Interpreting the results of InterCriteria Analysis: Pareto principle at work

Abstract

The present short note aims to propose a new, alternative, way to interpret the results of the intuitionistic fuzzy sets-based method for multicriteria decision support named InterCriteria Analysis. Given an <math>m \times n</math> dataset of multiple (''m'') objects evaluated numerically against multiple (''n'') criteria, the ICA method generates an <math>n \times n</math> table of intuitionistic fuzzy pairs <math>\langle \mu_{i,j}, \nu_{i,j} \rangle, \ i, j \in {1, 2, \ldots, n}</math> where the given pair indicates the extent of relation between the corresponding pair of criteria <math>C_i, C_j</math>. Traditionally, the interpretation of these intuitionistic fuzzy pairs regarding the extent of positive or negative dependence between two criteria (or, respectively, the lack of such) requires that two threshold values, both in the [0,1] interval too, are used. Now we propose to use only one such threshold value belonging to the [0,1] interval, for instance a minimal threshold of the degree of membership, while the other threshold {would} be essentially related to the size of the subset of intercriteria pairs being shortlisted for interpretation, rather than their degree of non-membership. We justify that the proposed approach, inspired by the Pareto Principle, in certain cases yields better results than the traditionally used one..