Decision making under fuzzy environment with incomplete information

Abstract

Cognitively speaking, some processes or steps included in decision-making can be a serious burden for decision makers. Pairwise comparisons are one of those steps to be handled carefully in order to obtain useful results. During pairwise comparisons of elements such as decision criteria, let alone providing exact quantitative judgments, a complete linguistic set of judgments may sometimes be hard to retrieve from decision makers. From that perspective, completing an incomplete pairwise comparison matrix is an interesting problem that many attempted to cover. For that purpose, when decision makers provided incomplete interval-valued fuzzy preference relations, Khalid and Beg proposed an approach to obtain the completed matrix in their study [1]. Using their insight, the purpose of this exploratory study is to analyze what happens when triangular fuzzy numbers (TFNs) are used for judgments and how powerful is the method in order to represent the will of the decision makers. In the study, a numerical application is provided using incomplete pairwise comparison matrices of dimension five, collected from 20 decision makers where their preferences are given using a linguistic set. The accuracy of the approach is then tested for different levels of confidence in order to provide insightful concluding remarks.