Some kinds of (C,CCq)-interval-valued fuzzy ideals of BCI-algebras

  • Authors:

  • Xueling Ma;Jianming Zhan;Bijan Davvaz;Young Bae Jun

  • Affiliations:

  • Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, PR China;Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, PR China;Department of Mathematics, Yazd University, Yazd, Iran;Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Republic of Korea

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

In this paper, we first introduce the notions of (positive implicative, implicative and commutative) interval-valued fuzzy ideals of BCI-algebras, which are generalizations of (positive implicative, implicative and commutative) fuzzy ideals, respectively, and investigate some of their related properties. The concept of quasi-coincidence of an interval-valued fuzzy point within an interval-valued fuzzy set is introduced. In fact, the concept is a generalized concept of quasi-coincidence of a fuzzy point within a fuzzy set. By using this new idea, we further introduce the notions of (positive implicative, implicative and commutative) (@?,@?@?q)-interval-valued fuzzy ideals of BCI-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval-valued fuzzy ideals are derived. The relationship among these generalized interval-valued fuzzy ideals of BCI-algebras is also considered.