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INTUITIONISTIC FUZZINESS OF IMPLICATIVE IDEALS IN BCK-ALGEBRAS

Jun, Young-Bae;Park, Chul-Hwan;Roh, Eun-Hwan

  • Received : 2007.05.25
  • Accepted : 2007.08.28
  • Published : 2007.09.25

Abstract

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.

Keywords

(Implicative) ideal;intuitionistic fuzzy (implicative) ideal

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