On \(\Lambda\)-generalized closed sets in interval-valued topological spaces

Abstract

In this paper, introduce a new class of sets called \( \Lambda_g\)-closed sets in interval-valued topological spaces. The concept is defined as a generalization of closed sets and is shown to be a weaker form of certain existing closed sets in interval-valued topology. Several fundamental properties of \( \Lambda_g\)-closed sets are established and their behavior with respect to basic set operations is investigated. We also introduce the notion of \( \Lambda_g\)-open sets as the complements of \( \Lambda_g\)-closed sets and study their basic properties. Furthermore, the relationships between \( \Lambda_g\)-closed sets and other well-known classes of sets such as closed sets, \(g\)-closed sets, and semi-closed sets are discussed. Various characterizations and results are obtained to highlight the structural behavior of these sets in interval-valued topological spaces. Suitable examples are provided to illustrate the introduced concepts and to show that the implications between different classes of sets are proper. The results obtained in this work contribute to the further development of generalized closed sets in an interval-valued topology.

1. Introduction

The idea of interval sets was originally proposed by Yao [6] as a useful approach for representing and approximating uncertain or complicated information. Subsequently, Kim et al. [4] described this concept using the term interval-valued sets and viewed it both as an extension of classical set theory and as a particular form of interval-valued fuzzy sets. In their study, they analyzed different types of interval-valued neighborhoods and grouped them into two broad classes. They also investigated the associated interval-valued closure and interior operators. More recently, Cheong et al. [1] developed the concept of interval-valued relations and explored their properties using a category-theoretic framework, which further broadened the applications of interval-valued structures in both theoretical and computational contexts.

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References

1. Cheong, M., Han, S. H., Baek, J. I., Hur, K., Interval-valued relations and their application to category theory, Annals of Fuzzy Mathematics and Informatics, 24(3) (2022), 281–299.Google Scholar
2. Dijitha, S., Navaneethakrishnan, M., A study on g-closed and g-open sets in interval-valued topology, Proceedings of the National Conference on INSTA'24, February 23, 2024, 33–39.Google Scholar
3. Dijitha, S., Navaneethakrishnan, M., A study on semi-closed and semi-open sets in interval-valued topology, Indian Journal of Natural Sciences, 15(88) (2025), 89791–89800.Google Scholar
4. Kim, J., Jun, Y. B., Lee, J. G., Hur, K., Topological structures based on interval-valued sets, Annals of Fuzzy Mathematics and Informatics, 20(3) (2009), 273–295.Google Scholar
5. Rajasekaran, I., Nethaji, O., On interval-valued Λ-sets and λ-closed sets via kernel operators, Annals of Communications in Mathematics, Accepted.Google Scholar
6. Yao, Y., Interval sets and interval-set algebras, Proceedings of the 8^th IEEE International Conference on Cognitive Informatics, 2009, 307–314.Google Scholar

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Nisha, P.S. & Rajasekaran, I. (2026). On \(\Lambda\)-generalized closed sets in interval-valued topological spaces. Asia Mathematika, 10(1), 87–95. https://doi.org/10.5281/zenodo.20997373

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