On fuzzy filters of pseudo BL-algebras

We introduce the concept of fuzzy filters of pseudo-BL-algebras and obtain some of their important properties. We further give several kinds of fuzzy filters, such as fuzzy Boolean filter, fuzzy normal filter, fuzzy prime filter, fuzzy ultrafilter and fuzzy obstinate filter and discuss the relations among the above fuzzy filters. We establish the Prime Fuzzy Filter Theorem in pseudo BL-algebras. By studying the relation between fuzzy Boolean filter and fuzzy normal filter in pseudo-BL-algebras, we solve an open problem that whether or not every Boolean filter is normal in pseudo-BL-algebras.