New Topological Approaches to Generalized Soft Rough Approximations with Medical Applications

Abstract

There are many approaches to deal with vagueness and ambiguity including soft sets and rough sets. Feng et al. initiated the concept of possible hybridization of soft sets and rough sets. They introduced the concept of soft rough sets, in which parameterized subsets of a universe set serve as the building blocks for lower and upper approximations of a subset. Topological notions play a vital role in rough sets and soft rough sets. So, the basic objectives of the current work are as follows: first, we find answers to some very important questions, such as how to determine the probability that a subset of the universe is definable. Some more similar questions are answered in rough sets and their extensions. Secondly, we enhance soft rough sets from topological perspective and introduce topological soft rough sets. We explore some of their properties to improve existing techniques. A comparison has been made with some existing studies to show that accuracy measure of proposed technique shows an improvement. Proposed technique has been employed in decision-making problem for diagnosing heart failure. For this two algorithms have been given.

Topological Models of Rough Sets and Decision Making of COVID-19

“…e second part is devoted to the application of the closure operators, proposed in the current paper, in the notion of rough sets. In fact, we have presented three models to approximate the rough sets, which are generalizations of previously presented methods (such as [2,4,8,11,13,20,22,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39]). We studied the properties of these approximations, and we were able to demonstrate all of Pawlak's properties, which were not fulfilled in some other generalizations such as Yao [26] without adding any conditions to the relation.…”

“…Rough set theory was established by computer scientist Pawlak [24,25] based on several difficulties in computer science to overcome this challenge by a modal approximation of a crisp set in the expressions of a pair of sets called the rough approximations of it. Many writers have focused on generalization rough sets [2,4,8,11,13,20,22,23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39].…”

Approximations by Ideal Minimal Structure with Chemical Application

“…Topological structures and their generalizations are of crucial importance in data analysis, which have manifested in different fields, for example, in physics [1], chemistry [2], medicine [3], soft set theory [4], etc. Lashin et al [5] used topological notions to study different issues in rough set theory in order to generalize Pawlak's concepts [6] in different applications and integrate the concepts of rough and fuzzy sets.…”

On g-regularity and g-normality in Fuzzy Soft Topological Spaces

“…After the discovery of fuzzy set theory by Zadeh [33], many authors generalized and applied this idea in different aspects see e. g. ( [1,2,14,19]. The concept of fuzzy topological space was introduced by Chang in [6].…”