Two new methods for decision-making with incomplete reciprocal fuzzy preference relations based on additive consistency

Abstract

ABSTRACT In this paper, we propose two new methods to solve the problem of incomplete reciprocal fuzzy preference relations. Sometimes decision-maker(s) might not be able to provide complete information about their preferences on the alternatives. In general, an incomplete preference relation can be completed if at least a set of nonleading diagonal preference values are known and each one of the alternatives is compared directly or indirectly at least once. However, this is not always the case. Sometimes, the decision-maker(s) might not be able to provide any information with regards to at least one of the alternatives, which is called the ignorance situation. We propose two new methods based on additive consistency for solving these two problems in a multi-attributes/group decision-making environment. The first method is based on a system of equations, which is suitable for estimating missing information in the general case. The second method, which is an extension of the system of equations, utilizes a goal programming model to address the ignorance situations. Our validation of these two methods shows that the proposed methods generate a high consistency level irrespective of the nature of the problem under study. The proposed methods outperform other comparable methods without a need to modify or change the original decision-maker(s) preferences.