Probabilistic model criteria with decision-theoretic rough sets

In dealing with risk in real decision problems, decision-theoretic rough sets with loss functions aim to obtain optimization decisions by minimizing the overall risk with Bayesian decision procedures. Two parameters generated by loss functions divide the universe into three regions as the decision of acceptance, deferment and rejection. In this paper, we discuss the semantics of loss functions, and utilize the differences of losses replace actual losses to construct a new “four-level” approach of probabilistic rules choosing criteria. Ten types of probabilistic rough set models can be generated by the “four-level” approach and form two groups of models: two-way probabilistic decision models and three-way probabilistic decision models. A reasonable decision with these criteria is demonstrated by an illustration of oil investment.     

三支决策与决策粗糙集融合模型

Paw lak粗糙集模型没有对正域、边界域和负域赋予语义,不能进行再决策,而三支决策对边界域赋予了新的语义,可以对边界域做出进一步刻画,对于边界域的进一步划分,依据属性的重要性,使满足条件的样本划入再决策域,不满足条件的样本继续保留在边界域中,降低了边界域样本处理的失误率.本文在对概率粗糙集模型、三支决策粗糙集的理论、贝叶斯理论的决策过程和决策粗糙集模型进行研究的基础上,提出了一种三支决策与决策粗糙集融合模型,与Paw lak-三支决策模型相比,其划分损失更小,处理结果更优.该模型运用三支决策理论对决策粗糙集的边界域赋予延迟决策的语义,对于延迟决策再运用三支决策理论进行迭代操作,对边界域样本进一步处理.在迭代的过程中,依据属性的重要程度将属性排序,从而客观的得到迭代过程中每次优先依据哪个属性进行划分.实验结果表明,该模型比单一运用决策粗糙集模型进行决策代价小,三支决策通过迭代对边界域处理的正确率有所提高,这为准确决策提供了一种新的方法.     

Three-way decisions based on decision-theoretic rough sets under linguistic assessment with the aid of group decision making

Based on decision-theoretic rough set model of three-way decisions, we augment the existing model by introducing linguistic terms. Considering the two types of parameters being used in the three-way decisions with linguistic assessment, a certain type of novel three-way decisions based on the Bayesian decision procedure is constructed. In this way, three-way decisions with decision-theoretic rough sets are extended to the qualitative environment. With the aid of multi-attribute group decision making, the values of these parameters are determined. An adaptive algorithm supporting consistency improvement of multi-attribute group decision making is designed. Then, we optimize the scales of the linguistic terms with the use of particle swarm optimization. The values of these parameters of three-way decisions are aggregated when proceeding with group decision making. Finally, the proposed model of three-way decisions with linguistic assessment is applied to the selection process of new product ideas.     

基于决策粗糙集的广义序贯三支决策方法

三支决策是求解动态不确定性问题的有效方法之一。相比传统的二支决策,序贯三支决策方法在信息不充分或证据不足时能有效平衡决策结果代价和过程代价。在研究多层次的粒结构、多选择的处理对象和多样化的代价结构的基础上,提出了一种基于决策粗糙集的广义序贯三支决策模型。该模型在每一层都考虑了7种不同的对象处理方式。最后,通过实验对比分析了该模型中7种方法的效率和性能。     

Three-way decisions with probabilistic rough sets

The rough set theory approximates a concept by three regions, namely, the positive, boundary and negative regions. Rules constructed from the three regions are associated with different actions and decisions, which immediately leads to the notion of three-way decision rules. A positive rule makes a decision of acceptance, a negative rule makes a decision of rejection, and a boundary rule makes a decision of abstaining. This paper provides an analysis of three-way decision rules in the classical rough set model and the decision-theoretic rough set model. The results enrich the rough set theory by ideas from Bayesian decision theory and hypothesis testing in statistics. The connections established between the levels of tolerance for errors and costs of incorrect decisions make the rough set theory practical in applications.     

三支决策-基于粗糙集与粒计算研究视角

从三支决策3个历史发展阶段出发,通过粗糙集和粒计算两个研究视角对三支决策的发展踪迹和演化过程进行介绍。分析了三支决策与粗糙集理论的历史脉络、内在联系和相互关系,探讨了决策粗糙集、概率粗糙集、粗糙集和三支决策之间的包含关系;探讨了基于多层次粒计算和多视角粒计算下的三支决策方法;提出了一个基于三支决策的粒计算研究框架模型。最后,给出了三支决策的研究现状和未来发展方向。     

不完备混合决策系统的三支决策模型与规则获取方法

现有三支决策主要针对各类完备信息系统或不完备单一型信息系统进行研究,而现实应用领域中数据往往呈现不完备性和复杂性等特征,为此,构建面向不完备混合决策系统的三支决策模型与规则获取方法。首先,计算不完备混合数据的完备邻域容差类,并将其代替等价类计算三支决策模型的条件概率;然后,根据扩展的损失函数区间概念获取各对象在乐观、折中和悲观决策下的不同阈值,进而针对不完备混合决策系统构造三种决策风险下的三支决策模型。最后,通过理论分析和医疗诊断实例详细分析了算法的有效性和可解释性,并通过实验比较和分析可知,所构模型较其他已有模型的分类过程更加合理有效,同时该模型也扩充了三支决策模型和知识发现的理论与应用研究。     

面向不完备邻域系统的三支决策粒计算方法

针对许多应用领域中的数据大多是连续型数值,且由于成本限制和隐私保护等因素导致数据呈现不完备性。为此,提出面向不完备邻域系统的三支决策粒计算方法,引入邻域概念改进非对称相似关系,并通过改进的非对称相似关系计算不完备邻域系统的邻域粒度;在此基础上计算对象属于决策类的最大条件概率,再根据三支决策规则分别将对象划分到各决策类的正域、负域和边界域;通过实验比较和分析,进一步验证了该方法能获得较好的划分准确率和较低的误划分损失,为三支决策对不完备邻域数据的分析和处理提供了一种有效可行的方法。     

基于证据理论的三支决策模型

三支决策模型和证据理论在概念、信息处理方式上存在着互通互补之处。首先,将证据理论基本概念引入到三支决策中,分析其延迟信任区间可能包含的可变语义,分别构建了基于证据理论的确定和可变三支决策模型。然后,通过调节信任系数取值,结合贝叶斯风险分析形成了乐观策略、悲观策略及其相应的决策规则,以满足特定语义环境下的应用需求。最后,通过对防空作战态势评估的风险分析说明了模型的具体应用过程。     

流计算模式下概率粗糙集三支决策的快速计算

概率粗糙集三支决策是不确定问题求解的一种重要理论,流计算模式是一种新型的动态内存计算形式,实施流计算模式下三支决策的快速动态计算是一项具有挑战性的新议题。本研究以流计算模式中的两个核心计算步骤即动态增量与动态减量作为研究对象,提出了一种流计算模式下概率粗糙集三支决策域的快速动态学习方法。首先对流计算模式中三支决策动态增量和动态减量的不同变化情况进行了数据建模。然后基于不同数据变化情况分别讨论了数据增量与数据减量时三支决策域的变化推理,并且基于上述理论给出了流计算模式下的三支决策动态增减学习算法。该算法能够以更低的时间复杂度获得与经典三支决策算法相同决策效果。最后通过八种UCI数据集的实验证明了流计算模式下三支决策动态增减学习算法在时间消耗上明显优于经典概率粗糙集三支决策算法,并且在不同阈值下具有稳定的决策效率。本研究表明了流计算模式下三支决策快速计算是可行的。