, Volume 15, Issue 8, pp 16011616
Analysis of alternative objective functions for attribute reduction in complete decision tables
 Jie ZhouAffiliated withDepartment of Computer Science and Technology, Tongji UniversityDepartment of Electrical and Computer Engineering, University of Alberta Email author
 , Duoqian MiaoAffiliated withDepartment of Computer Science and Technology, Tongji University
 , Witold PedryczAffiliated withDepartment of Electrical and Computer Engineering, University of Alberta
 , Hongyun ZhangAffiliated withDepartment of Computer Science and Technology, Tongji University
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Attribute reduction and reducts are important notions in rough set theory that can preserve discriminatory properties to the highest possible extent similar to the entire set of attributes. In this paper, the relationships among 13 types of alternative objective functions for attribute reduction are systematically analyzed in complete decision tables. For inconsistent and consistent decision tables, it is demonstrated that there are only six and two intrinsically different objective functions for attribute reduction, respectively. Some algorithms have been put forward for minimal attribute reduction according to different objective functions. Through a counterexample, it is shown that heuristic methods cannot always guarantee to produce a minimal reduct. Based on the general definition of discernibility function, a complete algorithm for finding a minimal reduct is proposed. Since it only depends on reasoning mechanisms, it can be applied under any objective function for attribute reduction as long as the corresponding discernibility matrix has been well established.
Keywords
Complete decision table Objective function for attribute reduction Discernibility function Minimal reduct Title
 Analysis of alternative objective functions for attribute reduction in complete decision tables
 Journal

Soft Computing
Volume 15, Issue 8 , pp 16011616
 Cover Date
 201108
 DOI
 10.1007/s0050001106907
 Print ISSN
 14327643
 Online ISSN
 14337479
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Complete decision table
 Objective function for attribute reduction
 Discernibility function
 Minimal reduct
 Industry Sectors
 Authors

 Jie Zhou ^{(1)} ^{(2)}
 Duoqian Miao ^{(1)}
 Witold Pedrycz ^{(2)}
 Hongyun Zhang ^{(1)}
 Author Affiliations

 1. Department of Computer Science and Technology, Tongji University, Shanghai, 201804, People’s Republic of China
 2. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, T6G 2G7, Canada