A multistage decision-making method for multi-source information with Shapley optimization based on normal cloud models.

It is difficult to make scientific decisions for multistage complex decision-making problems, which are heavily affected by multi-level attributes, stage changes, and multi-source heterogeneous information. The normal cloud model is an uncertainty transformation model for constructing mappings between numerical values and their linguistic representations, which can be used to describe multi-source evaluation information for a better reflection of the distribution characteristics and uncertainties. This study aims to develop an effective multi-level multi-attribute decision-making method based on normal cloud models to solve multistage evaluation problems with multi-source heterogeneous information. Firstly, an optimization model is established to capture stage weights and lower-level attribute weights based on cloud distance. Secondly, a bidirectional cloud projection measure is proposed to obtain the measurement values of upper-level attributes based on horizontal and vertical reference points. Thirdly, the comprehensive evaluation values of alternatives are obtained based on Shapley weights of the upper-level attributes. Finally, an illustrative example is presented to clarify the feasibility and superiority of the proposed method. The result indicates that our method is (1) a flexible evaluation framework based on target reference points in fuzzy environments, (2) a powerful measurement tool for aggregating multi-source information, and (3) an objective decision-making method considering the interrelationships between objects. It is of great significance for the enterprises to optimize their operation mechanisms and resource allocation based on these evaluation results. • The normal cloud model is used to deal with multi-source information. • The bidirectional cloud projection measure is proposed to aggregate multi-source information with two reference points. • The Shapley function is used to obtain the optimal fuzzy measure and interaction relationships among attributes. • A multistage decision-making method based on two reference points is established. [ABSTRACT FROM AUTHOR]