• 제목/요약/키워드: fuzzy implication algebra

검색결과 12건 처리시간 0.018초

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.

FUZZY n-FOLD POSITIVE IMPLICATIVE FILTERS IN LATTICE IMPLICATION ALGEBRAS

  • Jin, Young-Bae;Song, Seok-Zun
    • Journal of applied mathematics & informatics
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    • 제13권1_2호
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    • pp.153-163
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    • 2003
  • The fuzzification of a positive implicative filter is considered, and some of properties are investigated. The relation among fussy filter, fuzzy n-fold implicative filter, and fuzzy n-fold positive implication filter is discussed.

ON FUZZY FANTASTIC FILTERS OF LATTICE IMPLICATION ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun
    • Journal of applied mathematics & informatics
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    • 제14권1_2호
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    • pp.137-155
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    • 2004
  • Fuzzification of a fantastic filter in a lattice implication algebra is considered. Relations among a fuzzy filter, a fuzzy fantastic filter, and fuzzy positive implicative filter are stated. Conditions for a fuzzy filter to be a fuzzy fantastic filter are given. Using the notion of level set, a characterization of a fuzzy fantastic filter is considered. Extension property for fuzzy fantastic filters is established. The notion of normal/maximal fuzzy fantastic filters and complete fuzzy fantastic filters is introduced, and some related properties are investigated.

A NEW CONGRUENCE RELATION ON LATTICE IMPLICATION ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun
    • Journal of applied mathematics & informatics
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    • 제13권1_2호
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    • pp.385-392
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    • 2003
  • Using a fuzzy filter, a new congruence relation induced by the fuzzy filter is given in lattice implication algebras, and some of their properties are investigated.

ON FP-FILTERS AND FPD-FILTERS OF LATTICE IMPLICATION ALGEBRA

  • Lai, Jiajun;Xu, Yang;Chang, Zhiyan
    • Journal of applied mathematics & informatics
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    • 제26권3_4호
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    • pp.653-660
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    • 2008
  • In this paper, we consider the fuzzification of prime filters in Lattice Implication Algebras (briefly, LIAs), and introduce the concepts of fuzzy prime filters (briefly, FP-filters), and we also studied the properties of FP-filters. Finally, we investigate the properties of fuzzy prime dual filters (briefly, FPD-filters) in LIA, and the relations of them are investigated.

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ON FUZZY CLOSEDNESS IN LATTICE IMPLICATION ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun;Roh, Eun-Hwan
    • Journal of applied mathematics & informatics
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    • 제11권1_2호
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    • pp.341-355
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    • 2003
  • The fuzzification of ${\bigotimes}-closed$ set is considered, and its basic properties we investigated. Characterizations of fuazzy ${\bigotimes}-closed$ set we given. Using a collection of ${\bigotimes}-closed$ sets with additional conditions, a fuzzy ${\bigotimes}-closed$ set is stated. The theory of fuzzy topological ${\bigotimes}-closed$ sets is discussed.

IMPLICATIVE FILTERS OF R0-ALGEBRAS BASED ON FUZZY POINTS

  • Jun, Young-Bae;Song, Seok-Zun
    • 대한수학회논문집
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    • 제27권4호
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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.