Novel strict intuitionistic fuzzy similarity measures-based on fuzzy negation and their applications

The concept of similarity measure is fundamental for evaluating the consistency between intuitionistic fuzzy sets (IFSs). Several researchers have developed various intuitionistic fuzzy similarity measures (IFSimMs) utilizing intuitionistic fuzzy distance measures (IFDisMs) or combinations of membership and non-membership degrees of IFSs. Nevertheless, there is still ample room for the improvement, as some of these measures do not satisfy the axiomatic properties of IFSimMs and produce unreasonable results. In this paper, we first establish a dual relationship between IFDisMs and IFSimMs based on fuzzy negations, enabling the construction of an infinite number of IFSimMs from a given IFDisM. We then propose two novel IFSimMs by directly manipulating the membership and non-membership degrees of IFSs and prove that they satisfy the axiomatic properties of strict IFSimMs (SIFSimMs). Furthermore, a comparative analysis reveals that the proposed SIFSimMs do not yield any unreasonable results in various scenarios. Finally, we apply these SIFSimMs to pattern recognition, medical diagnosis, and clustering analysis problems, demonstrating their superior performance compared to some existing measures.