New types of fuzzy filters of BL-algebras

This paper introduces the concepts of (alpha, beta)-fuzzy (implicative, positive implicative, fantastic) filters and (beta) over bar, (alpha) over bar -fuzzy (implicative, positive implicative, fantastic) filters of BL-algebras, where alpha, beta is an element of {is an element of(gamma), q(delta), is an element of gamma boolean AND q delta, is an element of gamma boolean OR q delta), (alpha) over bar, (beta) over bar is an element of ((is an element of(gamma)) over bar, (q(delta)) over bar, (is an element of(gamma)) over bar boolean AND (q(delta)) over bar, (is an element of(gamma)) over bar boolean OR (q(delta)) over bar}, alpha not equal is an element of gamma boolean AND q delta and (beta) over bar not equal (is an element of(gamma)) over bar boolean AND (q(delta)) over bar, and some related properties are investigated. Special attention is paid to ((is an element of(gamma)) over bar, (is an element of(gamma)) over bar boolean AND (q(delta)) over bar)-fuzzy (implicative, positive implicative, fantastic) filters and ((is an element of(gamma)) over bar, (is an element of(gamma)) over bar boolean OR (q(delta)) over bar)-fuzzy (implicative, positive implicative, fantastic) filters which are generalizations of (is an element of, is an element of boolean OR q)-fuzzy (implicative, positive implicative, fantastic) filters and ((is an element of) over bar, (is an element of) over bar boolean OR (q) over bar)-fuzzy (implicative, positive implicative, fantastic) filters studied in Ma et al. (2008, 2009) [34,35]. It also points out that Examples 3.1.2, 3.1.9, 3.2.2, 3.2.9 and 3.3.9 in Ma et al. (2009) [35] are incorrect. (C) 2010 Elsevier Ltd. All rights reserved.