Incorporation of αM closed sets of neutrosophic over soft modal topological structures for revolutionizing hospital ranking with numerical insights

Abstract

The significance of Neutrosophic environments continues to grow across various disciplines through ongoing advancements. A notable recent development is the Neutrosophic Over Soft Modal Topological Structure (Nos -topology), which integrates Neutrosophic topological operations ⊞ (closure) and ⊡ (interior) with modal operations (modal closure) and ⊙ (modal interior). This work introduces two such structures for the first time, detailing their core properties and addressing challenges related to uncertainty and indeterminacy. Key concepts developed include Neutrosophic Over Soft Modal α closed, αg closed, and αm closed sets, along with various forms of continuity such as modal αm and strong continuity. A real-life application is presented for selecting the best cancer hospital using cosine correlation on Neutrosophic Over Sets, demonstrating the practicality and strength of the proposed framework.