Approximate Criterion Reduction in Multi-criteria Trilevel Ranking Analysis

This study explores the problem of criterion reduction in a specific class of multi-criteria decision-making problems known as trilevel rankings. A trilevel ranking trisects alternatives into three levels to represent the high, middle, and low, which can be viewed as a practice of three-way decision. By analyzing the trilevel structure, we present a formal definition of approximate criterion reduct. To construct an approximate criterion reduct, we introduce two measures for assessing the difference between trilevel rankings. The first one is a distance-based measure calculated by quantifying consistent, contradictory, and compatible pairs with respect to the two trilevel rankings. The second measure is built on a cost matrix that covers nine potential placements of alternatives, each with its associated cost. We design two heuristic algorithms for computing optimal approximate criterion reducts. These algorithms can be applied by using either of the proposed measures, offering flexibility and adaptability across a range of decision-making scenarios. Finally, we demonstrate the effectiveness of these algorithms through a series of experiments on real-world datasets.