Soft Computing

, Volume 15, Issue 8, pp 1601–1616

Analysis of alternative objective functions for attribute reduction in complete decision tables

  • Jie Zhou
  • Duoqian Miao
  • Witold Pedrycz
  • Hongyun Zhang
Original Paper

DOI: 10.1007/s00500-011-0690-7

Cite this article as:
Zhou, J., Miao, D., Pedrycz, W. et al. Soft Comput (2011) 15: 1601. doi:10.1007/s00500-011-0690-7

Abstract

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 

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Jie Zhou
    • 1
    • 2
  • Duoqian Miao
    • 1
  • Witold Pedrycz
    • 2
  • Hongyun Zhang
    • 1
  1. 1.Department of Computer Science and TechnologyTongji UniversityShanghaiPeople’s Republic of China
  2. 2.Department of Electrical and Computer EngineeringUniversity of AlbertaEdmontonCanada

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