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加权自适应多粒度决策理论粗糙集模型

Weighted Adaptive Multi-granularity Decision Theoretic Rough Set Model

  • 摘要: 多粒度粗糙集涉及到属性权重时通常利用指定的方式设定,对于属性颗粒结构对应的上、下近似集计算所需的概率阈值也常依赖于专家建议设定,使得现有粗糙集模型在实际应用中缺乏适应性。为此,提出1种加权自适应多粒度决策理论粗糙集模型(weighted adaptive multi-granulation decision-theoretic rough sets,WAMG-DTRS)。根据信息增益计算属性粒度的权重,通过设置权重系数控制颗粒结构数目,通过单参数决策理论粗糙集中阈值公式确定属性颗粒结构下不同对象对应的上、下近似集计算所需的概率阈值,使模型更好地适应实际应用需求。在该模型的基础上构建5种平均加权自适应多粒度决策理论粗糙集模型,进一步提高模型应用的适应性,且通过实例和实验证明模型的可行性。结果表明:调整权重系数可灵活调整WAMG-DTRS模型的上、下近似集规模;不同平均条件下的平均加权自适应多粒度决策理论粗糙集模型展现出不同的下近似集特性,并具有WAMG-DTRS模型灵活调控权重系数的能力,通过综合考虑不同平均条件可进一步提升模型的适应性和实用性。

     

    Abstract: When multi-granularity rough sets involve the weight of attributes, they are usually implemented in a specified way, and the probability thresholds required for calculating the upper and lower approximation sets corresponding to the attribute granular structure often rely on expert recommendations, which makes the existing rough set models lack adaptability in practical applications. To address this, a weighted adaptive multi-granularity decision theory rough set (WAMG-DTRS) model was proposed. The weight of the attribute granularity was calculated according to the information gain, and the weight coefficient was set to control the number of granular structures. The probability thresholds required for calculating the upper and lower approximate sets corresponding to different objects under the attribute granular structure were determined by the threshold formula in the single-parameter decision theory rough sets to better adapt to practical application needs. Based on this model, five types of average weighted adaptive multi-granularity decision theory rough sets constructed to further enhance the adaptability of model applications. The feasibility of these models were proved through practical examples and experiments. The results show that the scale of the upper and lower approximation sets in the WAMG-DTRS model can be flexibly adjusted by adjusting the weight coefficient, the average WAMG-DTRS models under different average conditions exhibit different characteristics of lower approximation sets and possess the ability of the WAMG-DTRS model to flexibly adjust the weight coefficients. By comprehensively considering different average conditions, the adaptability and practicality of the model can be further improved.

     

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