Construction of similarity measure for intuitionistic fuzzy sets and its application in face recognition and software quality evaluation

As a generalization of fuzzy sets, intuitionistic fuzzy sets (IFSs) are more capable of representing and addressing uncertainty in real-world problems. As a result, IFSs have been utilized in various areas of application. However, the distance and similarity measures between the two IFSs are still an open issue that has drawn much attention over the past few decades. Even though several intuitionistic fuzzy similarity measures (IFSMs) have been developed, a number of issues still exist, including counter-intuitive results, ‘the zero divisor problem,’ violation of similarity measure axioms, and being incompetent to detect minor changes in membership or non-membership. To overcome these shortcomings, a novel intuitionistic fuzzy similarity measure (IFSM) has been introduced in this study. Unlike existing measures, this method considered the global maximum and minimum of differences in memberships and differences in non-memberships, along with their individual differences, to construct an IFSM. Moreover, it has been shown that a convex combination of two similarity measures is also a similarity measure. Some numerical examples are employed to emphasize the advantages and strengths of the proposed method over existing ones. The suggested IFSM has been implemented on a few pattern classification issues to demonstrate its efficacy and a new face recognition method is also presented. Moreover, an entropy measure is introduced using the proposed IFSM, which is further used to construct the weights of attributes in the MADM method. Furthermore, the MADM technique, IF-E-TOPSIS, is constructed using the suggested IFSM and entropy measure. The effectiveness of this method is shown by utilizing it for software quality assessment, and the results are compared with existing ones to highlight the superiority of the proposed method.