MAM AND MOM BAG OPERATORS FOR AGGREGATION

Classes of bag operators that generalize the multivalued logic ''and'' and ''or'' operators are introduced. These new operators are called MAM (monotonic antimonotonic) and MOM (monotonic on monotonic) operators, respectively. We investigate the properties of these operators and show their relationship to triangular norms. In the framework of these bag operators we introduce a third operator which generalizes the averaging operator. Although all three operators are commutative and monotonic, they differ with respect the effect of the addition of an element to a bag. The concept of value functionality is introduced to include associativity.