Analysis of alternative objective functions for attribute reduction in complete decision tables |
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| Authors: | Jie Zhou Duoqian Miao Witold Pedrycz Hongyun Zhang |
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| Affiliation: | (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 |
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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. |
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