The OWA aggregation with uncertain descriptions on weights and input arguments

Since the ordered weighted averaging (OWA) operator was introduced by Yager to provide a method for aggregating multiple inputs that lie between the max and min operators, much research that deals with uncertain information on input arguments instead of numerical values has been conducted due to the fact that information provided by human beings is in fact often vague and imprecise. In this paper, the OWA operators with uncertain weights such as interval or weak ordinal descriptions, coupled with interval input arguments, are presented in order to identify the superior course of action among a multitude of courses of action. With the help of relaxation of information representation, a burden of information specification imposed on decision maker can be, to some extent, relieved, and thus with regard to the parameters, we can obtain a less-specific expression that renders human judgments readily available. To perform the OWA aggregation, we take into account the strength of preference based on a probabilistic measure and present a way of ordering the input arguments specified by interval numbers as well as two heuristic algorithms to allocate uncertain weights to the ordered input arguments for prioritizing the courses of action.