Multiplication, distributivity and fuzzy-integral II
Based on results of generalized additions and generalized multiplications, proven in Part 1, we first show a structure theorem on two generalized additions which do not coincide. Then we prove structure and representation theorems for generalized multiplications which are connected by a strong and weak distributivity law, respectively. Finally - as a last preparation for the introduction of a framework for a fuzzy integral - we introduce generalized differences with respect to t-conorms (which are not necessarily Archimedean) and prove their essential properties.
distributivity law fuzzy measures restricted domain pseudo-addition pseudo-multiplication choquet integral sugeno integral