基于不确定性与错误分类率博弈的序贯三支决策模型

Sequential Three-Way Decision Model Based on the Game Between Uncertainty and Error Classification Rate

在实际分类决策中,序贯三支决策模型为决策者提供了一个渐进式的决策方法.然而,现有序贯三支决策模型的研究从提高分类精度或减少不确定性的动机来求取每一粒层的决策阈值,缺乏对二者的综合考虑.为了解决这个问题,本文结合博弈论的思想构建了基于错误分类率与边界域不确定性博弈的序贯三支决策模型.首先,分析了序贯三支决策模型中边界域不确定性与决策区域错误分类率的变化关系并构建了二者之间的博弈;其次,从博弈终止的条件出发,基于纯策略纳什均衡原理,提出了求取每一粒层自适应决策阈值的优化模型;再次,为了比较不同模型的效果,从多目标决策的角度,设计了基于TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)的阈值选取方法;最后,通过UCI数据集进行了两种模型的对比实验.实验结果表明:基于博弈论的序贯三支决策模型求取的决策阈值具有更小的错误分类率以及更合理的阈值结构.

In actual classification decision,sequential three-way decision model provides decision-makers with a progressive decision-making method.However,the existing researches of the sequential three-way decision obtain the decision thresholds of each granularity layer motivated from improving classification accuracy or reducing uncertainty,which lacks a comprehensive consideration of the two factors.In order to solve this problem,this paper concerning the idea of game theory to construct a game-theoretic sequential three-way decision model between the error classification rate of decision regions and the uncertainty of the boundary region.Firstly,the relationship between the uncertainty of the boundary region and the error classification rate of the decision regions is analyzed,and then the game of the two players is constructed.Secondly,starting from the game stopping condition,an optimization model for calculating the adaptive decision thresholds of each granularity layer is designed based on the principle of pure strategy Nash equilibrium.Furthermore,to compare the performance of different models,from the perspective of multi-objective decision-making,another thresholds selection approach based on the TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)is designed.Finally,a comparative experiment of the two models was conducted through the UCI data sets.The experimental results show that the decision thresholds obtained by the game-theoretic sequential three-way decision model have a smaller error classification rate and a more reasonable threshold structure than multi-objective decision-making.