Decision making based on rough approximations generalized by j -fuzzy neighborhoods

Abstract

Rough set and fuzzy set theory are two distinct but related mathematical techniques, and both theories deal with uncertain and incomplete information in data analysis. Approximation operators and accuracy measures are the key points of rough set theory. Various generalizations on rough approximations have been proposed by many authors to reduce the boundary region and increase the accuracy percentage. One of these generalizations is the neighborhood system. The concept of the neighborhood system is a mathematical tool for handling inconsistent and limited knowledge. It can be applied to find the approximations to resolve the vagueness of data collection. This paper aims to examine $\mathfrak{j}$ -neighborhoods in the context of a binary fuzzy relation and to introduce the concept of $\mathfrak{j}$ -fuzzy neighborhoods. $\mathfrak{j}$ -fuzzy approximations are proposed and studied using these neighborhoods. Further, an example related to heart disease is discussed to demonstrate the significance of the proposed work and the result is compared with existing ones. A medical application is described using $\mathfrak{j}$ -fuzzy neighborhoods to categorise patients based on their COVID-19 infection.