On various neutrosophic topologies

Abstract

Purpose - Recently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NTSs) and also defined various notions of neutrosophic topologies on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and neutrosophic topologies on the non-standard interval. The purpose of this paper is to show that this is false. Design/methodology/approach - The possible relations between the intuitionistic fuzzzy topology and neutrosophic topologies are studied. Findings - Relations on IFT and neutrosophic topologies. 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.