Topological Approaches for Rough Continuous Functions with Applications

In this paper, we purposed further study on rough functions and introduced some concepts based on it. We introduced and investigated the concepts of topological lower and upper approximations of near-open sets and studied their basic properties. We defined and studied new topological neighborhood approach of rough functions. We generalized rough functions to topological rough continuous functions by different topological structures. In addition, topological approximations of a function as a relation were defined and studied. Finally, we applied our approach of rough functions in finding the images of patient classification data using rough continuous functions.

Automated summary

This paper focuses on further study of rough functions, introducing concepts of topological lower and upper approximations of near-open sets, and studying their basic properties. The study also defines and explores new topological neighborhood approaches of rough functions, and generalizes rough functions to topological rough continuous functions with different topological structures. Additionally, topological approximations of a function as a relation are defined and studied, with an application in finding images of patient classification data using rough continuous functions.