Bidirectional projection method for multi-attribute group decision making under probabilistic uncertain linguistic environment

The financial products selection in the financial services sector is a traditional multi-attribute group decision making (MAGDM) problem. Probabilistic uncertain linguistic sets (PULTSs) could be used to evaluate the financial products with uncertain linguistic terms and corresponding weights (probabilistic). The bidirectional projection (BP) method could take the bidirectional projection values into account. In this paper, we develop an integration model of information entropy and BP method under PULTSs. First of all, utilizing information entropy derives the priority weights of attributes. Next, utilizing the BP method of the PULTSs to obtain the final ranking of the alternatives. To depict the BP method, the formative vectors of two alternatives are defined, and a weighted vector model and inner product are improved under the PULTSs. In addition, through giving the case of financial products selection and some existing MAGDM methods for comparative analysis, it is proved that the method is practical and effective. The proposed approach also contributes to the effective selection of appropriate options in other decision-making matters.