Grey variable dual precision rough set model and its application

The purpose of this paper is to advance a novel grey variable dual precision rough set model for grey concept.

To obtain the approximation of a grey object, the authors first define the concepts of grey rough membership degree and grey degree of approximation on the basic thinking logic of variable precision rough set. Based on grey rough membership degree and grey degree of approximation, the authors proposed a grey variable dual precision rough set model. It uses a clear knowledge concept to approximate a grey concept, and the output result is also a clear concept.

The result demonstrates that the proposed model may be closer to the actual decision-making situation, can effectively improve the rationality and scientificity of the approximation and reduce the risk of decision-making. It can effectively achieve the whitenization of grey objects. The model can be degenerated to traditional variable precision rough fuzzy set model, variable precision rough set model and classic Pawlak rough set, when some specific conditions are met.

The method exposed in the paper can be used to solve multi-criteria decision problems with grey decision objects and provide a decision rule. It can also help us better realize knowledge discovery and attribute reduction. It can effectively achieve the whitenization of grey object.

This method proposed in this paper implements a rough approximation of grey decision object and obtains low-risk probabilistic decision rule. It can effectively achieve a certain degree of whitenization of some grey objects.