多粒度模糊粗糙集的表示问题

研究了多粒度模糊粗糙集的表示问题。利用模糊集的分解定理思想首次用截集构造了多粒度模糊粗糙集模型,建立了基于截集的悲观和乐观多粒度模糊粗糙集模型。在该模型中,从模糊集的截集角度定义了悲观及其乐观多粒度模糊粗糙集的上下近似集,解决了多粒度模糊粗糙集的数学结构问题,证明了多粒度模糊粗糙集可以用一簇经典的多粒度粗糙集来表示。最后利用该模型证明了多粒度模糊粗糙集的一些结论。     

多粒度模糊粗糙集研究

本文研究了模糊粗糙集中属性约简问题.利用模糊粗糙集和多粒度粗糙集各自优点的结合,提出了两类多粒度模糊粗糙集模型,使得两类粗糙集中的上下近似算子关于负算子对偶.同时研究了多粒度模糊粗糙集的性质及与单粒度模糊粗糙集的关系.并通过构造区分函数的方法提出了一类多粒度模糊粗糙集模型的近似约简方法.最后用一个实例核对了该类多粒度模糊粗糙决策系统近似约简方法的有效性.     

一类推广的多粒度双量化决策粗糙模糊集

多粒度决策粗糙集作为一种特殊的概率粗糙集模型，其主要运用条件概率来表示相对量化信息，却忽略了等价类与经典集重叠部分的绝对量化信息，而绝对量化信息在程度多粒度粗糙集中被广泛讨论。因此，本文基于逻辑析取和合取算子将多粒度决策粗糙集和程度多粒度粗糙集相结合，同时引入模糊集和标量基数的思想，提出两对推广的多粒度决策粗糙模糊集∨∨-MGDTRFS和∧∧-MGDTRFS.随后，讨论了∨∨-MGDTRFS和∧∧-MGDTRFS的相关性质，并且给出两者之间的联系。     

混合信息系统的邻域多粒度决策粗糙集及应用

为进一步有效处理混合型数据，在混合信息系统中引入邻域多粒度决策粗糙集；鉴于欧氏距离只考虑到数据之间的绝对距离，因此在模型中以卡方距离作为替代；在给定邻域半径之下，提出了混合信息系统的邻域多粒度决策粗糙集模型，对其相关性质进行了证明；实例分析结果表明，该模型具有更好的分类能力，并可通过调整相关参数使模型具有一定的容错性。     

程度多粒度粗糙集

多粒度粗糙集模型建立在一族而非仅仅一个不可分辨关系的基础上的。在融入一定程度误差的分类思想下,本文在多粒度粗糙集模型基础上将构建程度多粒度粗糙集,其中包括程度多粒度乐观近似算子和程度多粒度悲观近似算子两种形式。讨论了程度多粒度粗糙集的相关性质,并对程度多粒度粗糙集和经典的多粒度粗糙集进行了对比分析,得出了若干具有理论和应用价值的结果,从而为知识获取提供了一个新的不确定性方法。     

集值映射下的粗糙集

粗糙集是一种在信息系统中处理粗糙性和颗粒性的数据挖掘工具.本文从集值映射的角度研究并推广粗糙模型,使其能解决在论域和分类信息变化下对集合的近似问题.最后,讨论了集值映射下的粗糙集的性质.     

广义多值直觉模糊软集及其在多属性决策中的应用

软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。     

多源环境下学生综合素质的决策分析

在现实生活中,多源环境下大学生综合素质分析是一个非常重要的课题。针对此问题,本文从粒计算的角度出发,结合粗糙集决策的方法,构建了多源环境下大学生综合素质决策信息系统,用Matlab对该系统进行约简,并根据约简进行规则提取,对获得的规则进行分析和验证,得出了大学生综合素质决策结论。本文是多粒度粗糙集应用的一个范本,具有重要的理论和实践意义。     

一种广义多粒度变精度粗糙集北大核心

本文基于文献[4]提出的广义多粒度粗糙集进行模型推广,提出广义多粒度变精度粗糙集模型.在多粒度的粒度不确定性的基础上考虑类选择的不确定性,研究新模型的一些基本性质并以实例计算说明.本文给出的广义多粒度变精度粗糙集为多粒度粗糙集理论的研究和应用奠定一定的理论基础.     

基于混沌集群智能优化算法的多目标粗糙集属性约减

针对管理实践及大数据处理过程中具有多决策属性的粗糙集属性约减问题,将条件属性依赖度与知识分辨度进行结合构建属性权重,分别建立针对不同决策属性的约减目标函数,引入帕累托最优思想,将基于多决策属性的粗糙集属性约减问题转化为离散多目标优化问题。针对该问题的结构设计了具有集群智能优化思想的元胞自动机求解算法,在算法中引入基于个体的非支配解集平衡局部最优与全局最优的关系,引入混沌遗传算子增加种群多样性。以某铁路局设备安全风险处理数据为案例构建多决策属性粗糙集决策表进行优化计算并进行管理决策分析。研究发现:(1)相对于传统的NSGA-II与MO-cell算法,本文提出的算法具有更强的多目标属性挖掘性能;(2)帕累托最优思想可以较好地解释多决策属性粗糙集在管理实践中的意义。     

扰动模糊集的粗糙度

首先,将扰动模糊集和粗糙集理论相结合,提出了粗糙扰动模糊集的概念并研究了其基本性质.接着,通过引进扰动模糊集水平上、下边界区域的概念,克服了粗糙集理论中普遍存在的两个集合的上近似的交不等于两个集合的交的上近似(两个集合的下近似的并不等于两个集合的并的下近似)的缺陷.最后,定义了依参数的扰动模糊集的粗糙度的定义,讨论了其基本性质.     

Optimal scale selection for multi-scale decision tables

Human beings often observe objects or deal with data hierarchically structured at different levels of granulations. In this paper, we study optimal scale selection in multi-scale decision tables from the perspective of granular computation. A multi-scale information table is an attribute-value system in which each object under each attribute is represented by different scales at different levels of granulations having a granular information transformation from a finer to a coarser labelled value. The concept of multi-scale information tables in the context of rough sets is introduced. Lower and upper approximations with reference to different levels of granulations in multi-scale information tables are defined and their properties are examined. Optimal scale selection with various requirements in multi-scale decision tables with the standard rough set model and a dual probabilistic rough set model are discussed respectively. Relationships among different notions of optimal scales in multi-scale decision tables are further analyzed.     

基于双论域模糊粗糙集的应急决策模型与方法

以突发危机事件应急决策为应用背景,讨论了双论域上模糊粗糙集的基本理论,建立了基于模糊相容关系的双论域模糊粗糙集模型. 在此基础上,把突发危机事件应急决策转化为一个具有模糊决策对象的双论域决策近似空间上的粗糙近似问题,构建了基于双论域模糊粗糙集的应急决策模型.首先在双论域近似空间中计算模糊决策对象的上(下)近似,进而结合经典非确定型决策的思想给出了突发危机事件应急决策的规则.同时,给出了模型的算法.该模型给出了一种在不完全信息环境下应急决策的方法,给出了在充分考虑决策者个人偏好信息基础上的决策置信度以及最优决策规则.该方法能够比较充分地符合应急决策信息不充分、资源有限以及时间紧迫的基本特征, 进而对突发危机事件应急决策提供科学的理论基础和现实的决策方法.最后,通过应用算例说明了模型的应用过程,结果验证了本文给出模型的有效性。     

Evidence-theory-based numerical algorithms of attribute reduction with neighborhood-covering rough sets

Covering rough sets generalize traditional rough sets by considering coverings of the universe instead of partitions, and neighborhood-covering rough sets have been demonstrated to be a reasonable selection for attribute reduction with covering rough sets. In this paper, numerical algorithms of attribute reduction with neighborhood-covering rough sets are developed by using evidence theory. We firstly employ belief and plausibility functions to measure lower and upper approximations in neighborhood-covering rough sets, and then, the attribute reductions of covering information systems and decision systems are characterized by these respective functions. The concepts of the significance and the relative significance of coverings are also developed to design algorithms for finding reducts. Based on these discussions, connections between neighborhood-covering rough sets and evidence theory are set up to establish a basic framework of numerical characterizations of attribute reduction with these sets.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

A dominance intuitionistic fuzzy-rough set approach and its applications

Although the rough set and intuitionistic fuzzy set both capture the same notion, imprecision, studies on the combination of these two theories are rare. Rule extraction is an important task in a type of decision systems where condition attributes are taken as intuitionistic fuzzy values and those of decision attribute are crisp ones. To address this issue, this paper makes a contribution of the following aspects. First, a ranking method is introduced to construct the neighborhood of every object that is determined by intuitionistic fuzzy values of condition attributes. Moreover, an original notion, dominance intuitionistic fuzzy decision tables (DIFDT), is proposed in this paper. Second, a lower/upper approximation set of an object and crisp classes that are confirmed by decision attributes is ascertained by comparing the relation between them. Third, making use of the discernibility matrix and discernibility function, a lower and upper approximation reduction and rule extraction algorithm is devised to acquire knowledge from existing dominance intuitionistic fuzzy decision tables. Finally, the presented model and algorithms are applied to audit risk judgment on information system security auditing risk judgement for CISA, candidate global supplier selection in a manufacturing company, and cars classification.     

Mathematical programming in rough environment

Classical mathematics is usually crisp while most real-life problems are not; therefore, classical mathematics is usually not suitable for dealing with real-life problems. In this article, we present a systematic and focused study of the application of rough sets (Z. Pawlak, Rough sets, In. J. Comput. Informa. Sci. 11 (1982), pp. 341–356.) to a basic area of decision theory, namely ‘mathematical programming’. This new framework concerns mathematical programming in a rough environment and is called ‘rough programming’ (L. Baoding, Theory and Practice of Uncertain Programming, 1st ed., Physica-Verlag, Heidelberg, 2002; E.A. Youness, Characterizing solutions of rough programming problems, Eut. J. Oper. Res. 168 (2006), pp. 1019–1029). It implies the existence of the roughness in any part of the problem as a result of the leakage, uncertainty and vagueness in the available information. We classify rough programming problems into three classes according to the place of the roughness. In rough programming, wherever roughness exists, new concepts like rough feasibility and rough optimality come to the front of our interest. The study of convexity for rough programming problems plays a key role in understanding global optimality in a rough environment. For this, a theoretical framework of convexity in rough programming and conceptualization of the solution is created on the lines of their crisp counterparts.     

A fast heuristic attribute reduction approach to ordered decision systems

Rough set theory has shown success in being a filter-based feature selection approach for analyzing information systems. One of its main aims is to search for a feature subset called a reduct, which preserves the classification ability of the original system. In this paper, we consider ordered decision systems, where the preference order, a fundamental concept in dominance-based rough set approach, plays a critical role. In recent literature, based on the greedy hill climbing method, many heuristic attribute reduction algorithms are proposed by utilizing significance measures of attributes, and they are extended to deal with ordered decision systems. Unfortunately, they are often time-consuming, especially when applied to deal with large scale data sets with high dimensions. To reduce the complexity, a novel accelerator is introduced in heuristic algorithms from the perspectives of objects and criteria. Based on the new accelerator, the number of objects and the dimension of criteria are lessened thus making the accelerated algorithms faster than their original counterparts while maintaining the same reducts. Experimental analysis shows the validity and efficiency of the proposed methods.     

基于粗糙模糊集的聚类决策及应用

对基于粗糙模糊集的聚类问题进行了研究.首先,定义了粗糙模糊值与粗糙模糊集的相似度,给出了粗糙模糊集相似度的一般表达式;然后利用该公式构建了模糊相似矩阵,进而给出了粗糙模糊集的一种聚类方法;最后以实际算例说明了这种思想.