Dynamic Reduction Of Fuzzy ?-covering

Fuzzy covering is a natural extension of the covering by replacing the crisp set with a fuzzy set,and fuzzy ?-covering is a generalization of fuzzy covering.Since fuzzy ?-covering was proposed,many scholars devoted themselves to the research of related operators and models.However,few scholars studied the reduction of fuzzy ?-covering.After Yang et al defined the union reducible element and gave the reduction algorithm,Huang et al updated his reduction algorithm by the matrix method,and proposed a dynamic algorithm to calculate the reduction of a fuzzy ?-covering when the object changes.In the dynamic environment,the knowledge reduction of information system with the change of object set,attribute set and attribute value are an important issues.Therefore,how to update the reduction based on the existing information is an important task to improve the efficiency of knowledge discovering.Based on the approach of calculating reduction of fuzzy ?-covering when the object set changes which proposed by Huang et al,this paper further explores the following two aspects:(1)For the calculating reduction problem of fuzzy ?-covering when a covering element is added into or deleted from a fuzzy ?-covering.In this paper,we firstly study whether the fuzzy covering is still a fuzzy ?-covering after adding or deleting a covering element.Secondly,whether the reducible elements and the irreducible elements in fuzzy ?-covering remain irreducible or reducible in the fuzzy ?-covering after adding or deleting a covering element is studied.The dynamic algorithm for calculating reduction is designed to improve the efficiency.Finally,several UCI data sets are used to verify the validity of the proposed algorithm.(2)For the reduction change problem of fuzzy ?-covering when a covering element is coarsened or refined in fuzzy ?-covering.In this paper,we firstly proposes the definition of the coarsening and refining of the covering element in the fuzzy ?-covering approximation space.Secondly,we study whether the fuzzy covering is still a fuzzy ?-covering after coarsening and refining a covering element.Thirdly,whether the reducible elements and the irreducible elements in fuzzy ?-covering remain irreducible or reducible in the fuzzy?-covering after coarsening and refining a covering element is studied.The dynamic algorithm for calculating reduction is designed to improve the calculation efficiency.Finally,several UCI data sets are used to verify the validity of the proposed algorithm.