Similarity measure on intuitionistic fuzzy sets based on Benchmark Line and it’s diverse applications

Abstract

An intuitionistic fuzzy set (IFS) is an extension of fuzzy sets that can deal with inconsistent and uncertain information more accurately. In this paper, a novel similarity measure is presented that might be applied to several application issues in decision-making, pattern recognition, and medical diagnostics. IFSs are sources of information that contain both the membership and non-membership degrees of the elements in the set. As such, similarity measures based on geometric concepts might occasionally be misleading. Hence, five parameters are specified to develop the similarity measure. These parameters are membership information similarity, non-membership information similarity, maximum cross-information similarity, minimum cross-information similarity, and product cross-information similarity. Most of the existing similarity measures cannot reasonably determine the appropriate similarity degree when the IFS points lie on the benchmark line. On the other hand, product cross-information similarity is a new parameter introduced in this study that has a significant role in handling benchmark problems more effectively and reasonably. The proposed similarity measure compensates for several counterintuitive problems related to decision-making and pattern recognition. Complexity analysis illustrates the complexity level of the proposed measure, which is reliable. Finally, various challenges with applications in decision-making, pattern recognition, and medical diagnosis difficulties are used to validate the suggested similarity measure.