Algorithms for estimating missing elements of incomplete intuitionistic preference relations

Abstract

Preference relations as simple and efficient information description tools have been widely used in practical decision-making problems. Intuitionistic preference relation, which is often met in real problems, is usually utilized to provide the experts' vague or fuzzy opinions over objects under uncertain circumstances. Owing to the limitations of the experts' professional knowledge and experience, the provided preferences in an intuitionistic preference relation are usually incomplete. Consequently, how to estimate the missing information in an expert's incomplete intuitionistic preference relation becomes a necessary step in a decision-making process. In this paper, we define the concept of multiplicative consistent intuitionistic preference relation and develop two estimation algorithms. The first algorithm is used to estimate the missing elements using only the known preference values in an acceptable incomplete intuitionistic fuzzy preference relation with the least judgments. The second one is given for the estimation of missing elements of the acceptable incomplete intuitionistic fuzzy preference relations with more known judgments. The advantages of the developed algorithms over the existing one are detailedly analyzed, and some examples are provided to illustrate the solution processes of the algorithms and to verify their practicality and superiority. © 2011 Wiley Periodicals, Inc.