Abstract: Attribute reduction is one of the core contents of the study of rough set theory and a crucial component of the theory itself.This approach aims to minimize redundant information and extract a set of attributes that is both representative and pivotal.In the process of attribute reduction,a difference matrix is commonly employed to measure the relationships between attributes.By analyzing the difference matrix,researchers can identify attributes that contribute similar information in describing the system's behavior,facilitating the process of attribute reduction.The three-decision-based difference matrix attribute reduction algorithm,starting from the attributes of the difference matrix,characterizes the importance of attributes beyond the core.It establishes a novel approach to attribute reduction based on the three-decision theory,dividing the upper and lower approximations of traditional probability rough sets into the positive region,negative region,and boundary region within the framework of three decisions.The proposed algorithm provides decision rules based on different regions and controls the three decision thresholds through a decision loss function.Compared to similar algorithms,it yields more concise reduction sets and decision rules,and has a lower time complexity.

Key words: Three-way decision, Threshold value, Discernibility matrix, Importance degree, Attribute reduction