The optimal group continuous logarithm compatibility measure for interval multiplicative preference relations based on the COWGA operator

Abstract

The calculation of compatibility measures is an important technique employed in group decision-making with interval multiplicative preference relations. In this paper, a new compatibility measure called the continuous logarithm compatibility, which considers risk attitudes in decision-making based on the continuous ordered weighted geometric averaging (COWGA) operator, is introduced. We also develop a group continuous compatibility model (GCC Model) by minimizing the group continuous logarithm compatibility measure between the synthetic interval multiplicative preference relation and the continuous characteristic preference relation. Furthermore, theoretical foundations are established for the proposed model, such as the sufficient and necessary conditions for the existence of an optimal solution, the conditions for the existence of a superior optimal solution and the conditions for the existence of redundant preference relations. In addition, we investigate certain conditions for which the optimal objective function of the GCC Model guarantees its efficiency as the number of decision-makers increases. Finally, practical illustrative examples are examined to demonstrate the model and compare it with previous methods.