基于决策依赖度的粗糙集约简模型研究

为寻求高效的粗糙集约简模型,基于可分辨关系提出决策分辨约简、依赖性和依赖度等概念.与以往粗糙集约简模型相比,为提高约简精确性,提出性能为O(|P‖U|)的等价类划分方法和性能为O(|P‖U/C|)的属性重要性度量方法.同时给出了相关定理和等价命题,论证了传统决策约简模型和决策分辨约简模型的一致性.并基于属性重要性给出性能为O(|C|~2|U/C|)的求核方法和性能为Max{O(|C‖U|),O(|C|~2|U/C|)}的约简模型.新模型充分考虑了核属性和其他属性间的关联,从而有效降低冗余率,解决了对比模型存在的问题.理论和仿真实例分析表明新模型高效且结果准确率高.

Research on rough set reduction model based on decision dependency degree

To approach a good performance and practical model for attribute reduction in decision systems, the concept, distinguishable relation is given. Against the new concept, the "distinguishable reduction of decision system", "dependency" and "dependency degree" concepts are defined also in this paper. In order to improve the accuracy in the reduction result, one of the new methods which has time complexity of O(|P||U|) for equivalence class partition and another method which has time complexity of O(|P||U|) for attribute importance measurement are given. In the meanwhile, relevant theory and equivalent proposition are drawn out. After that, the consistence of the classic attribute reduction and distinguishable reduction is proved. Based on the attribute importance, a faster core set method which has upper limit of O(|C|²|U/C|) on time complexity and a reduction model which has time performance of Max{O(|C||U|), O(|C|²|U/C|)} are proposed here. The new reduction model thoroughly treats the relationship between the core set and other attributes, therefore, decreases the impact from analysis of distinguishable ability on single attribute. Thus, this model effectively reduces the redundancy in the reduction result and effectively solves the problems of model in contrast. The theoretical analysis and experimental result show that the new reduction model proposed here is feasible and meaningful.