Aggregation operators with annihilator
This paper is devoted to the study of a special kind of aggregation operators: commutative, non-decreasing binary operators F on [0,1] with annihilator and such that F(0,0)=0 and F(1,1)=1. A characterization of this kind of operators is given, including many examples and properties in the general case. Special attention is paid to the associative case, leading to a characterization by means of a median expression. This type of operators can be viewed as a generalization of both uninorms and nullnorms.
aggregation operator annihilator associativity uninorm nullnorm t-operator