Fuzzy implicative and Boolean filters of R0 algebras
The notions of fuzzy filters, fuzzy implicative filters and fuzzy Boolean filters are introduced in R0 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) ?x,y,z?L, f(x?z)?f(x?(z?y))?f(y?z), (4) ?x,y?L, f(x?y)=f(x?(y?y)), (5) ?x?L,n?1, f(nx)=f(x).
r0 algebra fuzzy implicative filter fuzzy boolean filter lattice implication algebra