Fuzzy implicative and Boolean filters of R-0 algebras
The notions of fuzzy filters, fuzzy implicative filters and fuzzy Boolean filters are introduced in R-0 algebras, respectively. Some of their properties are investigated. The relations between fuzzy implicative filters and fuzzy Boolean filters are discussed. The characterizations of fuzzy implicative filters are studied and the following is proved to be equivalent (1) a fuzzy filter f is implicative, (2) f is a fuzzy Boolean filter, (3) For Allx,y, z is an element of L, f (x --> z) greater than or equal to f (x --> (-z --> y)) boolean AND f (y --> z), (4) For Allx, y is an element of L, f (x --> y) = f (x --> (-y --> y)), (5) For Allx is an element of L, n greater than or equal to 1, f(nx) = f (x). (C) 2004 Elsevier Inc. All rights reserved.
r-0 algebra fuzzy implicative filter fuzzy boolean filter lattice implication algebra