Uncertainties with memory in construction of strict monotonic t-norms and t-conorms for finite ordinal scales: Basic definitions and applications

It is impossible to introduce strict monotonic t-norm on a finite chain. A proposed solution is to embed an initial scale into a totally ordered set of uncertainties with string or multiset based memory, and to define t-norm on this set. Applications of uncertainties with memory in fuzzy rule based systems in chemical technology and in the petroleum industry are discussed.