Counting semicopulas on finite structures

Abstract

Semicopulas are the operators chosen to model conjunction in the fuzzy/many-valued logics. In fact, a special kind of semicopula, called t-norm, is widely used in many applications of logic to engineering, computer science and fuzzy systems. The main result of this paper is the computation of the exact number of semicopulas that can be defined on a finite chain in terms of its length. The final formula is achieved via relating semicopulas with finite plane partitions.