Abstract
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.
Highlights
Many studies have appeared recently and dealt with generalizations of topological near-open sets [1, 2] and the possibility of using them in many life applications, including their use in data reduction and reaching some new decisions and conclusions
We generalize the concept of rough function to topological rough function by using topological structures. e topological spaces with rough sets are very useful in the field of digital topology which is widely applied in the image processing in computer sciences
Work e emergence of topology in the construction of some rough functions will be the bridge for many applications and will discover the hidden relations between data
Summary
Many studies have appeared recently and dealt with generalizations of topological near-open sets [1, 2] and the possibility of using them in many life applications, including their use in data reduction and reaching some new decisions and conclusions. In rough sets formulated by Pawlak, an equivalence relation on the universe of elements is determined based on their attribute values. It was early recognized that standard rough set model based on the indiscernibility relation is well suited in the case of nominal attributes. Other rough set theory applications in computer science (field of information retrievals) using topological generalizations can be found in [33–40]. E goal of Section 3 is to introduce the concepts of topological lower and upper approximations of near-open sets and discuss their basic.
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