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.
['József Dombi']
Towards a General Class of Operators for Fuzzy Systems