A Fuzzy Group Decision Making and Its Application Based on Compatibility with Multiplicative Trapezoidal Fuzzy Preference Relations

This paper proposes a fuzzy group decision-making model based on a new compatibility measure with multiplicative trapezoidal fuzzy preference relations (MTFPRs). First, the logarithm least square model is proposed to derive priority weights of MTFPR. Some concepts of compatibility for MTFPR are then presented to measure deviation between MTFPR and its expected fuzzy preference relation. Then an iterative algorithm is developed to help individual MTFPR reach acceptable compatibility, and we prove that the group fuzzy preference relation is acceptably compatible under the condition that all individual MTFPRs and their expected preference relations are all of acceptable compatibility. Furthermore, in order to determine the weights of decision makers (DMs), an optimal model is put forward based on criterion of minimizing the group compatibility index with MTFPRs in GDM. Finally, an application of new approach is analyzed by comparing with the existing methods investment selection. The main advantages of proposed approach are (1) an optimal model is put forward to derive the priority vectors of MTFPR; (2) an iterative and convergent algorithm is developed to improve the compatibility of MTFPR by adjusting a pair of elements of MTFPR once; and (3) DMs' weights in GDM are determined by an optimal model based on the compatibility measure.