Year: 2025
Type: article
Abstract: Neutrosophic set theory, an advanced framework for error reduction, extends fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). It enhances effectiveness by refining the definition of indeterminacy, a concept for situations where values cannot be precisely determined. In this paper, we propose dividing indeterminacy into two components based on membership: relative truth (RT), which leans toward truth, and relative falsehood (RF), which leans toward falsehood. This approach improves accuracy by considering, relative truth and relative falsehood, rather than a single indeterminate value. The modified neutrosophic set, called the quadri-portioned neutrosophic soft set (QPNSS), includes four membership attributes: absolute truth, relative truth, relative falsehood, and absolute falsehood, offering greater clarity in uncertain situations. New operations are introduced on QPNSS, such as the quadri-partitioned neutrosophic soft set, subsets, complement, absolute set, set difference, and null set. AND and OR operations are also defined. Additionally, a quadri-partitioned neutrosophic soft topological space (QPNSTS) is defined, with key results presented. We define and explore new concepts such as pre-open (p-open) sets, interior, and closure. The paper also examines QPNS compactness, reducibility to finite sub-covers, and other important properties like the intersection of QPNS p-closed sets and QPNS p-compact spaces. This work contributes to the theoretical understanding of QPNS spaces, particularly in soft topological spaces.
Language: English
Topic: Fuzzy and Soft Set Theory
Field: Decision Sciences
Domain: Social Sciences
Open Access status: diamond
Funder: Northern Border University
OpenAlex ID: W4410003569