Determination of criteria weights in solving multi-criteria problems

Abstract

A multi-criteria (MC) problem comprises of units to be analyzed under a set of evaluation criteria. Solving a MC problem is basically the process of finding the overall performance or overall quality of the units of analysis by using certain aggregation method. Based on these overall measures of each unit, a decision can be made whether to sort them, to select the best or to group them according to certain ranges. Prior to solving the MC problems, the weights of the related criteria have to be determined with the assumption that the weights represent the degree of importance or the degree of contribution towards the overall performance of the units. This paper presents two main approaches which are called as subjective and objective approaches, where the first one involves evaluator(s) while the latter approach depends on the intrinsic information contained in each criterion. The subjective and objective weights are defined if the criteria are assumed to be independent with each other, but if they are dependent, there is another type of weight, which is called as monotone measure weight or compound weights which represent degree of interaction among the criteria. The measure of individual weights or compound weights must be addressed in solving multi-criteria problems so that the solutions are more reliable since in the real world, evaluation criteria always come with different degree of importance or are dependent with each other. As the real MC problems have their own uniqueness, it is up to the decision maker(s) to decide which type of weights and which method are the most applicable ones for the problem under study.