不完备信息系统中的多重代价决策粗糙集

Multi-cost based decision-theoretic rough sets in incomplete information systems

决策粗糙集源于贝叶斯决策准则,利用代价矩阵生成了构建概率粗糙集所需的一对阈值.通过代价对目标事物的近似使得决策粗糙集模型对代价敏感,使决策粗糙集成为一种十分重要的粗糙集方法.然而,大多数的决策粗糙集模型仅使用一个代价矩阵进行描述,来求解完备信息系统中的问题.这种方法并未考虑机器学习和数据挖掘中的一个重要问题,即现实生活中代价本身所具有的多样与变化特性.为解决该问题,首先,通过使用多重代价矩阵将多代价策略引进决策粗糙集;然后,在不完备信息系统中,分别提出了乐观与悲观两种形式的多代价决策粗糙集方法,讨论了这两种新的决策粗糙集模型与基于单代价矩阵决策粗糙集模型之间的关系,并且给出了乐观和悲观这两种决策粗糙集决策代价的总代价计算公式.最后,在四组UCI数据集上对几种不同的决策粗糙集的决策代价进行了对比分析.实验结果表明,乐观决策粗糙集得到的决策代价是一种较优的代价,并且随着代价矩阵的增加,代价的值将会保持在一个稳定的值.揭示了决策理论粗糙集的潜在应用并且为其提供了新的研究方向.

Decision-theoretic rough set comes from Bayesian decision procedure,in which a pair of the thresholds is derived by the cost matrix for the construction of probabilistic rough set.Decision-theoretic rough set is a crucial rough set approach.By introducing the cost into probabilistic approximation of the target,the model of decision-theoretic rough set is actually sensitive to cost.However,most of the previous results about decision-theoretic rough set only use one and only one cost matrix to deal with the problems of the complete information systems.This method does not take the property of multiplicity and variability of cost into consideration,which is an important issue in machine learning and data mining.To solve such problems,a multi-cost strategy is firstly introduced into decision-theo-retic rough set by using multiple cost matrixes.Moreover,the optimistic and pessimistic multi-cost decision-theoretic rough set models are proposed in incomplete information systems,respectively.Furthermore,the relationships are discussed between the two new decision-theoretic rough sets and the single cost matrix based decision-theoretic rough set.Then,we describe the formulas of the whole decision costs of optimistic and pessimistic multi-cost decision-theoretic rough set models.Finally,the several different decision costs of multi-cost decision-theoretic rough sets determined by decision-theoretic rough sets are tested on four UCI data sets.Experimental results show that the optimistic multi-cost decision-theoretic rough set model can generate the lowest decision cost.With the increase of the cost matrixes,all kinds of the whole decision costs will keep a steady value at last.The study suggests potential application areas and new research trends concerning decision-theoretic rough set.