • pp.419-426
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    • 2014
  • In this paper, we introduce the notion of a positive implicative filter in BE-algebras. We show that every positive implicative filter is a filter in BE-algebras. We give some examples that a filter may not be a positive implicative filter and also a positive implicative filter may be not an implicative filter in BE-algebras. We also give some equivalent conditions of a positive implicative filter in BE-algebras.

FUZZY FOLDNESS OF IMPLICATIVE ORDERED FILTERS IN IMPLICATIVE SEMIGROUPS

  • Jun, Young-Bae;Park, Chul-Hwan
    • Honam Mathematical Journal
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    • v.29 no.2
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    • pp.279-288
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    • 2007
  • The notion of fuzzy n-fold implicative ordered filters in implicative semigroups is introduced, and related properties are investigated. Relations between fuzzy ordered filters and fuzzy n-fold implicative ordered filters are provided. Characterizations of a fuzzy n-fold implicative ordered filter are given, and an extension property for a fuzzy n-fold implicative ordered filter is obtained.

IMPLICATIVE ORDERED FILTERS OF IMPLICATIVE SEMIGROUPS

  • Jun, Young-Bae
    • Communications of the Korean Mathematical Society
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    • v.14 no.1
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    • pp.47-55
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    • 1999
  • This paper continues the investigations of implicative semigroups and of their ordered filters which were started in general case by M.W. Chan and K. P. Shum [3]. In particular, the notion of an implicative ordered filter of an implicative semigroup is introduced. We state some equivalent conditions for an ordered filter to be an implicative ordered filter and obtain the so called extension property for implicative ordered filters.

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Positive implicative and associative filters of lattice implication algebras

  • Jun, Young-Bae;Yang Xu;Keyun Qin
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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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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IMPLICATIVE FILTERS OF R0-ALGEBRAS BASED ON FUZZY POINTS

  • Jun, Young-Bae;Song, Seok-Zun
    • Communications of the Korean Mathematical Society
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    • v.27 no.4
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    • pp.669-687
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    • 2012
  • As a generalization of the concept of a fuzzy implicative filter which is introduced by Liu and Li [3], the notion of (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filters is introduced, and related properties are investigated. The relationship between (${\in}$, ${\in}{\vee}q_k$)-fuzzy filters and (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filters is established. Conditions for an (${\in}$, ${\in}{\vee}q_k$)-fuzzy filter to be an (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filter are considered. Characterizations of an (${\in}$, ${\in}{\vee}q_k$)-fuzzy implicative filter are provided, and the implication-based fuzzy implicative filters of an $R_0$-algebra is discussed.

ON n-FOLD IMPLICATIVE VAGUE FILTERS IN BE-ALGEBRAS

  • Park, Sang-Tae;Ahn, Sun-Shin
    • The Pure and Applied Mathematics
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    • v.19 no.2
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    • pp.127-136
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    • 2012
  • In this paper, we introduce the notion of an implicative vague filter in BE-algebras, and investigate some properties of them. Also we give conditions for a vague set to be an implicative vague filter, and we characterize implicative vague filters in BE-algebras. We define the notion of $n$-fold implicative vague filters in BE-algebras and we give characterizations of $n$-fold implicative vague filters and $n$-fold implicative BE-algebras.

INT-SOFT POSITIVE IMPLICATIVE FILTERS IN BE-ALGEBRAS

  • PARK, JUNG HEE;KIM, YOUNG HEE
    • Journal of applied mathematics & informatics
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    • v.33 no.3_4
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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.

WEAK IMPLICATIVE FILTERS OF BE-ALGEBRAS

  • RAO, M. SAMBASIVA
    • Journal of applied mathematics & informatics
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    • v.35 no.5_6
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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.

INT-SOFT FILTERS IN LATTICE IMPLICATION ALGEBRAS

  • Jun, Young Bae;Xu, Yang;Zhang, Xiaohong
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1483-1495
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    • 2016
  • The notion of int-soft (implicative) filters in lattice implication algebras is introduced, and related properties are investigated. Characterizations of int-soft (implicative) filters are discussed. Conditions for an int-soft filter to be an int-soft implicative filter are provided. Extension property for int-soft implicative filters is established.