Generalized fuzzy filters of R 0-algebras

Abstract

In this paper, we introduce the notions of interval valued $${(\in,\in\vee q)}$$-fuzzy filters and interval valued $${(\in,\in\vee q)}$$-fuzzy Boolean (implicative) filters in R 0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that an interval valued fuzzy set F in R 0-algebras is an interval valued $${(\in,\in\vee q)}$$-fuzzy Boolean filter if and only if it is an interval valued $${(\in,\in\vee q)}$$-fuzzy implicative filter.