Some Novel Correlation Coefficients of Probabilistic Dual Hesitant Fuzzy Sets and their Application to Multi-Attribute Decision-Making

This paper aims to propose a novel correlation coefficient (CC) that is more realistic in a probabilistic dual hesitant fuzzy (PDHF) setting. As is well known, CC is a very useful tool for measuring the correlation between two sets and plays a crucial role in multi-attribute decision-making (MADM) issues. Some CCs in fuzzy settings have been proposed one after another, and decision-making methods based on CCs have been proposed and applied to related practical decision-making issues. However, when reviewing CC in PDHF setting, we found that the range of CC values is all [0,1], but this is not entirely in line with reality because the range of CC in the real number range is [−1,1]. Therefore, it is imperative to propose a novel CC that is more in line with reality. This not only provides theoretical support for the development of PDHFS but also better solves practical problems, which has very important theoretical and practical significance. Firstly, we defined the mean membership degree and mean non-membership degree of probabilistic dual hesitation fuzzy element (PDHFE). Secondly, in order to maintain consistency and order in the lengths of MD and NMD in two PDHFSs, a method of adding PDHFE to shorter MD or NMD and a sorting method after adding new elements were defined. Thirdly, a new CC and its weighted form have been developed, and some of its excellent performance has been studied in detail. Fourthly, a multi-attribute decision-making method based on PDHFWCC was established, and specific calculation steps were provided. Finally, the constructed MADM method will be used for evaluating project manager candidates to demonstrate the feasibility and practicality of the proposed MADM method. Meanwhile, a comparison was made between the MADM method and several existing MADM methods, demonstrating the effectiveness of the MADM method and highlighting its advantages.