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

作者：Zhou Jie^*; Miao Duoqian; Pedrycz Witold; Zhang Hongyun

来源：Soft Computing, 2011, 15(8): 1601-1616.

DOI：10.1007/s00500-011-0690-7

• Complete decision table
• Objective function for attribute reduction
• Discernibility function
• Minimal reduct

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.

• 出版日期2011-8
• 单位同济大学