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Research Paper | Mathematics | Volume 15 Issue 6, June 2026 | Pages: 1098 - 1101 | India
Characterization of Fuzzy Topological Approximations of Multisets
Abstract: The theory of multisets provides an efficient mathematical framework for representing collections containing repeated elements, while fuzzy set theory addresses uncertainty through graded membership values. Topological approximation operators have been widely used in rough set theory to describe vague concepts. In this paper, we introduce fuzzy topological ap- proximations of multisets by combining fuzzy multiset topology with rough approximation theory. New lower and upper approximation operators are defined using fuzzy multiset interior and closure operators. Fundamental properties of these approximations are established, including monotonicity, idempotency, duality, and boundary characterization. Furthermore, relation- ships among fuzzy topological approximations, rough multisets, and fuzzy multiset topological spaces are investigated. Several illustrative examples are provided to demonstrate the applicability of the proposed model. The results generalize classical topological approximations of multisets and provide a new framework for uncertainty modeling in decision systems and information processing.
Keywords: Fuzzy multiset, multiset topology, rough multiset, fuzzy approximation space, lower approximation, upper approximation
How to Cite?: Rakesh Kumar, "Characterization of Fuzzy Topological Approximations of Multisets", Volume 15 Issue 6, June 2026, International Journal of Science and Research (IJSR), Pages: 1098-1101, https://www.ijsr.net/getabstract.php?paperid=SR26619083212, DOI: https://dx.doi.org/10.21275/SR26619083212