Priority Degrees and Distance Measures of Complex Hesitant Fuzzy Sets With Application to Multi-Criteria Decision Making

Abstract

The notion of a complex hesitant fuzzy set (CHFS) is one of the better tools in order to deal with complex information. Since distance plays a crucial role in order to differentiate between two things or sets, in this paper, we first develop a priority degree for the comparison between complex hesitant fuzzy elements (HFEs). Then a variety of distance measures are developed, namely, Complex hesitant normalized Hamming-Hausdorff distance (CHNHHD), Complex hesitant normalized Euclidean-Hausdorff distance (CHNEHD), Generalized complex hesitant normalized Hausdorff distance (GCHNHD), Complex hesitant hybrid normalized Hamming distance (CHHNHD), Complex hesitant hybrid normalized Euclidean distance (CHHNED), Generalized complex hesitant hybrid normalized distance (GCHHND) and their weighted forms. Moreover, the continuous form of the proposed distances is also developed. Further, the proposed distances are applied to medical diagnosis problems for their effectiveness and application. Furthermore, a multi-criteria decision making (MCDM) approach is developed based on the TOPSIS method and proposed distances. Finally, a practical example related to the effectiveness of COVID-19 tests is presented for the application and validity of the proposed method. A comparison study was also done with the method that was already in place to see how well the new method worked.INDEX TERMS Complex fuzzy sets, priority degree, distance measure, closeness coefficient, TOPSIS method.

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