Abstract
In recent years, “mathematical orientations on real-life problems”, which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components. Classical set theory and interpretation methods fail to represent, express and solve the problems of these types or cause to make wrong decisions. For this reason, in this study, we provide definitions and methods to present information and problem representations in more detail and precision. This paper introduces three new topologies called covering-based rough fuzzy, covering-based rough intuitionistic fuzzy and covering-based rough neutrosophic nano topology. Some fundamental definitions such as open set, closed set, interior, closure and basis are given. Neutrosophic definitions and properties are mainly investigated. We give some real life applications of covering-based rough neutrosophic nano topology in the final part of the paper and an explanatory example of decision making application by defining core point.
Highlights
The world of science has been working on and producing uncertain, incomplete, indeterminate, and indiscernible structures since crisp structures are understood to be unable to solve most real-life problems
With the proposed new definitions, we presented wider versions of the approach space topologies and gave an example that can be applied to real life problems
Some new topologies and their definitions on covering property have been given in this paper
Summary
The world of science has been working on and producing uncertain, incomplete, indeterminate, and indiscernible structures since crisp structures are understood to be unable to solve most real-life problems. To compare the method with some existing methods, Lellis Thivagar and his collaborations [34]–[36], which provides intensive studies especially in the fields of Nano Topology and its applications, has given the definition of Nano topology within the framework of neutrosopy, but with this structure, they pointed out that one could find applications in areas such as Geographical Information Systems (GIS) field including remote sensing, object reconstruction from airborne laser scanner, real time tracking, routing applications and modeling cognitive agents [37] They did not give a specific application example. While a decision-making process is generally in the form of algorithms consisting of five or six steps, our method can only make a definition with the core definition
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