Interval valued -fuzzy filters of pseudo BL-algebras

  • Authors:

  • Jianming Zhan;Wiesław A. Dudek;Young Bae Jun

  • Affiliations:

  • Hubei Institute for Nationalities, Enshi, Department of Mathematics, 445000, Hubei Province, People’s Republic of China;Wrocław University of Technology, Institute of Mathematics and Computer Science, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland;Gyeongsang National University, Department of Mathematics Education, Wybrzeże Wyspiańskiego 27, 660-701, Chinju, South Korea

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications
  • Year:
  • 2008

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Abstract

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued -fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo BL-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo BL-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.