Dominance of t-norms and its transitivity

            Peter Sarkoci 

  Slovak Technical University, Bratislava

We consider a generalization of Minkowski inequality, so-called
Mulholland inequality. We present its applications in the framework of
triangular norms (operations naturally appearing as conjunctions in
fuzzy logic), in particular constructions of product probabilistic
metric spaces, preservation of T-transitivity under aggregation, etc.
The answer to the question whether the dominance of t-norms is
transitive will be presented (solution of an old open problem
formulated by Tardiff, Schweizer, and Sklar).  The soft maximum
(=log-sum-exp operation) plays in important role in this context.