Abstract
A new notion of fuzzy T-type filter in pseudo-BCI algebra is introduced, some properties and equivalent conditions are presented. The relationship among fuzzy T-type filters, fuzzy q-filters and fuzzy associative filters are discussed, the following results are proved: (1) every fuzzy q-filter of a pseudo-BCI algebra X is a fuzzy T-type filter of X; (2) a fuzzy filter of a pseudo-BCI algebra X is a fuzzy associative filter of X if and only if it is both a fuzzy T-type filter and a fuzzy p-filter of X. For a fuzzy T-type filter to be a fuzzy q-filter, necessary and sufficient conditions are given. Moreover, an open problem on fuzzy T-type filter is proposed.
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