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.