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

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  • S. M. Elsayed
  • Tareq M. Al-Shami

Abstract

In this work, we modify the definition of intuitionistic fuzzy points so that the definition is concise, generalizes fuzzy points, and excludes 0˜. 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 R0 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.

Suggested Citation

  • S. M. Elsayed & Tareq M. Al-Shami, 2025. "Investigating Novel Types of Coincidence and Quasi‐Coincidence Relations and Studying Equivalent Intuitionistic Fuzzy Sets," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:8699936
    DOI: 10.1155/jom/8699936
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    References listed on IDEAS

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    1. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    2. Selma Özçağ & Doğan Çoker, 2000. "A note on connectedness in intuitionistic fuzzy special topological spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-10, January.
    3. A. A. Ramadan & S. E. Abbas & A. A. Abd El-Latif, 2005. "Compactness in intuitionistic fuzzy topological spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-14, January.
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