Abstract:
In multi-granulation rough sets, attribute weights are typically assigned through predetermined methods, while the probability thresholds required for computing upper and lower approximations of attribute granular structures often rely on expert recommendations. This makes existing rough set models lack adaptability in practical applications. To address this, a weighted adaptive multi-granularity decision-theoretic rough set (WAMG-DTRS) model was proposed. The weights of the attribute granularity were calculated according to information gain, and the number of granular structures was controlled by the setting weight coefficients. 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 applications. Based on this model, five types of average weighted adaptive multi-granularity decision-theoretic rough sets models were constructed, further improving the adaptability of the model. The feasibility of these models was proved through practical examples and experiments. The results show that adjusting the weight coefficients can flexibly control the scale of the upper and lower approximation sets in the WAMG-DTRS model. The average weighted adaptive multi-granulation decision-theoretic rough set models under different average conditions exhibit varying characteristics in the lower approximation sets and retain the ability of the WAMG-DTRS model to flexibly adjust weight coefficients. By considering different average conditions, the adaptability of the model can be further enhanced.