近似空间的笛卡尔积粗集模型及其可分解性

为处理人工智能中不精确和不确定的数据和知识,Pawlak提出了粗集理论。之后粗集理论得到拓广,人们提出了许多新的粗集模型。拓展的方法主要有两种,一种是减弱对等价关系的依赖,另一种是把讨论问题的论域从一个拓展到两个。Y. Y. Yao提出了一种基于两个论域的粗集模型。现研究基于两个近似空间的笛卡尔积粗集模型,给出了积近似空间的概念,刻画了可分解集合的上(下)近似、近似精度和粗糙度。最后研究了笛卡尔积粗集模型的可分解问题,给出了一个近似空间积可分解的充分必要条件。     

积模糊粗集模型及其模糊知识粒的表示和分解

为处理人工智能中不精确和不确定的数据和知识,Pawlak提出了粗集理论。之后粗集理论被推广,其方法主要有二:一是减弱对等价关系的依赖;二是把研究问题的论域从一个拓展到多个。结合这两种思想,研究基于两个模糊近似空间的积模糊粗集模型及其模糊粗糙集的表示和分解。根据这种思想,可以从论域分解的角度探索降低高维模糊粗糙集计算的复杂度问题。先对模糊近似空间的分层递阶结构———λ-截近似空间进行研究,得到不同层次知识粒的相互关系;然后定义模糊等价关系的积,并研究其性质及算法;最后构建基于积模糊等价关系的积模糊粗集模型,并讨论了该模型中模糊粗糙集的表示及分解问题,分别从λ-截近似空间和一维模糊近似空间的角度去处理,给出了可分解集的上(下)近似的一个刻画,及模糊可分解集的上(下)近似的λ-截集分解算法。     

两个论域上的粗集结构

粗集理论是处理不精确和不确定的数据的工具,自Pawlak 提出了粗集理论后,粗集模型得到拓广,人们提出了许多新的粗集模型,在用特征函数的方法表示上下近似的基础上研究两个论域上的粗集结构。统一了粗集的各种推广模型,使得特征函数的方法与通常的集合论的方法形成互补,对粗集结构的简化及推理有帮助,可以加深对粗集结构的认识。     

基于矩阵的双论域模糊概率粗糙集增量更新算法

双论域模糊概率粗糙集是针对双论域信息系统的一种新的数据挖掘模型,现实应用中的双论域信息系统总是处于动态更新中,针对该问题提出一种基于矩阵的双论域模糊概率粗糙集增量式更新方法.首先,通过矩阵方法重新对双论域模糊概率粗糙集进行表示;然后,在矩阵表示模型的基础上,分别研究双论域信息系统两个论域中对象增加和减少时模型的增量式更新机制;最后,基于该增量式更新提出相应的增量式更新算法.实验分析表明:相比较于非增量式更新算法,所提出的增量式更新算法可以在很短的时间内完成模型的动态更新,从而验证算法的有效性;同时,与其他相关算法相比,所提出算法具有一定的优越性.     

近似空间关系代数ASRA及应用

粗定位模型是一种基于粗集的近似区域表示模型 ,基于定性空间推理理论对其进行了代数形式化 .通过空间关系矩阵和 2 4 9种基本空间关系构造了近似空间关系代数 ASRA;讨论了 ASRA的公理和基本性质 ,研究了ASRA和 RCC5关系映射中存在的不确定性 ;把 ASRA应用于 GIS,提出了基于 ASRA的空间关系判定算法ASRA- RCC.与同类算法相比 ,ASRA- RCC能够同时支持确定和近似区域 ,并且具有较高的效率     

带标记的不完备双论域模糊概率粗糙集中近似集动态更新方法

当不完备双论域模糊概率粗糙集获取缺省值时,传统的静态算法更新近似集的时间效率较低,为了解决这个问题,对带标记不完备双论域模糊概率粗糙集的近似集动态更新方法进行了研究。首先,给出了带标记的不完备双论域信息系统的相关定义,运用矩阵提出了带标记的不完备双论域模糊概率粗糙集的模型,证明了其相关定理,给出了一种带标记的不完备双论域模糊概率粗糙集的近似集计算方法,并对其进行了讨论分析。其次,当不完备双论域模糊概率粗糙集获取缺省值时,给出了动态更新其近似集的相关定理,并进行了证明,进而设计了一种带标记的不完备双论域模糊概率粗糙集中近似集动态更新算法,并分析讨论了其算法复杂度。最后,在6个UCI数据集和3个人工数据集上进行仿真实验,实验结果表明,该动态更新算法提高了更新近似集的时间效率,并结合实例证明了该动态算法更新近似集时不影响结果的正确性,验证了该动态更新算法的有效性。     

Vague集间的相似性度量及应用

论文提出了一种描述Vague集间的不确定关联度概念,并提出了一种新的Vague集间相似性度量模型,它不但考虑了Vague集论域元素间的物理意义,而且也考虑了论域元素间的不确定关联程度,因此,它比已存在的Vague集间相似度量模型更加精细地刻画了Vague集间的相似性,从而在基于Vague集的不确定性智能信息处理领域中可有广泛应用。     

对象集变化时近似集动态维护的矩阵方法

目前粗糙集模型中概念的上、下近似集的计算方法大多是基于静态信息系统的.而实际的信息系统是随时间动态变化的,通常包括对象集、属性集和属性值3种类型的粒度变化,这些变化必然引起概念近似集的动态变化.如何快速、有效地更新概念的近似集是基于粗糙集的动态知识更新中的热点研究问题之一.而利用既有知识的增量式更新方法是一种有效的近似集动态更新方法.在信息系统动态变化的客观环境下,以矩阵作为表达和运算工具从一个全新的视角研究信息系统的论域随时间变化时,变精度粗糙集模型中概念的上、下近似集的增量式更新方法,并构造出近似集增量式更新的矩阵算法,随后分析了算法的时间复杂度.进一步,在MATLAB平台上开发出增量式更新和非增量式更新近似集的两种矩阵算法的程序,最后在UCI的6个数据集上测试了两种矩阵算法的性能并将实验结果进行比较,结果表明增量式更新的矩阵算法可行、简洁和高效.     

双论域上的S-粗集及应用

原始从单论域出发讨论动态系统的知识发现和规则挖掘,其应用范围受到极大限制。通过构造性方法对原始的Ｓ-粗集粗糙集模型进行推广,提出双论域上的Ｓ-粗集模型。分析了S-粗集与Z.Pawlak 粗集、以及单论域Ｓ-粗集与双论域Ｓ-粗集的关系。并讨论了双论域Ｓ-粗集一些相关性质及在疾病诊断上的应用。     

2维不相关鉴别矢量集算法

在人脸识别算法中,已有的计算不相关鉴别矢量集的算法均是基于图像向量模型的,因而将遇到所谓的小样本问题,而且由于采用迭代求解方式,算法运算速度缓慢,为此提出了一种新的求取不相关鉴别矢量集的算法,即一种基于图像矩阵模型的2维不相关鉴别矢量集算法。算法由于采用了图像矩阵模型,解决了小样本问题,通过对类内散布矩阵的白化变换,使得推广的2维线性鉴别分析模型具有类似的2维主成分分析模型的形式,从而将两种算法的模型有效地联系起来,进而可以非迭代地求得2维不相关鉴别矢量集,不但求解速度快且数值解稳定。在ORL和Yale人脸库上的实验结果表明,该算法不但减少了计算时间,同时也提高了识别率,为求解不相关鉴别矢量集提供了一个新的思路。     

两个论域上的覆盖粗糙模糊集模型

粗糙集模型的扩展是粗糙集研究的主要内容之一,目前已经存在许多有关粗糙集模型的扩展形式。其中基于覆盖而建立的粗糙集模型得到了很大的发展,然而学者们主要是针对单个论域进行研究的,但是实际生活中的问题却往往是在多个论域上的,如在医疗诊断中的应用等。同时考虑到在实际生活中,研究的对象往往是不确定的,即带有模糊的。基于以上考虑,提出了在两个论域上的覆盖粗糙模糊集模型,并对近似算子的性质进行了研究。     

Rough fuzzy approximations on two universes of discourse

In rough set theory, the lower and upper approximation operators can be constructed via a variety of approaches. Various fuzzy generalizations of rough approximation operators have been made over the years. This paper presents a framework for the study of rough fuzzy sets on two universes of discourse. By means of a binary relation between two universes of discourse, a covering and three relations are induced to a single universe of discourse. Based on the induced notions, four pairs of rough fuzzy approximation operators are proposed. These models guarantee that the approximating sets and the approximated sets are on the same universes of discourse. Furthermore, the relationship between the new approximation operators and the existing rough fuzzy approximation operators on two universes of discourse are scrutinized, and some interesting properties are investigated. Finally, the connections of these approximation operators are made, and conditions under which some of these approximation operators are equivalent are obtained.     

区间直觉模糊粗糙集

将模糊粗糙集推广到区间直觉模糊粗糙集,基于区间直觉模糊等价关系和两个论域之间的一般区间直觉模糊关系,给出了区间直觉模糊粗糙集模型的不同形式,并讨论了一些相关性质。     

Variable precision rough set model over two universes and its properties

The extension of rough set model is an important research direction in the rough set theory. In this paper, based on the rough set model over two universes, we firstly propose the variable precision rough set model (VPRS-model) over two universes using the inclsion degree. Meantime, the concepts of the reverse lower and upper approximation operators are presented. Afterwards, the properties of the approximation operators are studied. Finally, the approximation operators with two parameters are introduced as a generalization of the VPRS-model over two universes, and the related conclusions are discussed.     

Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making

Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision‐making in unconventional emergency management. We establish an approach to online emergency decision‐making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision‐making in order to illustrate the validity of the proposed method.     

Fuzzy preference based rough sets

Preference analysis is an important task in multi-criteria decision making. The rough set theory has been successfully extended to deal with preference analysis by replacing equivalence relations with dominance relations. The existing studies involving preference relations cannot capture the uncertainty presented in numerical and fuzzy criteria. In this paper, we introduce a method to extract fuzzy preference relations from samples characterized by numerical criteria. Fuzzy preference relations are incorporated into a fuzzy rough set model, which leads to a fuzzy preference based rough set model. The measure of attribute dependency of the Pawlak’s rough set model is generalized to compute the relevance between criteria and decisions. The definitions of upward dependency, downward dependency and global dependency are introduced. Algorithms for computing attribute dependency and reducts are proposed and experimentally evaluated by using two publicly available data sets.     

Pythagorean Fuzzy Multigranulation Rough Set over Two Universes and Its Applications in Merger and Acquisition

Pythagorean fuzzy set, an extension form of intuitionistic fuzzy set, which owns many advantages for dealing with uncertainties, and it has been developed to deal with various complex decision‐making problems. Furthermore, based on lower and upper approximations induced by multiple binary relations, the multigranulation rough set has become one of the most promising directions in rough set theory. To combine the two ideas and explore the practical decision‐making problems, we develop a new multigranulation rough set model, called Pythagorean fuzzy multigranulation rough set over two universes. In the framework of our study, we introduce the models of Pythagorean fuzzy rough set over two universes and Pythagorean fuzzy multigranulation rough set over two universes, respectively. Both the definition and basic properties are explored. Finally, we give a general algorithm, which is applied to a decision‐making problem in merger and acquisition, and the effectiveness of the algorithm is demonstrated by a numerical example.