三支决策代价目标函数的关系及推理研究

Relationship and Reasoning Study for Three-way Decision Cost Objective Functions

三支决策是不确定问题求解的重要理论。经典的决策粗糙集模型通过计算三支区域总体决策最小化风险,给出了一种有效的三支决策阈值求解方案。然而对于决策粗糙集理论中代价目标函数之间的逻辑关系及其三支决策阈值间的推理,目前尚未有研究进行深入讨论。首先,提出了一种基于三支决策代价目标函数间逻辑关系的新型阈值计算方法。其次,根据不同损失函数取值分布情况下的三支决策阈值推导,分别给出了不同阈值的三支分类语义解释。最后,通过一组典型的实例证明了提出的基于三支决策代价目标函数的阈值计算方法及三支决策分类的推理是有效的。

Three-way decision（3 WD）is an important method for solving problems under uncertainty.The classical decision rough set theory provides an efficient tri-partition threshold solving method by minimizing the overall decision risk.However,the logical relationship among the three-way decision cost objective functions and its threshold reasoning still need further study.In this study,threshold solution model based on logical relationship among the cost objective functions of three-way decision was constructed.Furthermore,the derivation method of three-way decision thresholds for different loss function values distribution was studied,and the three-way classification semantic interpretation of different domain values was given respectively.Finally,a set of typical examples show that the three-way classification based on the above cost objective functions reasoning is valid.