CODAS Method for Multi-Attribute Decision-Making Based on Some Novel Distance and Entropy Measures Under Probabilistic Dual Hesitant Fuzzy Sets

Probabilistic dual hesitant fuzzy set (PDHFS) as an extension of the generalization of hesitant fuzzy set (HFS) and dual hesitant fuzzy set (DHFS). It not only reflects the hesitant attitude of decision-makers (DMs), but also reflects probabilistic information. It is a more powerful and important tool to express uncertain information. As we all know, the distance and entropy measures are very useful tool in the MADM problems. In many fuzzy environments, their distance and entropy measures are proposed, and the MADM methods depend on the distance and entropy measures are given. First, to overcome the disadvantages of destroying the original information caused by artificially adding elements, we defined the membership degree (MD) mean, non-membership degree (NMD) mean and standard deviation for PDHFE, based on above definitions, the mean and standard deviation distance were proposed. Secondly, without the aid of other auxiliary functions, we built some novel PDHF entropy measures. Third, depend on the distance and entropy measures built, we integrate the classical CODAS method with the PDHF setting, and build a novel MADM technique to solving the MADM problem. Finally, the built MADM technique is used to the evaluation of enterprise credit risk to testify the practicability and feasibility of the built MADM technique. Meanwhile, the MADM technique built in this study is compared with some existing methods, and the advantages of the MADM technique proposed in this study are put forward, which has a better effect in solving MADM problems.