Notice of RetractionProduct model of grade lower approximation operators based on two parameters

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.

Grade is an important quantitative index, and graded rough set model is an important improved rough set model. This paper is to explore product operation of grade lower approximation operators. Based on logical product operation, this paper proposes product model of grade lower approximation operators based on two parameters. Essence, basic structure and properties are obtained in the new model. Macroscopic algorithm and structural algorithm are proposed and analyzed, and by comparison it obtains an important conclusion that structural algorithm has advantages in time complexity and space complexity. Finally an example is given to illustrate the new model and its algorithms. Product model of grade lower approximation operators based on two parameters has extended graded rough set model partially, and it obtains idempotent property of grade lower approximation operators.