Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras

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.