Some neighborhood-related fuzzy covering-based rough set models and their applications for decision making

Abstract

Fuzzy rough set (FRS) has a great effect on data mining processes and the fuzzy logical operators play a key role in the development of FRS theory. In order to generalize the FRS theory to more complicated data environments, we firstly propose four types of fuzzy neighborhood operators based on fuzzy covering by overlap functions and their implicators in this paper. Meanwhile, the derived fuzzy coverings from an original fuzzy covering are defined and the equalities among overlap function-based fuzzy neighborhood operators on a finite fuzzy covering are also investigated. Secondly, we prove that new operators can be divided into seventeen groups according to equivalence relations, and the partial order relations among these seventeen classes of operators are discussed, as well. And then, two types of neighborhood-related fuzzy covering-based rough set models are proposed via the overlap function-based fuzzy neighborhood operators and the t-norm-based fuzzy neighborhood operators. Furthermore, the groups and partially order relations are also discussed. Finally, a novel fuzzy TOPSIS methodology is put forward to solve a biosynthetic nanomaterials select issue, and the rationality and enforceability of our new approach is verified by comparing its results with nine different methods.