The aim of this paper is to introduce and develop a new class of sets namely neutrosophic vague generalized pre-closed sets in neutrosophic vague topological space.

The term topology was introduced by Johann Beredict Listing in the 19th century. Closed sets are fundamental objects in a topological space. In this paper, we use neutrosophic vague sets and topological spaces and we construct and develop a new concept namely “neutrosophic vague topological spaces”. By using the fundamental definition and necessary example we have defined the neutrosophic vague topological spaces and have also discussed some of its properties. Also we have defined the neutrosophic vague continuity and neutrosophic vague compact space in neutrosophic vague topological spaces and their properties are deliberated.

The main objective of this paper is to make known to a new concept of generalised neutrosophic bipolar vague sets and also defined neutrosophic bipolar vague topology in topological spaces. Also, we introduce generalized neutrosophic bipolar vague closed sets and conferred its properties.

The aim of this paper is to introduce a new class of sets called neutrosophic vague rw closed sets and neutrosophic vague rw-open sets, neutrosophic vague rwT1/2 space and neutrosophic vague rwTw in neutrosophic vague topological spaces. Further we analyse some of its properties.

Vague sets and neutrosophic sets play an inevitable role in the developing scenario of mathematical world. In this modern era of artificial intelligence most of the real life situations are found to be immersed with unclear data. Even the newly developed concepts are found to fail with such problems. So new sets like Plithogenic and new combinations like neutrosophic vague arose. Classical set theory dealt with single universe and can be studied by taking it’s subsets.

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets.

This paper committed to the investigation of Neutrosophic topological spaces. In this paper Generalized Alpha Closed Sets and Generalized Alpha Open Sets are presented. Some of its properties are contemplated.