• Title/Summary/Keyword: intuitionistic fuzzy (implicative) ideal

Search Result 3, Processing Time 0.015 seconds

INTUITIONISTIC FUZZINESS OF IMPLICATIVE IDEALS IN BCK-ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan;Roh, Eun-Hwan
    • Honam Mathematical Journal
    • /
    • v.29 no.3
    • /
    • pp.377-402
    • /
    • 2007
  • After the introduction of fuzzy sets by Zadeh, there have been a number of generalizations of this fundamental concept. The notion of intuitionistic fuzzy sets introduced by Aranassov is one among them. In this paper, we apply the concept of an intuitionistic fuzzy set to implicative ideals in BCK-algebras. The notion of an intuitionistic fuzzy implicative ideal of a BCK-algebra is introduced, and some related properties are investigated. An extension property for intuitionistic fuzzy implicative ideals is established. Characterizations of an intuitionistic fuzzy implicative ideal are given. Conditions for an intuitionistic fuzzy ideal to be an intuitionistic fuzzy implicative ideal are given. Using a collection of implicative ideals, intuitionistic fuzzy implicative ideals are established.

SOME RESULTS ON FUZZY IDEAL EXTENSIONS OF BCK-ALGEBRAS

  • Jeong, Won-Kyun
    • East Asian mathematical journal
    • /
    • v.26 no.3
    • /
    • pp.379-387
    • /
    • 2010
  • In this paper, we prove that the extension ideal of a fuzzy characteristic ideal of a positive implicative BCK-algebra is a fuzzy characteristic ideal. We introduce the notion of the extension of intuitionistic fuzzy ideal of BCK-algebras and some properties of fuzzy intuitionistic ideal extensions of BCK-algebra are investigated.

BIFUZZY IDEALS OF PSEUDO MV-ALGEBRAS

  • Cho Yong-Uk;Jun Young-Bae;Song Seok-Zun
    • Journal of applied mathematics & informatics
    • /
    • v.22 no.1_2
    • /
    • pp.475-489
    • /
    • 2006
  • After the introduction of fuzzy sets by Zadeh [8], there have been a number of generalizations of fundamental concept. The notion of intuitionistic fuzzy sets introduced by Atanassov is one among them. An intuitionistic fuzzy set is also called a bifuzzy set according to [5]. In this paper, we apply the concept of a bifuzzy set to (implicative) ideals in pseudo MV-algebras. The notion of a bifuzzy (implicative) ideal of a pseudo MV-algebra is introduced, and some related properties are investigated. Conditions for a bifuzzy set to be a bifuzzy ideal are given, and characterizations of a bifuzzy (implicative) ideal are provided. Using a family of ideals, bifuzzy ideals are established.