Two new similarity measures for intuitionistic fuzzy sets and its various applications

In this paper, two new tools of decision-making problems, namely similarity measures between intuitionistic fuzzy sets, are being forwarded. In general, parameters like the difference of membership degrees and the difference of nonmembership degrees are very prominent factors while constructing these tools. Various studies are evident which tried to incorporate concepts like the cross-evaluation factor and the difference of hesitancy factors. In some studies, it is claimed that the use of the hesitancy parameter is not proper. In this study, the hesitancy factor is being incorporated effectively. Furthermore, another prominent parameter is the difference in the minimum of cross-evaluation factor along with the difference in the maximum of cross-evaluation factor, which is not being used earlier. The incorporation of these parameters produces outperforming results, and the limitations of the existing methods are overcome. The numerical examples discussed to show the performance of the proposed distance measure. Furthermore, the applicability of the proposed similarity measures is exhibited by various applications in pattern recognition, face-mask selection, and clustering problems.