Abstract: Pseudo MTL-algebra (or psMTL-algebra, WPBL-algebra) is a new class of algebra system as an algebraic counterpart of the non-commutative fuzzy logic system psMTL. The aim of this paper is to investigate the filter theory of pseudo MTL-algebra. Some new properties of pseudo MTL-algebra are given, and an important counterexample is constructed to show that the sufficient and necessary condition for the normal filter in pseudo BL-algebra is not true in pseudo MTL-algebra. A new equivalent condition for the normal filter in pseudo MTL-algebra is established. Moreover, by these results, quotient algebra of pseudo MTL-algebra is built.

Key words: non-commutative fuzzy logic, pseudo MTL-algebra, WPBL-algebras, normal filter, counterexample