Neutrosophic Sets and Systems
Abstract
This paper introduces a new class of Neutrosophic closed sets, termed Neutrosophic γ-generalized α-closed sets (Ne.(γGα)CS), together with their corresponding open sets (Ne.(γGα)OS), within the framework of Neutrosophic Topological Spaces (NTS). The study is motivated by limitations in existing classes of Neutrosophic closed sets, including α-closed, semi-closed, and γ-closed sets, which often lack sufficient flexibility for modeling hybrid structures characterized by partial membership, indeterminacy, and uncertainty. To overcome these limitations, the proposed Ne.(γGα)CS are defined using β-closure operators and α-open supersets, providing a more comprehensive framework that extends and unifies several previously established concepts. The properties of these sets are investigated through rigorous theoretical analysis, supported by counterexamples demonstrating that converse implications do not generally hold. Furthermore, the study examines their algebraic properties, including union, intersection, and inclusion relations. A comparative analysis shows that the proposed structures generalize earlier forms of Neutrosophic closed sets while preserving important topological properties. The results contribute to the further development of Neutrosophic topology and provide a foundation for future research in uncertainty modeling, generalized topological structures, and decision-making systems. This work enhances the expressive power of Neutrosophic topology and suggests potential applications in domains requiring sophisticated treatment of vagueness and imprecision.
Recommended Citation
Kalaiselvi, B.; K. Sivakumar; S. Chandrasekar; P. Kalarani; and A. Kesavan. "Advancing Neutrosophic Topology through Gamma Generalized Alpha Closed Sets." Neutrosophic Sets and Systems 98, 1 (2026). https://digitalrepository.unm.edu/nss_journal/vol98/iss1/2