A goal programming approach to group decision-making with three formats of incomplete preference relations

This paper proposes a goal programming approach to solve the group decision-making problem where the preference information about alternatives provided by decision makers can be represented in three formats, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations and incomplete linguistic preference relations. In the approach, a transformation function is introduced to transform the incomplete linguistic preference relation into an incomplete fuzzy preference relation. To narrow the gap between the collective opinion and each decision maker's opinion, a liner goal programming model is constructed to integrate the three different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. Thus, the ranking order of alternatives or selection of the most desirable alternative(s) is obtained directly according to the computed collective ranking values. A numerical example is also used to illustrate the feasibility and the applicability of the proposed approach.