On Neutro-Topological Spaces and Their Properties

Abstract

There is a lot of ambiguous information in the real world that crisp values can't manage. The fuzzy set theory was proposed by Zadeh. It is an age-old and excellent tool for dealing with uncertain information. As a result, intuitionistic fuzzy set theory was suggested. However, these theories are incapable of dealing with all forms of uncertainty, such as indeterminate and inconsistent data in various decision-making situations. To address this shortfall, Smarandache proposed the neutrosophic set theory by introducing a degree of indeterminacy as an independent component. In this current decade, neutrosophic environments are mainly interested by different fields of researchers. Recently, Smarandache introduced theNeutroAlgebra and AntiAlgebras. NeutroAlgebras and AntiAlgebras represent a new research subject that is based on real-world examples. In this chapter, some properties of NeutroTopological space are introduced and studied with examples. Several definitions of NeutroInterior, NeutroClosure, and NeutroBoundary are defined, and the authors also studied its properties with examples.