基于多粒度粗糙直觉犹豫模糊集的最优粒度选择方法

为了对含有多属性的直觉犹豫模糊决策信息系统进行约简,获取最优粒度,运用多粒度粗糙集处理直觉犹豫模糊决策信息系统中的不确定信息,并对多粒度粗糙直觉犹豫模糊集的最优粒度选择方法进行了研究.首先,在直觉犹豫模糊集的基础上引入属性信息,给出粗糙直觉犹豫模糊集的概念,提出乐观、悲观多粒度粗糙直觉犹豫模糊集的下、上近似这4种模型,且研讨了它们的性质.其次,主要定义了基于悲观多粒度粗糙直觉犹豫模糊集下近似的粒度质量相似度和内、外粒度重要度的计算公式,设计了其最优粒度选择算法.最后,通过葡萄酒测评的案例,分别基于乐观、悲观多粒度粗糙直觉犹豫模糊集的下、上近似这4种情况,计算出最优粒度并进行了分析,验证了该算法在直觉犹豫模糊决策信息系统中的约简是有效的.     

动态粗糙模糊集及其在模糊规则提取中的应用

基于粗糙模糊集的规则提取方法通常分为两步:首先利用粗糙模糊集进行属性约简,然后采用提取模糊规则的方法提取规则.在规则提取的预处理阶段通过属性约简某种程度上可以缩短规则提取的时间,但其固有的不足导致不利于产生良好的规则.在模糊规则产生过程中避开属性约简,可以提高规则提取方法的适用性,降低计算复杂度.本文提出了动态粗糙模糊集的概念,基于此的规则提取算法不再依赖于属性约简,而是基于粒度序和逐步缩小的论域.首先,通过两种不同方式定义了动态粗糙模糊集并得到一些重要性质;在此基础上提出一种新的模糊规则提取算法;最后通过对比实验说明了算法的有效性.     

模糊粗糙集的鱼病规则获取方法

针对鱼病诊断中存在随机性、诊断信息的模糊性和信息获取的不完备性等不确定因素。首先给出模糊的鱼病诊断过程,由于该方法存在模糊诊断矩阵较难获取的缺点。利用粗糙集理论无需先验知识的优点,将粗糙集理论和模糊集结合用于鱼病的诊断中。鱼病的症状模糊集形成条件属性,疾病模糊集形成决策属性构成模糊信息表,给出了模糊信息表属性约简和鱼病诊断规则获取的算法步骤,最后以实例演示了鱼病诊断的规则获取过程。论文为鱼病的诊断提供了一种全新的方法。     

基于变精度粗糙直觉模糊集的决策规则获取

以直觉模糊目标信息系统为研究对象,以粗糙集和直觉模糊集为工具,以知识发现为目的,给出了从直觉模糊决策表中获取决策规则的一种有效方法。即通过对Pawlak粗糙隶属函数的定义进行推广,给出粗糙直觉模糊隶属函数,利用新的粗糙隶属函数,建立了变精度粗糙直觉模糊集模型。在此模型基础上定义了变精度粗糙直觉模糊集的近似质量和近似约简,由近似约简导出概率决策规则集,从而给出了直觉模糊决策表的概率决策规则获取方法。最后,以实例说明了这一方法的有效性。关键词：     

F-模糊集属性信息系统的知识获取

模糊集属性信息系统的知识获取是一个新的研究领域，与其相关的理论和方法具有重要意义。本文提出了一种新的概念F-模糊集，给出了一种在F-模糊集属性信息系统中进行知识获取的方法。     

多粒度覆盖粗糙模糊集模型不确定性研究

针对覆盖粗糙模糊集中存在的上下近似不一致问题.引入一种更为合理的覆盖粗糙模糊集模型,讨论了该模型的结构与相关性质,定义了基于此模型的粗糙度度量方法.基于覆盖粗糙模糊集中粗糙度相等的情形,提出模糊集中极大模糊集的概念,并利用模糊集与极大模糊集的距离问题定义了模糊集的优劣次序,从而有效解决了模糊集在覆盖粗糙模糊集中粗糙度的度量问题.通过引入粗糙熵等相关概念,证明了此模型中仍然存在随最简覆盖变细,两种度量单调减少的规律,并通过实例进行了验证.从而为进一步揭示粗糙集、粗糙模糊集及覆盖粗糙模糊集之间的不确定性度量规律提供了理论依据.     

一种基于粗糙-模糊集理论的分类规则挖掘方法

提出了一种基于粗糙-模糊集理论的分类规则挖掘方法,以解决信息不完整情况下的推理和决策问题,并给出了该方法的流程图。利用基于粗糙集的特征属性约简算法和基于模糊集的决策规则归纳方法,可以挖掘出样本中隐藏的关联规则,形成决策。最后,将其应用于一个具体的信息系统中,结果令人满意,证明该方法是可行的且是有效的。     

一种应用软粗糙模糊集的多属性决策方法

将软粗糙模糊集应用于多属性决策问题,用软粗糙模糊集分析模糊知识表达系统,定义了软模糊决策系统、决策分类模糊软集依赖度、条件双射软集对决策分类模糊软集的重要性、软模糊决策系统的约简、软模糊决策系统的决策规则等概念,借助这些概念给出了一种基于软粗糙模糊集的多属性决策算法,通过实例分析说明了该算法的可行性。     

智能决策中的模糊近似

信息表通过目标集合来描述，目标通过条件属性和决策属性进行描述，在对这样的信息表分析处理过程中，粗糙集理论是一个非常有用的工具，粗糙集合理论的主要观点就是知识的上下近似，在实际中，条件属性和决策属性的概念通常是模糊的，而且可以利用模糊集合来说明，提出了基于模糊集合和粗糙集结合的一种新方法，对包含度进行了定义，给出了截近似和综合函数的概念，应用这些概念并结合具体例子讨论了条件属性和决策属性之间的关系，为决策过程中对条件属性权值的指定提供了理论基础。     

一种基于粗糙2模糊集集成模型的决策分析方法

针对信息系统为连续属性的情况，提出一种将粗糙集与模糊集相结合来获取决策规则的方法，这种基于粗糙—模糊集集成模型求取决策规则的方法通过一个模糊隶属函数将连续属性值表示成模糊值，从而避免了连续属性的离散化问题，同时给出了连续属性值转换成模糊值的表示形式，提出了模糊相似关系和模糊相似类的概念，给出了粗糙—模糊近似空间的下、上近似及其性质以及模糊相似关系下属性约简的方法，最后以自修复飞行控制系统的效能评估为例，给出了自修复效能评估的决策规则。     

一种基于模糊粗糙集知识获取方法

本文介绍了粗糙集和模糊粗糙集的上下近似。并且利用模糊粗糙上下近似算子，论述了在不完备模糊信息系统中知识获取的一种方法。应用这种方法能够让隐藏在不完备模糊信息系统中的知识，以决策规则的形式表示出来。最后给出了一种实现算法和实例。     

粗糙模糊集的构造与公理化方法

用构造性方法和公理化研究了粗糙模糊集．由一个一般的二元经典关系出发构造性地定义了一对对偶的粗糙模糊近似算子，讨论了粗糙模糊近似算子的性质，并且由各种类型的二元关系通过构造得到了各种类型的粗糙模糊集代数．在公理化方法中，用公理形式定义了粗糙模糊近似算子，各种类型的粗糙模糊集代数可以被各种不同的公理集所刻画．阐明了近似算子的公理集可以保证找到相应的二元经典关系，使得由关系通过构造性方法定义的粗糙模糊近似算子恰好就是用公理化定义的近似算子。     

Characterization of rough set approximations in Atanassov intuitionistic fuzzy set theory

The primitive notions in rough set theory are lower and upper approximation operators defined by a fixed binary relation and satisfying many interesting properties. Many types of generalized rough set models have been proposed in the literature. This paper discusses the rough approximations of Atanassov intuitionistic fuzzy sets in crisp and fuzzy approximation spaces in which both constructive and axiomatic approaches are used. In the constructive approach, concepts of rough intuitionistic fuzzy sets and intuitionistic fuzzy rough sets are defined, properties of rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are examined. Different classes of rough intuitionistic fuzzy set algebras and intuitionistic fuzzy rough set algebras are obtained from different types of fuzzy relations. In the axiomatic approach, an operator-oriented characterization of rough sets is proposed, that is, rough intuitionistic fuzzy approximation operators and intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of upper and lower intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of crisp/fuzzy relations which produce the same operators.     

基于模糊集和粗糙集联系度的商务决策系统

粗糙集理论和模糊集理论都是研究信息系统中知识的不完整、不确定性问题,把集对分析中的联系度概念应用于粗糙集中,说明了粗糙集联系度与下近似集和上近似集的值化的关系,将粗糙集联系度理论与模糊集理论相结合,提出了一种基于模糊集和粗糙集联系度的综合评价方法,实例验证了该方法对一大类复杂信息系统的知识发现具有一定的应用价值。     

Application of fuzzy logic and variable precision rough set approach in a remote monitoring manufacturing process for diagnosis rule induction

Rough set has been shown to be a valuable approach to mine rules from a remote monitoring manufacturing process. In this research, an application of the fuzzy set theory with the fuzzy variable precision rough set approach for mining the causal relationship rules from the database of a remote monitoring manufacturing process is presented. The membership function in the fuzzy set theory is used to transfer the data entries into fuzzy sets, and the fuzzy variable precision rough set approach is applied to extract rules from the fuzzy sets. It is found that the induced rules are identical to the practical knowledge and fault diagnosis thinking of human operators. The induced rules are then compared with the rules induced by the original rough set approach. The comparison shows that the rules induced by the fuzzy rough set are expressed in linguistic forms, and are evaluated by plausibility and future effectiveness measures. The fuzzy rough set approach, being less sensitive to noisy data, induces better rules than the original rough set approach.     

模糊近似空间上的粗糙模糊集的公理系统

粗糙集理论是近年来发展起来的一种有效的处理不精确、不确定、含糊信息的理论，在机器学习及数据挖掘等领域获得了成功的应用．粗糙集的公理系统是粗糙集理论与应用的基础．粗糙模糊集是粗糙集理论的自然的有意义的推广．作者研究了模糊近似空间上的粗糙模糊集的公理系统，用三条简洁的相互独立的公理完全刻划了模糊近似空间上的粗糙模糊集，同时还把作者给出的公理系统与粗糙集的公理系统做了对比，指出了两者的区别．     

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.     

Induction of multiple fuzzy decision trees based on rough set technique

The integration of fuzzy sets and rough sets can lead to a hybrid soft-computing technique which has been applied successfully to many fields such as machine learning, pattern recognition and image processing. The key to this soft-computing technique is how to set up and make use of the fuzzy attribute reduct in fuzzy rough set theory. Given a fuzzy information system, we may find many fuzzy attribute reducts and each of them can have different contributions to decision-making. If only one of the fuzzy attribute reducts, which may be the most important one, is selected to induce decision rules, some useful information hidden in the other reducts for the decision-making will be losing unavoidably. To sufficiently make use of the information provided by every individual fuzzy attribute reduct in a fuzzy information system, this paper presents a novel induction of multiple fuzzy decision trees based on rough set technique. The induction consists of three stages. First several fuzzy attribute reducts are found by a similarity based approach, and then a fuzzy decision tree for each fuzzy attribute reduct is generated according to the fuzzy ID3 algorithm. The fuzzy integral is finally considered as a fusion tool to integrate the generated decision trees, which combines together all outputs of the multiple fuzzy decision trees and forms the final decision result. An illustration is given to show the proposed fusion scheme. A numerical experiment on real data indicates that the proposed multiple tree induction is superior to the single tree induction based on the individual reduct or on the entire feature set for learning problems with many attributes.     

粗糙集与模糊神经网络集成在故障诊断中的研究

考虑模糊聚类的数据离散功能,粗糙集理论对决策系统的约简能力,以及模糊神经网络在模式识别方面具有的优势,提出了粗糙集一自适应模糊神经网络推理系统（ANFIS）集成进行故障诊断的方案：首先,应用SOM方法离散故障诊断数据中的连续属性值;然后,基于粗糙集理论计算诊断决策系统的约简,按照实际需要确定诊断条件;最后,根据系统约简设计ANFIS进行故障诊断。4135柴油机的实际诊断结果验证了文中提出集成故障诊断方案的可行性。在数据充分的条件下,该方案可以推广应用于其它机械设备。