Investigating Novel Types of Coincidence and Quasi‐Coincidence Relations and Studying Equivalent Intuitionistic Fuzzy Sets

In this work, we modify the definition of intuitionistic fuzzy points so that the definition is concise, generalizes fuzzy points, and excludes . We establish new forms of relations between intuitionistic fuzzy sets and demonstrate that every quasi‐coincidence relation is coincidence. Then, we present and examine the concept of equivalence of intuitionistic fuzzy sets. We also study their prominent features and characteristics that aid in our comprehension of how they affect and are influenced by the other concepts in intuitionistic fuzzy topological spaces. Moreover, we define the concept of intuitionistic fuzzy R 0 topological spaces using the equivalence of each intuitionistic fuzzy set with its closure. Elucidative examples are provided to demonstrate the invalidity of some implementation results.