多粒化的模糊粗糙集代数

众所周知,一个粗糙集代数是由一个集合代数加上一对近似算子构成的。首先利用公理化的方法探讨经典的多粒化模糊粗糙集代数系统,可知经典的多粒化模糊粗糙集代数没有很好的性质;其次,引入 具有最小(大)元的等价关系的定义,并给出了基于具有最小(大)元等价关系的多粒化模糊近似算子的概念,在此基础上讨论了模糊粗糙集代数的性质,并得到了诸多结果。     

广义多粒度粗糙集属性约简和matlab计算

定义了基于广义多粒度粗糙集的属性约简,研究了约简的一些基本性质,给出matlab计算的过程,并给出计算实例。定义了信息系统的严格协调、软不协调性、粒度协调、粒度不协调,定义了广义多粒度下约简、粒度约简、（下/上近似）分布协调约简、（下/上近似）质量协调约简,并给出部分结论。广义多粒度粗糙集的约简适用于乐观多粒度粗糙集和悲观多粒度粗糙集。研究结果可完善多粒度粗糙集理论,为理论研究和应用奠定基础。     

一种能处理定性参数输入的推广模糊神经网络软测量建模方法

针对生产过程中存在多种类属型数据和混合型数据,而大多数软测量方法只能处理数值型数据的问题,提出了一种基于粗糙集方法的推广模糊神经网络软测量建模方法,该方法既可以接受定量参数输入,也可以接受定性参数输入.首先建立模糊-清晰混合规则的定义,对具有混合类型属性的样本集进行离散化处理后,利用粗糙集的约简算法进行规则提取,获得最小决策集.由得到的混合决策规则构建推广模糊神经网络,使用样本集训练网络参数.最后将该方法应用于蒸发器的污垢热阻值估计,取得了良好的效果.     

多粒度邻域粗糙直觉模糊集模型*

针对名义型属性和数值型属性并存的混合型数据,结合多粒度邻域粗糙集和直觉模糊集,分别定义模糊覆盖粗糙隶属度和非隶属度.基于不同的属性集序列和不同的邻域半径,构建多粒度邻域粗糙直觉模糊集模型,证明模型相关性质.然后提出乐观和悲观多粒度邻域粗糙直觉模糊集的近似集,并讨论模型性质.最后使用文中模型计算实例,说明其能较好地解决名义型属性和数值型属性的混合型数据的处理问题.     

变精度模糊粗糙集的一种定义

模糊粗糙集模型同经典粗糙集模型类似,容易受到噪音数据的影响.针对该问题,受变精度粗糙集模型的启发,提出了变精度模糊粗糙集的概念.针对现有变精度模糊粗糙集模型尚不能满足一些基本性质的缺陷,重新定义了模糊近似空间中某一模糊集的β-下近似和β-上近似,该定义方式能够满足上述的基本性质.     

基于局部可调节多粒度粗糙集的属性约简

经典的多粒度粗糙集模型采用多个等价关系(多粒度结构)来逼近目标集。根据乐观和悲观策略,常见的多粒度粗糙集分为两种类型:乐观多粒度粗糙集和悲观多粒度粗糙集。然而,这两个模型缺乏实用性,一个过于严格,另一个过于宽松。此外,多粒度粗糙集模型由于在逼近一个概念时需要遍历所有的对象,因此非常耗时。为了弥补这一缺点,进而扩大多粒度粗糙集模型的使用范围,首先在不完备信息系统中引入了可调节多粒度粗糙集模型,随后定义了局部可调节多粒度粗糙集模型。其次,证明了局部可调节多粒度粗糙集和可调节多粒度粗糙集具有相同的上下近似。通过定义下近似协调集、下近似约简、下近似质量、下近似质量约简、内外重要度等概念,提出了一种基于局部可调节多粒度粗糙集的属性约简方法。在此基础上,构造了基于粒度重要性的属性约简的启发式算法。最后,通过实例说明了该方法的有效性。实验结果表明,局部可调节多粒度粗糙集模型能够准确处理不完备信息系统的数据,降低了算法的复杂度。     

基于双重粒化准则的邻域多粒度粗糙集模型

为了从多粒度、多层次的角度有效处理名义型属性和数值型属性并存的混合数据, 首先基于不同的属性集序列和不同的邻域半径构建双重粒化准则, 建立基于双重粒化准则的邻域多粒度粗糙集模型; 然后给出该模型的相关性质, 提出该模型下的属性约简算法, 约简结果可以根据实际问题的需要灵活选择合适的属性集和邻域半径. 实例分析验证了所提出模型和算法的有效性.

     

可变直觉模糊多粒度粗糙集模型及其近似分布约简算法

为了在多粒度粗糙集模型中对目标概念达到更好的近似逼近效果,首先将直觉模糊粗糙集与多粒度粗糙集结合,提出直觉模糊多粒度粗糙集模型。由于该模型的目标近似存在过于宽松的缺陷,因此通过引入参数的方式对所提模型进行改进,提出一种可变直觉模糊多粒度粗糙集模型,并证明了该模型的有效性,同时基于该模型提出了相应的近似分布约简算法。在仿真实验结果中,所提出的下近似分布约简结果比已提出的模糊多粒度决策理论粗糙集约简和多粒度双量化决策理论粗糙集多了2~4个属性,所提出的上近似分布约简算法比这些算法少了1~5个属性,同时约简结果的近似精度拥有了更为合理且优越的表现。因此,理论和实验结果均验证了所提的可变直觉模糊多粒度粗糙集模型在近似逼近和数据降维方面均具有更高的优越性。     

多粒化的粗糙集代数

众所周知,一个粗糙集代数是由一个集合代数加上一对近似算子构成的。一方面 ,在公理化的方法下对经典的多粒化粗糙集代数系统进行了讨论,可知经典的粗糙集代数没有很好的性质;另一方面,给出了单调等价关系的定义,并给出了基于单调等价关系的多粒化近似算子的概念,在此基础上讨论了粗糙集代数的性质,并得到了诸多结果。     

多重概率粗糙集模型

基于多重集合,对Z.Pawlak粗集意义下的概率粗糙集模型的论域进行了扩展,提出了基于多重集的概率粗糙集模型,即多重概率粗糙集模型,给出了该模型的完整定义、相关定理和重要性质,其中包括多重论域定义、多重概率粗糙近似集的定义及其各种性质的证明、多重概率粗糙集的近似精度定义、可定义集与属性约简的定义、多重集意义下的粗糙近似算子之间的关系及其与Z.Pawlak意义下的粗糙近似算子之间的关系等。多重概率粗糙集可充分反映知识颗粒间的重叠性,对象的重要度差别及其多态性,这样有利于用粗糙集理论从保存在关系数据库中的具有一对多、多对多依赖性的且具有不完全性或存在统计性的数据中挖掘知识。     

On intuitionistic fuzzy rough sets and their topological structures

In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.     

基于蕴涵的区间值直觉模糊粗糙集

提出一种基于区间值直觉模糊蕴涵的区间值直觉模糊粗糙集模型.首先,介绍了区间值直觉模糊集、区间值直觉模糊关系和区间值直觉模糊逻辑算子的概念;然后,利用区间值直觉模糊三角模和区间值直觉模糊蕴涵,在区间值直觉模糊近似空间中定义了区间值直觉模糊集的上近似和下近似;最后,给出并证明了这些近似算子的一些性质.     

基于模糊集截集的模糊粗糙集模型

基于L.A.Zadeh模糊集的截集的概念给出了论域U上任意模糊子集的上、下近似的刻画,得到了基于模糊集的截集的粗糙集模型,亦即模糊粗糙集,实现了用论域U中的模糊集近似论域上的任意模糊集,进一步推广了Z.Pawlak粗糙集模型,扩展了粗糙集的应用范围。最后,研究了其基本性质以及其与其他粗糙集模型的关系。     

Soft fuzzy rough set-based MR brain image segmentation

Fuzzy sets, rough sets are efficient tools to handle uncertainty and vagueness in the medical images and are widely used for medical image segmentation. Soft sets are a new mathematical approach to uncertainty and vagueness. In this paper, a hybrid segmentation algorithm based on soft sets namely soft fuzzy rough c-means is proposed to extract the white matter, gray matter and the cerebro spinal fluid from MR brain image with bias field correction. In this algorithm, soft fuzzy rough approximations are applied to obtain the rough regions of image. These approximations are free from defining thresholds, weight parameters and are less complex compared to the existing rough set based algorithms. Soft sets use similarity coefficients to find the similarity of the clusters formed in present and previous step. The proposed algorithm does not involve any negative region, hence all the pixels participate in clustering avoiding clustering mistakes. Also, the histogram based centroids choose the centroids close to the ground truth that in turn effect the definition of approximations, standardizing the clusters. The proposed algorithm evaluated through simulation, compared it with existing k-means, rough k-means, fuzzy c-means and other hybrid algorithms. The soft fuzzy rough c-means algorithm outperforms the considered algorithms in all analyzed scenarios even in extracting the tumor from the brain tissue.     

On generalized intuitionistic fuzzy rough approximation operators

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.     

Knowledge acquisition in incomplete fuzzy information systems via the rough set approach

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.     

一般等价关系下直觉模糊粗糙集模型及其性质的研究

系统研究了一般等价关系下直觉模糊粗糙集模型,给出该模型多种定义形式,详细阐述了上下近似的性质,定义了直觉模糊粗糙集截集的概念,最后给出了该直觉模糊粗糙集模型的分解定理和表现定理,并证明定理的正确性。