加权多粒度直觉模糊信息系统的粗糙集模型及其决策*

针对现有多粒度直觉模糊粗糙集决策模型的不足,提出粒度加权的多粒度直觉模糊粗糙集模型.首先研究加权多粒度直觉模糊粗糙集的基本性质,分析加权多粒度直觉模糊粗糙集与乐观多粒度、悲观多粒度直觉模糊粗糙集之间的关系,并给出这几种模型不确定度量之间的关系.然后给出决策规则的置信度和支持度定义以及决策规则的获取方法,弥补目前常用的多粒度直觉模糊粗糙集的不足.最后通过决策实例分析验证文中模型的有效性.     

诱导覆盖关系下的加权多粒度粗糙集及应用

为从更多角度进一步分析多属性覆盖决策信息系统,提出了诱导覆盖关系下的加权多粒度粗糙集。分析了采用专家经验确定粒度权重的局限性,引入基于分类质量的粒度权重赋值方法,使决策结果更具客观性;将诱导覆盖关系引入加权多粒度粗糙集,给出完整的粗糙上下近似;讨论了几种度量参数之间的关系,并对相关性质和定理进行证明;通过实例分析验证了模型的有效性和实用性。     

可变多粒度粗糙集模型

通过分析乐观多粒度粗糙集和悲观多粒度粗糙集的不足之处,提出一种可变多粒度粗糙集模型。研究可变多粒度粗糙集、乐观多粒度和悲观多粒度粗糙集的性质,讨论它们之间度量的关系,研究可变多粒度粗糙集决策规则获取的方法。提出一种基于属性重要度的启发式约简的算法。实例分析结果验证该方法的可行性。     

可变粒度粗糙集

分析乐观多粒度粗糙集和悲观多粒度粗糙集的不足之后,提出一种可变粒度粗糙集模型,定义了可变粒度粗糙集的下、上近似集,研究了可变粒度粗糙集与这两种多粒度粗糙集的性质,证明了可变粒度粗糙集是多粒度粗糙集的泛化,最后给出几种可变粒度粗糙集的度量因子,研究了变粒度粗糙集与多粒度粗糙集度量之间的关系.     

可变粒度粗糙集

分析乐观多粒度粗糙集和悲观多粒度粗糙集的不足之后,提出一种可变粒度粗糙集模型,定义了可变粒度粗 糙集的下、上近似集,研究了可变粒度粗糙集与这两种多粒度粗糙集的性质,证明了可变粒度粗糙集是多粒度粗糙集 的泛化,最后给出几种可变粒度粗糙集的度量因子,研究了变粒度粗糙集与多粒度粗糙集度量之间的关系。     

基于加权粒度和优势关系的程度多粒度粗糙集近似集的动态并行更新算法

随着大数据集的不断更新,经典的多粒度粗糙集理论不再适用。为此,提出加权粒度优势关系程度悲观多粒度粗糙集与加权粒度优势关系程度乐观多粒度粗糙集的相关理论。在此基础上,给出了一种基于加权粒度和优势关系的程度多粒度粗糙集近似集的动态并行更新算法。最后,通过实验验证了所提算法的有效性,其能够应对海量动态更新的数据变化并提升运行效率。     

限制优势关系下的加权多粒度粗糙分析方法

作为多粒度粗糙集的推广,提出了限制优势关系下的加权多粒度粗糙分析方法。分析了优势关系粗糙集和多粒度粗糙集的局限性,引入限制优势关系对加权多粒度粗糙集进行改进,充分考虑到属性的偏好关系和粒度的重要性差别,使其适用于不完备的高维或分布式有序信息系统;由此得出粗糙近似,讨论了其与限制优势关系下的乐观、悲观多粒度粗糙集的关系,并对相关性质和定理进行证明;通过实例验证了该方法的有效性和实用性。     

条件概率描述下的多粒度覆盖粗糙集模型研究

在覆盖空间中,利用元素的最小描述并结合条件概率的概念,将经典多粒度粗糙集进行拓展,提出了3种条件概率描述下的多粒度覆盖粗糙集模型;研究了模型的一些基本性质,指出它们是一些已有多粒度覆盖粗糙集模型的泛化形式;最后探讨了几种模型之间的关系.     

优势关系下多粒度粗糙集排序方法及其应用

排序方法是多粒度粗糙集研究的一个重要内容。分析了现有优势关系多粒度粗糙集排序方法的优缺点,对现有排序公式进行改进,使其构造的优势关系矩阵满足对称互补性,且能有效克服方法失效问题。同时,基于相对优势度的视角提出优势关系多粒度粗糙集排序新方法;考虑不同粒度的重要性问题,定义了优势关系多粒度粗糙集的加权排序公式,讨论了公式的含义与性质;最后实例说明了两种方法的实用性和有效性。     

程度多粒度软粗糙集模型

多粒度粗糙集的研究是近几年来研究的热门课题之一。提出了一种介于乐观和悲观多粒度软粗糙集的新模型——程度多粒度软粗糙集。首先,通过计数函数建立了程度多粒度软粗糙集模型;其次,讨论了程度多粒度软粗糙近似算子的性质;再次,定义并研究了程度多粒度软粗糙集的不确定性度量及性质;最后,通过医院对病人诊断的案例验证了模型的实用性。     

MGRS: A multi-granulation rough set

The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of sets described by a single binary relation on the universe. In the view of granular computing, the classical rough set theory is established through a single granulation. This paper extends Pawlak’s rough set model to a multi-granulation rough set model (MGRS), where the set approximations are defined by using multi equivalence relations on the universe. A number of important properties of MGRS are obtained. It is shown that some of the properties of Pawlak’s rough set theory are special instances of those of MGRS.Moreover, several important measures, such as accuracy measureα, quality of approximationγ and precision of approximationπ, are presented, which are re-interpreted in terms of a classic measure based on sets, the Marczewski-Steinhaus metric and the inclusion degree measure. A concept of approximation reduct is introduced to describe the smallest attribute subset that preserves the lower approximation and upper approximation of all decision classes in MGRS as well. Finally, we discuss how to extract decision rules using MGRS. Unlike the decision rules (“AND” rules) from Pawlak’s rough set model, the form of decision rules in MGRS is “OR”. Several pivotal algorithms are also designed, which are helpful for applying this theory to practical issues. The multi-granulation rough set model provides an effective approach for problem solving in the context of multi granulations.     

New and improved: grey multi-granulation rough sets

Rough set has drawn great attention in recent decades, among which multi-granulation rough set (MGRS) is an arresting direction. It constructs a formal theoretical framework to solve complex problems under the circumstance of multiple binary relations. However, the fusion of multi-granulation rough set and grey system for acquiring knowledge is still a gap. Toward this end, we devise a grey multi-granulation rough set (GMGRS) by taking multiple grey relational relations into consideration under the framework of MGRS. In grey information system, the constructed grey relational relation that measures the relationship among objects can be used to further establish multiple binary relations. Based on two different approximate strategies (seeking common reserving difference and seeking common eliminating difference), two types of GMGRS are presented, respectively. After discussing several important properties of GMGRS, we discover that the properties of the proposed GMGRS are synchronous with the classical MGRS. Meanwhile, to obtain the attribute reduction under GMGRS, we reconstruct significance measure and termination criterion based on the θ-precision pessimistic GMGRS. Last but not least, theoretical studies and practical examples demonstrate that our proposed GMGRS largely enrich the MGRS theory and provide a new technique for knowledge discovery, which is practical in real-world scenarios.     

基于覆盖粗糙集模型的层次聚类算法

目前大部分聚类算法只适用于处理属性取值为单值的数值型数据,介绍了一种新的基于粗糙集理论的聚类算法,该算法不仅可用于取值为单值的数值型数据聚类,而且能够用于取值为多值的非数值型数据聚类.该算法利用基于相容关系的属性最小覆盖来求解对象各属性的对象属性信息粒.在此基础上,通过对象属性信息粒和对象粗糙相似度的运算构建各对象的相容粒.最后,把具有相同相容粒的对象视为同一等价类,从而实现对论域的聚类,进而对数据对象进行层次聚类.实验结果表明,该算法是可行的.     

Multi-granulation rough sets based on tolerance relations

The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues, the classical rough set model was extended to multi-granulation rough set model (MGRS). This paper extends the single-granulation tolerance rough set model (SGTRS) to two types of multi-granulation tolerance rough set models (MGTRS). Some important properties of the two types of MGTRS are investigated. From the properties, it can be found that rough set model based on a single tolerance relation is a special instance of MGTRS. Moreover, the relationship and difference among SGTRS, the first type of MGTRS and the second type of MGTRS are discussed. Furthermore, several important measures are presented in two types of MGTRS, such as rough measure and quality of approximation. Several examples are considered to illustrate the two types of multi-granulation tolerance rough set models. The results from this research are both theoretically and practically meaningful for data reduction.     

加权粗糙集的矩阵表示

在加权近似空间中提出了关系矩阵和布尔列向量加权α下乘法和加权α上乘法的概念。证明了加权α下乘法就是加权下近似,加权α上乘法就是加权上近似,从而为加权粗糙集（可变精度粗糙集、经典粗糙集）的计算和研究提供了一种新的矩阵方法。最后给出了计算加权上下近似的算法。     

基于粗糙集和Petri网的随机流网络可靠性评价方法

针对随机流网络可靠性建模难的问题,提出一种基于粗糙集和Petri网相结合的随机流网络可靠性评价方法.建立了随机流网络在确定网络状态下的Petri网模型,并利用粗糙集方法求得网络中各边状态对系统状态的重要度;然后以此作为随机流网络的Petri网模型中各变迁的优先因子来控制模型中变迁的激发;最后通过蒙特卡罗仿真求得随机流网络可靠度的估计值.仿真结果表明,该方法是一种计算随机流网络可靠性的有效方法.     

基于置信优势关系的粗糙集近似模型

不完备有序信息处理是现实生活中的常见问题. 多种拓展优势关系及其粗糙集模型被提出并用于解决不完全的偏好决策问题, 但均未考虑序关系特性, 与现实语义存在矛盾. 对此, 提出一种置信优势关系及其粗糙集近似模型, 讨论了基于置信优势关系的粗糙集模型与已有模型的关系. 与现有的拓展关系相比, 该置信优势关系满足序关系特性, 避免了语义上的矛盾. 定理证明和实例分析表明, 置信优势关系粗糙集近似模型的近似精度和分类精度更优.

     

基于粗糙集的犹豫模糊多属性决策方法

针对属性值为犹豫模糊元的决策问题,提出一种基于粗糙集理论的多属性决策方法.首先,依据属性值与理想点的贴近度和给定的阀值得到判断矩阵;然后,根据判断矩阵对属性集进行约简,确定属性权重;最后,基于TOPSIS思想,计算各方案与理想点的综合贴近度,得到方案的优劣次序,并通过算例分析表明了该方法的有效性.