Observations on non-commutative fuzzy logic

The paper presents some results on the logic psBL (pseudo-basic fuzzy logic, the generalization of BL not assuming commutativity of conjunction) and on the analogous logic psMTL – a non-commutative version of the monoidal t-norm logic MTL of Esteva and Godo.Partial support of the project No LN00A056 (ITI) of the Ministry of Education (MMT) of the Czech Republic is acknowledged. Thanks are due to F. Esteva and the anonymous referee for their comments on a draft of this paper.