Exploring Multicriteria Elicitation Model Based on Pairwise Comparisons: Building an Interactive Preference Adjustment Algorithm

Abstract

Pairwise comparisons have been applied to several real decision making problems. As a result, this method has been recognized as an effective decision making tool by practitioners, experts, and researchers. Although methods based on pairwise comparisons are widespread, decision making problems with many alternatives and criteria may be challenging. This paper presents the results of an experiment used to verify the influence of a high number of preferences comparisons in the inconsistency of the comparisons matrix and identifies the influence of consistencies and inconsistencies in the assessment of the decision-making process. The findings indicate that it is difficult to predict the influence of inconsistencies and that the priority vector may or may not be influenced by low levels of inconsistencies, with a consistency ratio of less than 0.1. Finally, this work presents an interactive preference adjustment algorithm with the aim of reducing the number of pairwise comparisons while capturing effective information from the decision maker to approximate the results of the problem to their preferences. The presented approach ensures the consistency of a comparisons matrix and significantly reduces the time that decision makers need to devote to the pairwise comparisons process. An example application of the interactive preference adjustment algorithm is included.

Learning Pairwise Comparisons with Machine Learning for Large-Scale Multi-Criteria Decision Making Problems

“…Multi-criteria methods can be separated into three groups: 1) aggregation methods, whose main representatives are the multi-attribute utility theory, such as AHP [5], Analytic Network Process (ANP) [17] and Best-Worst Method (BWM) [18]; 2) outranking methods, such as the Preference Ranking Organisation Method of Enrichment Evaluations (PROMETHEE) [19] and Elimination Et Choix Traduisant la Realité (ELECTRE) [20] and their derivatives, and 3) interactive methods, such as multi-objective linear programming (MOLP) [21]. For the reader interested in an extensive review and classification of the multi-criteria decision-making methods, see [2] (in Portuguese).…”

“…However, for the aggregation methods, the literature has reported several inconsistencies in the formulation of these matrices. Inconsistency, as explained by [21], arises when some opinions of a comparisons matrix contradict others and, surely, the larger the matrix size the greater the chances of inconsistency in the evaluations. These authors described two distinct situations that the inconsistency may appear: intercriteria and intra-criterion.…”

“…Several studies have reported concerns related to the applicability of this type of procedure in situations where the number of criteria and alternatives is quite large, e.g. [21] to cite a few.…”

Multiple-Criteria Heuristic Rating Estimation

“…When creating a decision model based on pairwise comparisons of alternatives, one of the problems we face is determining the nature of the objects under study. Some may be tangible, i.e., they can be measured and weighed; others are intangible and difficult to decide on by direct measurement [1]. For example, available methods such as AHP cannot deal with this problem effectively.…”

Multiple-criteria Heuristic Rating Estimation

“…It also quickly gained opponents who very often rightly pointed out the imperfections of the method [1,4,12]. One of the problems is the representation of measurable entities, such as distance, weight or area [40]. In particular, if we can measure a given object and have an exact value, there is no point in relying on experts' opinions on this entity.…”