Some types of generalized fuzzy filters of BL-algebras

Authors:
Jianming Zhan;Yang Xu
Affiliations:
Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, PR China;Department of Applied Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China
Venue:
Computers & Mathematics with Applications
Year:
2008

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Abstract

The aim of this paper is to introduce the notions of interval valued (@?,@?@?q)-fuzzy Boolean (implicative, positive implicative and fantastic) filters in BL-algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued (@?,@?@?q)-fuzzy filter in BL-algebras is an interval valued (@?,@?@?q)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (@?,@?@?q)-fuzzy positive implicative filter and an interval valued (@?,@?@?q)-fuzzy fantastic filter.