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

作　　者：张宇 汪小燕 ZHANG Yu;WANG Xiaoyan(School of Computer Science&Technology,Anhui University of Technology,Maanshan 243032,China)

机构地区：[1]安徽工业大学计算机科学与技术学院,安徽马鞍山243032

出　　处：《安徽工业大学学报(自然科学版)》2025年第2期178-188,共11页Journal of Anhui University of Technology(Natural Science)

基　　金：国家自然科学青年基金项目(61806004);安徽省自然科学基金项目(1808085MF196)。

摘　　要：多粒度粗糙集涉及属性权重时,通常利用指定的方式设定,而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,这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)。通过信息增益计算属性粒度的权重,并通过设置权重系数控制颗粒结构数目。同时,利用单参数决策理论粗糙集中的阈值公式确定属性颗粒结构中不同对象对应的上、下近似集计算所需的概率阈值,从而使模型更好地适应实际应用需求。在WAMG-DTRS模型的基础上,进一步构建5种平均加权自适应多粒度决策理论粗糙集模型,以进一步提高模型应用的适应性。通过实例和实验验证,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WAMG-DTRS模型展现出不同的下近似集特性,并具备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,可以进一步提升模型的适应性。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 decisiontheoretic 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.

关 键 词：自适应阈值 权重 多粒度 决策理论 粗糙集 信息增益 粒计算 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]