The inconsistency of fuzzy triangular relational products in the light of pseudo-strictly monotonic fuzzy connectives

The theory of fuzzy relational products (a relatively new inference scheme) was pioneered by W. Bandler and L.J. Kohout (1978; 1980). The original definitions of triangular products as set by Bandler and Kohout were modified by B. DeBaets and B. Kerre (1993; 1994) after they proved that the original ones were bearing the shortcoming of the non-emptiness requirements and cannot be trusted as a proper deductive scheme. An attempt to apply the improved inference definitions in a real life field, namely medical diagnosis, produced unexpected results. This is because the fuzzy connectives (Kliene-Dines and Luckasievic) do not exhibit the strong property of pseudo-strict monotonicity. The purpose of the paper, apart from being an empirical-oriented research study, is to try the improved definitions by instantiating them with well-known pseudo-strictly monotonic fuzzy connectives