In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic supra pre- continious functions. Furthermore, the concepts of neutro- sophic supra pre-open maps and neutrosophic supra pre-closed maps in terms of neutrosophic supra pre-open sets and neutrosophic supra pre-closed sets, respectively, are introduced and several prop- erties of them are investigated.

We introduce the notion of neutrosophic Φ-open set and neutrosophic Φ-continuous mapping via neutrosophic topological spaces and investigate several properties of it. By defining neutrosophic Φ -open set, neutrosophic Φ -continuous mapping, and neutrosophic Φ –open mapping, we prove some remarks, theorems on neutrosophic topological spaces.

In this paper, we introduce and investigate a new class of sets and functions between supra topological spaces called neutrosophic -supra open set and neutrosophic -supra continuous function.

In this paper, we introduce and investigate a new class of sets and functions between topological space called neutrosophic semi-supra open set and neutrosophic semi-supra open continuous functions respectively.

The aim of this paper is to introduced neutrosophic crisp supra topological spaces (NCSTS) and neutrosophic crisp supra bi and tri-topological spaces, new types of open and closed sets in neutrosophic crisp supra bi and tri-topological spaces, the closure and interior of neutrosophic crisp supra bi and tri-topological space, new concepts of open and closed sets, their properties are investigated.

The primary aim of this paper is to introduce the neutrosophic supra topological spaces. Neutrosophic subspaces and neutrosophic mappings are presented by which some contradicting examples of the statements of Abd-Monsef and Ramadan[9] in fuzzy supra topological spaces are derived. Finally, a new method is proposed to solve medical diagnosis problems by using single valued neutrosophic score function.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.