Fuzzy anti-grouped filters and fuzzy normal filters in pseudo- BCI algebras
Xiaohong Zhang · Journal of Intelligent & Fuzzy Systems · 2017
The notions of fuzzy anti-grouped filter and fuzzy normal filter in pseudo- BCI algebra are introduced, some properties and equivalent conditions are presented. A counterexample is constructed to show that a fuzzy anti-grouped filter may be not a fuzzy p -filter, by this, a mistake in some literatures is revised. The relationships among some special kinds of fuzzy filters are discussed, the following results are proved: (1) a fuzzy filter of a pseudo- BCI algebra X is fuzzy p -filter if and only if it is both a fuzzy normal filter and a fuzzy anti-grouped filter of X ; (2) a fuzzy filter of a pseudo- BCI algebra X is a fuzzy associative filter if and only if it is both a fuzzy anti-grouped filter and a fuzzy T -type filter of X , if and only if it is both a fuzzy anti-grouped filter and a fuzzy q -filter of X . Moreover, a method for constructing new fuzzy anti-grouped filter via any fuzzy filter is proposed.