Towards a General Class of Operators for Fuzzy Systems

Our starting point is the multiplicative utility function which is extensively used in the theory of multicriteria decision making. Its associativity is shown and as its generalization a class of operators is introduced with fine and useful properties. As in special cases, it reduces to well-known operators of fuzzy set theory: min/max, product, Einstein, Hamacher, Dombi, and drastic. As a consequence, we generalize the addition of velocities in Einstein´s special relativity theory to multiple moving objects. Also, a new form of the Hamacher operator is given, which makes multiargument calculations easier. We examine the De Morgan identity which connects the conjunctive and disjunctive operators by a negation. It is shown that in some special cases (min/max, drastic, and Dombi) the operator class forms a De Morgan triple with any involutive negation.