Multiplicative and Implicative Importance Weighted Averaging Aggregation Operators with Accurate Andness Direction

Importance weighted averaging aggregation operators play a key role in utilizations of electronic data and information resources for retrieving, fusing, and extracting information and knowledge, as needed for decision making. Two central issues in the choice of such operators are the kind of importance weighting and the andness (or conjunction degree) of the operator. We present and discuss two main kinds of importance weighting, namely multiplicative and implicative, each yielding a particular kind of operator for a particular kind of aggregation problems. Importance weighting generalizations of each kind are proposed for each of two classes of averaging operators, namely the Power Means and the Ordered Weighted Averaging operators, each in a De Morgan dual form for increased efficacy. For each class is proposed a function for a rather accurate direct control of the andness. Operators of the same kind appear to behave rather similarly at the same andness, independent of the class of averaging operators generalized. Keywords— Aggregation operators, averaging operators, andness, orness, importance weighting, implicative importance.