• Title/Summary/Keyword: fuzzy filter

Search Result 316, Processing Time 0.027 seconds

ON FUZZY FANTASTIC FILTERS OF LATTICE IMPLICATION ALGEBRAS

  • Jun, Young-Bae;Song, Seok-Zun
    • Journal of applied mathematics & informatics
    • /
    • v.14 no.1_2
    • /
    • pp.137-155
    • /
    • 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.

HESITANT FUZZY SET THEORY APPLIED TO FILTERS IN MTL-ALGEBRAS

  • Jun, Young Bae;Song, Seok-Zun
    • Honam Mathematical Journal
    • /
    • v.36 no.4
    • /
    • pp.813-830
    • /
    • 2014
  • The notions of a (Boolean, prime, ultra, good) hesitant fuzzy filter and a hesitant fuzzy MV -filter of an MTL-algebras are introduced, and their relations are investigated. Characterizations of a (Boolean, ultra) hesitant fuzzy filter are discussed. Conditions for a hesitant fuzzy set to be a hesitant fuzzy filter, and for a hesitant fuzzy filter to be a Boolean hesitant fuzzy filter are provided.

IMPLICATIVE FILTERS OF R0-ALGEBRAS BASED ON FUZZY POINTS

  • Jun, Young-Bae;Song, Seok-Zun
    • Communications of the Korean Mathematical Society
    • /
    • v.27 no.4
    • /
    • pp.669-687
    • /
    • 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.

FUZZY TRANSITIVE FILTERS OF BE-ALGEBRAS

  • Rao, M. Sambasiva
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.30 no.2
    • /
    • pp.213-226
    • /
    • 2017
  • The concept of fuzzy transitive filters is introduced in BE-algebras. Some sufficient conditions are established for every fuzzy filter of a BE-algebra to become a fuzzy transitive filter. Some properties of fuzzy transitive filters are studied with respect to fuzzy relations and cartesian products.

BCK- lters Based on Fuzzy Points with Threshold

  • Jun, Young-Bae;Song, Seok-Zun;Roh, Eun-Hwan
    • Kyungpook Mathematical Journal
    • /
    • v.51 no.1
    • /
    • pp.11-28
    • /
    • 2011
  • The notions of ($\overline{\in}$, $\overline{\in}{\vee}\overline{qk}$)-fuzzy BCK-filters and fuzzy BCK-filters with thresholds are introduced, and several related properties are investigated. Characterizations of such notions are displayed, and implication-based fuzzy BCK-filters are discussed.

NEW TYPES OF FUZZY BCK-FILTERS

  • Jun, Young-Bae
    • Honam Mathematical Journal
    • /
    • v.31 no.2
    • /
    • pp.157-166
    • /
    • 2009
  • Using more general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset, the notion of ($({\in},{\in}{\bigvee}q_{\kappa})$)-fuzzy BCK-filters is introduced, and related properties are investigated. Many characterizations of ($({\in},{\in}{\bigvee}q_{\kappa})$)-fuzzy BCK-filters are provided. Relations between an ($({\in},{\in}{\bigvee}q_{\kappa})$)-fuzzy BCK-filter and a fuzzy BCK-filter are established.

FUZZY n-FOLD POSITIVE IMPLICATIVE FILTERS IN LATTICE IMPLICATION ALGEBRAS

  • Jin, Young-Bae;Song, Seok-Zun
    • Journal of applied mathematics & informatics
    • /
    • v.13 no.1_2
    • /
    • pp.153-163
    • /
    • 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.

FUZZY FOLDNESS OF IMPLICATIVE ORDERED FILTERS IN IMPLICATIVE SEMIGROUPS

  • Jun, Young-Bae;Park, Chul-Hwan
    • Honam Mathematical Journal
    • /
    • v.29 no.2
    • /
    • pp.279-288
    • /
    • 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.

MORE GENERAL FORMS OF (∈, ∈ VQk) FUZZY FILTERS OF ORDERED SEMIGROUPS

  • Khan, Asghar;Muhammad, Shakoor;Khalaf, Mohammed M.
    • Honam Mathematical Journal
    • /
    • v.39 no.2
    • /
    • pp.199-216
    • /
    • 2017
  • In the paper [Y. B. Jun, B. Davvaz and A. Khan, Filters of ordered semigroups based on the fuzzy points, JIFS 24 (2013) 619-630]. Jun et al. discussed the notion of (${\in},{\in}{\vee}q_k$)-fuzzy left (resp., right) filters as a generalization of the notion of (${\in},{\in}{\vee}q$)-fuzzy left (resp., right) filters of ordered semigroups. In this article, we try to obtain a more general form that (${\in},{\in}{\vee}q_k$)-fuzzy left (resp., right) filters in ordered semigroups. The notion of (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filters is discussed, and several properties are investigated. Characterizations of an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filter are established. A condition for an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp., right) filter to be a fuzzy left (resp., right) filter is provided. The important achievement of the study with an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (right) filter is that the notion of an (${\in},{\in}{\vee}q_k$)-fuzzy left ( right) filter and hence an (${\in},{\in}{\vee}q$)-fuzzy left (resp. right) filter are special cases of an (${\in},{\in}{\vee}q_k^{\delta}$)-fuzzy left (resp. right) filter, and thus several results in published papers are becoming corollaries of our results obtained in this paper.

L-filters and L-filter convergence

  • Ko, Jung-Mi;Kim, Yong-Chan
    • International Journal of Fuzzy Logic and Intelligent Systems
    • /
    • v.9 no.1
    • /
    • pp.59-64
    • /
    • 2009
  • In this paper, we study the relations between L-fuzzy topologies and L-filters on a strictly two-sided, commutative quantale lattice L. We define an L-fuzzy neighborhood filter and introduce the notion of L-filter convergence in L-fuzzy topological spaces.