MADM based on distance and correlation coefficient measures with decision-maker preferences under a hesitant fuzzy environment

In multiple attribute decision making (MADM), hesitant fuzzy sets (HFSs) are powerful tools for expressing uncertain and vague information. Recently, MADM problems with hesitant fuzzy information have attracted increasing attention, and many MADM methods have been developed. However, only a limited amount of research has considered MADM problems that simultaneously determine attribute weights and decision-maker (DM) preferences. Therefore, we propose an MADM approach for such problems under a hesitant fuzzy environment. First, we derive extended distance and correlation coefficient measures for HFSs that are more reasonable and effective when the DM preferences are considered. We then apply the extended distance measure to subjective and objective preference information to determine attribute weights, and use these to calculate the weighted correlation coefficient between the ideal choice and each alternative. Further, we determine the ranking order of all alternatives, from which it is easy to identify the best choice. Finally, we present an example that demonstrates the practicality of the proposed approach.