A group decision making method with interval valued fuzzy preference relations based on the geometric consistency

This paper investigates a group decision making (GDM) method with interval valued fuzzy preference relations (IVFPRs). According to the geometric consistency of IVFPR, the max-consistency index and min-consistency index of an IVFPR are developed respectively. Combining the max-consistency index with min-consistency index, the geometric consistent index of an IVFPR is defined to measure the consistency level of the IVFPR by considering decision maker's (DM's) risk attitude. For improving the unacceptable geometric consistency of an IVFPR, a goal programming model is constructed to derive an acceptable geometric consistent IVFPR. By regarding the geometric consistent conditions of an IVFPR as fuzzy constraints, a fuzzy logarithmic program is established to generate the interval priority weights. In GDM problems, the individual interval priority weights are obtained by solving the corresponding fuzzy logarithmic programs. The similarities between DMs are calculated based on their individual interval priority weights. Subsequently the confidence degrees of DMs are defined to determine DMs' weights. To obtain the collective interval priority weights, a parametric linear program is constructed and transformed into a linear program to resolve. The order of alternatives is generated by the collective interval priority weights. Some examples are analyzed to verify the effectiveness of the proposed method.