Abstract
Multiplicative preference relation is the most common tool used to express decision makers' preferences over pairs of criteria. Due to the decision makers' own personal experience, learning, situation, state of mind, or the complexity of the considered decision-making problems, in many cases, the decision makers cannot or are unwilling to provide their preferences over some pairs of criteria, and thus may construct incomplete multiplicative preference relations in which some of the elements are missing, we call these problems group decision-making problems with incomplete multiplicative preference relations. In this paper, we first investigate the approach to extending each incomplete multiplicative preference relation to a complete multiplicative preference relation by making use of the multiplicative transitivity properties. Then, we present some deviation measures to evaluate the consensus among the individual multiplicative preference relations and their collective multiplicative preference relation. On the basis of the above results, finally, we develop a consensus reaching process of group decision making with incomplete multiplicative preference relations, which establishes a sound theoretical basis for the priorities of criteria.
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