Interval neutrosophic sets and topology

Purpose - In 2005, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology. Design/methodology/approach - The paper investigates the possible relations between INSs and topology. Findings - Relations on INSs and neutrosophic topology. Research limitations/implications - Clearly, the paper is confined to IFSs and NSs. Practical implications - The main applications are in the mathematical field. Originality/value - The paper shows original results on fuzzy sets and topology.