三支决策理论的扩展与仿真实验

Expansion and Simulation Experiment of Three-way Decision Theory

基于三支决策理论在实际决策中只能将决策对象划分为正域、负域和边界域的局限性,文章立足于传统的三支决策理论,对三支决策理论进行扩展,提出了N支决策理论,使传统的三支决策理论成为特例,扩大了三支决策理论的应用范围。借助贝叶斯理论和决策代价表,以决策的平均损失最小为原则,给出了N支决策理论所需要的阈值和评价函数。最后以鸢尾花分类问题为例,用N支决策理论和K-均值快速聚类两种方法进行分类,通过比较误判率的大小验证N支决策理论的有效性。

Aiming at the limitation of three-way decision theory which can only divide decision objects into positive domain,negative domain and boundary domain in actual decision-making, this paper expands the three-way decision theory based on the traditional three-way decision theory, and proposes the N-way decision theory so as to make the traditional three-way decision theory a special case, thus expanding its application scope. With the help of Bayesian theory and decision cost table, the paper takes minimum average loss of decision-making as the principle to give a threshold and evaluation function. Finally, taking the classification of iris as example, the paper uses two methods of N-way decision theory and K-means fast clustering to conduct classification, and compares the misjudgment rates to verify the effectiveness of N-way decision theory.