The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making

Abstract

The complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods.

A consensus algorithm based on the worst consistency index of hesitant fuzzy preference relations in group decision-making

“…Fuzzy sets are widely used [12], but they can only use one preference value to express the DM's preference. In order to solve this problem, Torra [13] defined the hesitant fuzzy set (HFS) which employs several values to express the membership degree of the alternative, and now has been widely investigated recently College of Management and Economics, Tianjin University, Tianjin 300072, People's Republic of China [14,15]. Based on the concept of HFS and FPR, Xia and Xu [16] defined hesitant fuzzy preference relation (HFPR).…”

Analysis of Hamming and Hausdorff 3D distance measures for complex pythagorean fuzzy sets and their applications in pattern recognition and medical diagnosis

“…To enlarge the representing domain, Ullah et al [36] proposed the concept of complex Pythagorean fuzzy sets (CPyFSs), and Liu et al [20] introduced the concept of complex qrung orthopair fuzzy sets (Cq-ROFSs). Since then, CIFSs, CPyFSs, and Cq-ROFSs have been widely applied to various fields, such as MCDM/MADM [1][2][3][4][5][6]12,15,[20][21][22]24,25,32,38,40], medical diagnosis [13,[27][28][29]32], pattern recognition [12,13,27,36], cluster analysis [12,47], and image processing [16].…”