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

  • Authors:

  • Jie Zhou;Duoqian Miao;Witold Pedrycz;Hongyun Zhang

  • Affiliations:

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

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue on advances in computational intelligence and bioinformatics
  • Year:
  • 2011

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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.