Some types of generalized fuzzy filters of BL-algebras

The aim of this paper is to introduce the notions of interval valued (epsilon, epsilon vq)-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 (epsilon, epsilon vq)-fuzzy filter in BL-algebras is an interval valued (epsilon, epsilon vq)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (epsilon, epsilon vq)-fuzzy positive implicative filter and an interval valued (epsilon, epsilon vq)-fuzzy fantastic filter. (c) 2008 Elsevier Ltd. All rights reserved.