Variable precision fuzzy rough sets based on overlap functions with application to tumor classification

Abstract

Overlap functions, which can be characterized as a type of non-associative binary aggregation operators, have emerged as one of the most extensively utilized aggregation operators in numerous applications, including image processing, information fusion, and classification problems. At the same time, fuzzy rough sets have also been widely used in these fields due to their excellent ability to handle continuous and uncertain information. However, the variable precision fuzzy rough set model based on overlap functions and its applications have not been fully studied. For instance, some basic properties are invalid and there is a lack of practical applications. In this paper, both overlap functions and precision parameters are introduced into the fuzzy rough sets, namely the overlap function-based variable precision fuzzy rough set (OVPFRS), which is then used in the practical problem of tumor classification. First, considering the existing overlap function-based rough set models, the OVPFRS model is established, and some underlying properties of this model are explored. Second, on the basis of the proposed model, a method for attribute reduction is developed. Finally, the new method is applied to the classification of tumor data from the real world. Through experimentation and comparison with other attribute reduction methods, it has been demonstrated that our model is flexible and the algorithm is viable and effective.