... and are of fundamental importance in decision-making. Averaging operators are, in general, not associative.DeÞnition 3.4 An averaging operator (or mean) is a continuous binaryoperation⊕ :[0, ... used as a modeling language for real situations or systems,it is not only important that the operators satisfy certain axioms or have certainformal qualities (such as associativity and commutativity), ... of averaging oper-ators. Continuous t-norms and t-conorms are averaging operators. The arith-metic mean (x + y) /2 is, of course, an averaging operator, as are geometric© 2003 by Chapman &...