A New Inventive Approach to Nano Fuzzy Soft Topological Space Using Mathematical Analysis

The important theme of this paper is to define a lower and upper approximation for the set under consideration in order to examine a novel class of topological field known as Nano fuzzy soft topological space. Fuzzy topology coverts ordered structure to topological structure by using by its own criteria conditions. Nano topology is defined with the help of equivalence relation so that even micro spacing is included in the topological space. The condition of these two topological space has been merged and a new space known as Nano fuzzy topological space has been investigated and studied. Soft sets are an abstraction of fuzzy set theory which was interposed to deal with uncertainty conditions using parameters. Using soft sets, Nano fuzzy topology can be extended to a new form called Nano fuzzy soft topological space and it can be used to study matters of vagueness by defining a proper boundary layer. Since this concept depends upon defining appropriate boundary layers using topological concepts, it easy to determine the key components for a particular problem by properly defining three important regions which are upper approximation area, lower approximation area and boundary region. The use of Nano fuzzy soft topological space in predicting the cause of a disease has been discussed in this paper. It can be extended to study any complex problems in real life by converting it to a Nano fuzzy soft topological space using the three main key factors.