A multi-attribute decision making method for TODIM based on mixed correlation coefficients for probabilistic linguistic term sets

In the face of multi-attribute decision problems in complex situations, most traditional multi-attribute group decision methods are based on the assumption that the decision maker is perfectly rational, while in the face of complex decision problems, the decision maker usually has the psychological characteristics of limited rationality and may use more than one linguistic term to describe the decision information when expressing the decision information To this end, this paper selects probabilistic language term sets to describe complex preference information. First, to address the problem that the current probabilistic linguistic term set correlation coefficient cannot appropriately measure the degree of correlation among probabilistic linguistic term sets, this paper proposes a new probabilistic linguistic term set correlation coefficient from three characteristic factors of probabilistic linguistic term sets: mean, variance, and length rate. To integrate the attribute index weights, probabilistic linguistic term set weighted mixed correlation coefficients are proposed. Second, this paper introduces the TODIM method, which can consider the psychological behavior of decision makers, and proposes a TODIM multi-attribute decision making method based on probabilistic linguistic term sets with mixed correlation coefficients. Finally, through an empirical analysis of four Internet listed companies in a newfirst-tier city in China, this study verifies the rationality and validity of the proposed method. The results show that the mixed correlation coefficient can comprehensively measure the correlation between probabilistic linguistic term sets, which provides an important method for future multi-attribute decision making problems.