The Optimal Approximation Of Rough Sets And Its Applications In Reduction

Rough set theory is an effective mathematical tool to deal with imprecise,uncertain and incomplete data.Approximation and reduction are two main problems of rough set study.In the classical rough set and its expand models,many scholars use two precise sets:the upper and lower approximation to depict the target set.But in this paper,by using the similarity degree between two sets,we focus on researching one precise set(optimal approximation)to depict the target set and giving its application in reduction.The main contents are as follows:(1)For the problem of rough approximation,a heuristic algorithm about the optimal ap-proximation is given.Because optimal approximation is an precise set and between the upper and lower approximation,firstly,we find some equivalence classes in boundary region to make the similarity degree become larger.Secondly,regarding the significance degree of equivalence class as heuristic information,a heuristic algorithm is designed to search the optimal approximation.Finally,by defining the correct degree of decision rules,we compare and analysis the decision effect with different approximation.Examples show that utilizing optimal approximation can get the highest correct degree of decision rules.(2)For the problem of reduction in inconsistent decision system,firstly,we put forward the optimal approximation allocation reduction?the optimal approximation distribution reduc-tion?the optimal approximation similarity distribution reduction and optimal approximation reduction,and study the relationship among them.Secondly,basing on the significance degree of attribute,we design a heuristic algorithm of the optimal approximation similarity distribution reduction;basing on the discernibility matrix,we design a algorithm of the optimal approxima-tion allocation reduction.Finally,basing on the discernibility matrix,we compare the reduction with other literatures.Results show that the optimal approximation allocation reduction can get a higher degree of support and coverage when extracting rules to a certain extent.