New distances for dual hesitant fuzzy sets and their application in clustering algorithm

What is it about?

Compared to hesitant fuzzy sets and intuitionistic fuzzy sets, dual hesitant fuzzy sets can model problems in the real world more comprehensively. Dual hesitant fuzzy sets explicitly show a set of membership degrees and a set of non-membership degrees, which also imply a set of important data: hesitant degrees.The traditional definition of distance between dual hesitant fuzzy sets only considers membership degree and non-membership degree, but hesitant degree should also be taken into account. To this end, using these three important data sets, we first propose a variety of new distance measurements for dual hesitant fuzzy sets in this paper. In these distance definitions, membership degree, non-membership-degree and hesitant degree are of equal importance. Second, we propose a clustering algorithm by using these distances in dual hesitant fuzzy information system. Finally, a numerical example is used to illustrate the performance and effectiveness of the clustering algorithm. Accordingly, the results of clustering in dual hesitant fuzzy information system are compared using the distance measurements mentioned in the paper, which verifies the utility and advantage of our proposed distances.

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Photo by Markus Spiske on Unsplash

Photo by Markus Spiske on Unsplash

Why is it important?

Using these three important data sets (membership degree, non-membership degree and hesitant degree), we first propose a variety of new distance measurements (the generalized normalized distance, generalized normalized Hausdorff distance and generalized normalized hybrid distance) for dual hesitant fuzzy sets in this paper. In addition, we apply these distances to the clustering algorithm and prove that it can improve the clustering accuracy.

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