The Group Decision Making Based On The Incomplete Preference Relations

In group decision making, decision makers often make use of some types of preference relations to express their preference information to projects.A decision maker compares every two projects of the n projects, and presents a complete preference relation, at least comparing n(n-1)/2 times. When n is large, the work of comparing is also large, thus the decision makers may make mistakes in comparing. And the decision makers might not own adequate knowledge about some comparisons, or not want to express their opinions to some sensitive problems directly, thus difficultly give complete preference relations. For the above two reasons, it’s necessary to consider preference relations with incomplete information, i.e., incomplete preference relations. And it is meaningful to research into the reconstruction methods, sorting methods and group aggregation methods of the incomplete ones in theory and practice.We mainly researched on the conditions of two reconstruction methods of the incomplete fuzzy preference relations, and the group decision making of two new types of preference relations with incomplete information in this dissertation:1. The conditions of two reconstruction methods, the iteration method and the optimization method, for the incomplete fuzzy preference relations were studied. To the iteration method, by demostrating, we pointed out the shortcoming of a sufficient condition from the literature, that a set of n-1 nonleading diagonal preference values, where each one of the alternatives was compared at least once, was known, and proposed a new proposition, then gave a new sufficient and necessary condition,based on which we proposed the graph method to inspect the iteration method if applicable, and used an example to validate the inspecting method, and also proposed the only case where this method wasn’t applicable. And to the optimization method, we gave a wider condition where the method could guarantee the uniqueness of the estimates for the problems than the literature, then gave an instance to test and verify the condition, and also proposed the only case where this method wasn’t applicable. By means of these contributions, we proposed a new policy for reconstructing incomplete fuzzy preference relations by the two methods.2. The group decision making based on the incomplete intuitionistic linguistic preference relations was studied. Taking the 2-tuple fuzzy linguistic representation model as base, we introduced the definitions of the intuitionistic linguistic preference relation and the incomplete intuitionistic linguistic preference relation, and the score function and the accuracy function, which were used for the comparison of the intuitionistic fuzzy linguistic values. And we described the transitivity properties of the preference relations. We presented an optimization model to reconstruct the incomplete preference relations, and an approach to aggregate the mixture of incomplete and complete ones. And we gave an example to validate our reconstruction model and aggregation method, and compared the new preference relation with the traditional linguistic preference relation, and showed the merit of the new preference relation.3. The group decision making based on incomplete hybrid preference relations was studied. A new type of hybrid preference relation was proposed. We gave a method to uniform the preference relation, and studied the reconstruction of the incomplete one and the aggregation of the mixture of incomplete and complete ones. And we gave an example to validate our methods,and also presented a comparative of our sorting method with the sorting method in the literature, and pointed out the merits of our methdod.