A Multi-Attribute Group Decision Making Method Based on Novel Distance Measures and Regret Theory Under Probabilistic Dual Hesitant Fuzzy Sets

Probabilistic dual hesitant fuzzy set (PDHFS), as a decision information preference combining membership degree (MD) and non-membership degree (NMD) and probability, is an important tool to express uncertain information powerfully. It is well known that distance measures are very useful tools in multi-attribute decision making (MADM) and multi-attribute group decision making (MAGDM) field, and distance measures have been proposed in many fuzzy information environments. In this study, firstly, the analysis of literatures reveals that the existing distance formulas of PDHFSs have certain defects. In order to measure distances of different PDHFSs more effectively, this paper takes the distances between MDs and between NMDs into account, not only the distances between products of MDs and corresponding probabilities and between products of NMDs and corresponding probabilities. Secondly, the similarity-trust analysis method based on the novel distance measure is used to calculate the expert weights and the maximum deviation method based on the novel distance measure is used to calculate the attribute weights. Next, this paper adds the consideration of the mental activities of decision-makers (DMs) into MAGDM, extends the group satisfaction index into the MAGDM method under PDHFSs, calculates the perceived utility of DMs based on regret theory, and ranks the alternatives using the evaluation based on distance from average solution (EDAS) method. Finally, the proposed MAGDM method is applied to the decision-making for the prevention of radiation, and the validity and feasibility of the proposed method are verified using parametric sensitivity analysis and comparative analysis