Distance and similarity measures for normal wiggly dual hesitant fuzzy sets and their application in medical diagnosis.

The normal wiggly dual hesitant fuzzy set (NWDHFS) is a modern mathematical tool that can be used to express the deep ideas of membership and non-membership information hidden in the thought-level of decision-makers (DMs). To enhance and expand the applicability of NWDHFSs, this study originates several types of distance and similarity measures between two NWDHFSs. The present paper first revises the basic operational laws of normal wiggly dual hesitant fuzzy elements (NWDHFEs) and then generalizes the rule of length extension for normal wiggly dual hesitant fuzzy setting. Meanwhile, we introduce a variety of distance and similarity measures under the background of NWDHFSs. After that, a family of weighted distance and similarity measures based on NWDHFS is presented and analyzed for discrete and continuous cases. The stated measures are the extension of several existing measures and have the capability to handle uncertain and vague information with a wider range of information. DMs can select the most suitable alternative based on these measures by determining the gap between each alternative and the ideal one. Finally, a practical example concerning disease detection is addressed to demonstrate the applicability and merits of the developed theory and depict the differences between the presented distance and similarity measures.