Efficient Andness-Directed Importance Weighted Averaging Operators

Importance weighted averaging is a central information processing task in multicriteria decision problems of many kinds, such that selection, classification, object recognition, query answering, and information retrieval. These problems are characterized by a query, i.e., a set of importance weighted criteria, and a set of options queried. While each criterion determines a ranking of the options, the task of the averaging operator is essentially to aggregate these rankings into an overall ranking under the consideration of the criterion importance. We present a class of such operators, based on the power means, namely the Andness-directed Importance Weighted Averaging (AIWA) operators. The operators are equipped with an approximate andness measure allowing an easy, direct control of the andness in the unit interval. The aggregation behavior of the operators appears to be similar to that of importance weighted maximum entropy OWA operators. However, AIWA operators aggregates n arguments (criterion satisfaction values) in O(n) time as opposed to O(n log n) time for OWA operators. An interesting property provided by AIWA operators is decomposability, allowing us to consider new or improved criteria without recomputing with all arguments. Overall, the AIWA operators appear to be effective as andness controlled, importance weighted averaging operators, as well as easy to apply and computationally efficient.