Abstract

Group decision-making is a field of decision theory that has many strengths and benefits. It can solve and simplify the most complex and hard decision problems. In addition, it helps decision-makers know more about the problem under study and their preferences. Group decision-making is much harder and complex than individual decision-making since group members may have different preferences regarding the alternatives, making it difficult to reach a consensus.

In this thesis, we deal with three interrelated problems that decision-makers encounter during the process of arriving at a final decision. Our work addresses decision-making using preference relations. The first problem deals with incomplete reciprocal preference relations, where some of the preference degrees are missing. Ideally, the group members are able to provide preferences for all the alternatives, but sometimes they might not be able to discriminate between some of the alternatives, leading to missing values. Two methods are proposed to handle this problem. The first is based on a system of equations and the second relies on goal programming to estimate the missing information. The former is suitable to complete any incomplete preference relation with at least