A preference degree for intuitionistic fuzzy values and application to multi-attribute group decision making

This paper proposes a novel preference degree algorithm to rank intuitionistic fuzzy values (IFVs) and applies it to multi-attribute group decision making (MAGDM) with IFVs. First, the concept of preference degree of IFVs is defined according to the geometrical representation of IFVs. Some useful properties of the defined preference degree are discussed. Combining the preference degree with the hesitation margin of IFVs, a novel preference degree algorithm is designed to rank a series of IFVs. In MAGDM problems with IFVs, the attribute weights would be usually diverse for different decision makers (DMs). To derive the attribute weights for each DM objectively, a multi-objective programming model is constructed and transformed into a linear program to resolve. Then, the consensus indices are calculated from three levels based on the individual fuzzy reciprocal preference relations and the collective one. To determine DMs’ weights, a linear goal programming model is established by maximizing the consensus index of group of DMs. Using the intuitionistic fuzzy weighted average operator, the individual comprehensive values of alternatives are obtained and further integrated into the collective comprehensive values of alternatives. The ranking order of alternatives is generated by the designed preference degree algorithm. At length, the validity of the proposed method is illustrated with a construction organization selection example.