The uncertain OWA aggregation with weighting functions having a constant level of orness

Since the ordered weighted averaging (OWA) operator was introduced by Yager [IEEE Trans Syst Man Cybern 1988; 18:183-190], numerous aggregation operators have been presented in academic journals. Apart from a setting where exact numerical assessments on weights and input arguments can be obtained, the issue of generalizing the OWA to take into account uncertainties in weights and/or input arguments has been considered. Recently, Xu and Da [Int J Intell Syst 2002; 17:569-575] proposed an uncertain OWA operator in which input arguments are given in the form of interval numbers. The interval numbers within the interval sometimes do not have the same meaning for the decision maker as is implied by the use of interval ranges. Thus, we present a way of prioritizing interval numbers, taking into account the strength of preference based on the probabilistic measure. Further, rank-based weighting functions having constant values of orness irrespective of the number of objectives aggregated are presented and a final rank ordering of courses of action is performed by the use of those weighing functions. (c) 2006 Wiley Periodicals, Inc.