Learning the weights using attribute order information for multi-criteria decision making tasks

Abstract

In multi-criteria decision making, the importance of decision criteria (decision attributes) plays a crucial role. Ranking is a useful technique for expressing the importance of decision criteria in a decision-makers’ preference system. Since weights are commonly utilized for characterizing the importance of criteria, weight determination and assessment are important tasks in multi-criteria decision making and in voting systems as well. In this study, we concentrate on the connection between the preference order of decision criteria and the decision weights. Here, we present an easy-to-use procedure that can be used to produce a sequence of weights corresponding to a decision-makers’ preference order of decision criteria. The proposed method does not require pairwise comparisons, which is an advantageous property especially in cases where the number of criteria is large. This method is based on the application of a class of regular increasing monotone quantifiers, which we refer to as the class of weighting generator functions. We will show that the derivatives of these functions can be used for approximating the criteria weights. Also, we will demonstrate that using weighting generator functions, weights can be inverted in a consistent way. We will deduce the generators for arithmetic and geometric weight sequences, and we will present a one-parameter generator function known as the tau function in continuous-valued logic. We will show that using these weighting generator functions, the weight learning task can be turned into a simple, one-parameter optimization problem.