Abstract
This paper presents a study of new structure in nano topology. We propose an alternative formulation of nano topological space induced by different neighbourhoods. We also define different types of neighbourhood based on covering of the universe. The properties of various types of neighbourhood such as Right (NR), Left (NL), Intersection (NI) and Union (NU) of neighbourhoods are discussed. Further, we analysed their indiscernibility matrix and the indiscernibility function which gives the CORE based on nano topology in neighbourhood when applied in real life application.
Highlights
The covering approximation spaces can be studied using covering-based rough set theory (Thuan, 2009; Wang, He, Chen, & Hu, 2014; Zhu, 2009), which is a mathematical tool for dealing with data mining, vagueness and granularity in information systems
The purpose of this paper is to introduce a new structure of nano topology induced by different types of neighbourhood which is right, left neighbourhood and union, intersection of neighbourhood based on covering of the universe
Example 4.4 Consider Example 4.3 and to find the neighbourhood of boundary region as follows (Table 3): 5. Indiscerniblity matrix for the basis in neighbourhood such as Right (NR) (X) we study the indiscernibility matrix of the basis B = NR of the nano topology induced by right neighbourhood
Summary
The covering approximation spaces can be studied using covering-based rough set theory (Thuan, 2009; Wang, He, Chen, & Hu, 2014; Zhu, 2009), which is a mathematical tool for dealing with data mining, vagueness and granularity in information systems. We study the nano topological space approach by using the concept of different types of neighbourhood induced by covering of the univese. M. Lellis Thivagar introduced nano topological space on a subset X of a universe, defined as lower and upper approximations of X. The purpose of this paper is to introduce a new structure of nano topology induced by different types of neighbourhood which is right, left neighbourhood and union, intersection of neighbourhood based on covering of the universe. We developed an algorithm to find the core of complete information system by using the indiscernibility matrix This algorithm is defined in nano topology induced by different neighbourhoods and applied to analyse the real life problems. We provide an example for a better understanding of the subject
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