实值信息系统的属性约简

实值信息系统是连续值信息系统的广义形式,其属性值是实际问题反映出来的真实数据。通过在实值信息系统上定义一种相容关系,主要讨论了这种关系下实值信息系统与实值决策表基于粗糙集理论的属性约简,给出了区分函数的定义与约简的判定定理,得到了计算约简的具体方法,并将所得结论用于无线电信号数据分析处理上。     

连续属性信息系统的规则约简新方法

连续属性信息系统的规则约简根本问题是属性在连续范围取任何实值,使得应用与离散属性的规则约简方法难于使用。因此解决连续属性信息系统的规则约简问题为当前研究领域所关注。该文结合粗集与模糊集理论与方法提出了一种新的数据处理与规则约简方法,并给出了该方法的实验结果。     

一种基于粗糙集理论的规则提取方法

规则提取是实现智能信息系统的重要环节,也是一个难点。针对信息系统中的规则提取问题,提出了一种基于粗糙集的研究方法,并对规则提取涉及到的属性约简、属性值约简等问题进行了研究。根据粗糙集中的不可分辨关系建立了可辫识向量,以利用可辨识向量的加法法则运算求得核属性以及属性重要性,然后以核属性为基础、属性重要性为启发信息,求得信息表的一个属性约简。在此基础上,利用条件属性与决策属性之间的对应关系,对信息表中的每条规则通过删除冗余属性值来完成信息表的属性值约简,最终实现规则提取。数值实例和试验表明本算法是有效、可行的。     

一种实值属性信息系统的粗集约简方法

本文研究应用粗集理论对实值信息系统属性进行约简的方法，对实值属性信息系统进行约简的根本问题是如何对实值属性离散化，通过对离散化方法与属性约简的关系进行研究，提出实值属性离散化的一种自动确定属性类别的方法，并结合粗集理论给出了对实值属性信息系统约简的算法，用所提出的算法进行了实验，并给出了实验结果。     

区间值信息系统的概念格约简方法

区间值信息系统是属性值取值为区间值形式的一种特殊信息系统。通过把区间值信息系统转化为0-1形式背景,利用概念格属性约简方法,区间值信息系统协调集的判定定理,并引入可辨识属性矩阵,研究区间值信息系统上基于概念格属性约简的理论方法。     

基于扩展粗糙集模型的集值不完备信息系统决策研究

在客观世界中信息系统往往是不完备的。该文将粗糙集模型经过扩展后应用于属性值为集合值的不完备信息系统,给出了几种不同的上下近似集定义,着重建立和分析了一种不完备决策表,研究了对应的粗糙集模型扩展后的属性约简的方法,并根据约简生成了决策规则。     

优势关系下直觉模糊目标信息系统的上近似约简

传统的粗糙集理论对决策属性值为直觉模糊数的直觉模糊目标信息系统不能直接属性约简.文中在直觉模糊目标信息系统中引入优势关系,基于优势关系定义条件属性集的上近似决策协调集,给出上近似约简的判定定理,建立该信息系统条件属性集的上近似约简模型,并给出上近似约简的算法步骤.在决策属性值为直觉模糊数的一些目标信息系统中,利用条件属性集的上近似约简,可得到更为简洁的决策规则.最后给出一个实例验证算法的有效性.     

基于粗糙集的一种属性值约简算法及其应用

阐述粗糙集理论的基本概念,并且对属性约简和值约简算法进行研究,提出了一种基于粗糙集的属性值约简算法.通过实例介绍该算法的应用.研究表明,该算法不仅能得到最佳的决策规则,而且能够大大降低信息系统所需的存储空间,该算法可以解决各种有关的实际问题.     

基于粗糙集的推理通道消除

基于粗糙集理论对推理通道问题进行了研究。通过采用属性约简和属性值约简方法对数据库中的数据进行处理。在属性值约简基础之上,采用一种改进算法找出了数据库中推理规则集。进一步,将推理规则集中属性频率高的属性安全级别提高至决策属性的安全级别,从而消除推理通道。最后通过一个实例表明提出的消除通道算法是有效的。     

一种属性与值约简及规则提取算法

本文提出了一种属性与值约简及规则提取算法。该算法无需求出分明矩阵,而是从决策表中直接提出关于属性值分明的属性构造分明函数,并且可以同时求出属性约简和属性值约简。在此基础上提取规则不仅节约了空间,而且提高了效率,并通过实例进行了验证。     

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.     

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.     

Elicitation of classification rules by fuzzy data mining

Data mining techniques can be used to find potentially useful patterns from data and to ease the knowledge acquisition bottleneck in building prototype rule-based systems. Based on the partition methods presented in simple-fuzzy-partition-based method (SFPBM) proposed by Hu et al. (Comput. Ind. Eng. 43(4) (2002) 735), the aim of this paper is to propose a new fuzzy data mining technique consisting of two phases to find fuzzy if–then rules for classification problems: one to find frequent fuzzy grids by using a pre-specified simple fuzzy partition method to divide each quantitative attribute, and the other to generate fuzzy classification rules from frequent fuzzy grids. To improve the classification performance of the proposed method, we specially incorporate adaptive rules proposed by Nozaki et al. (IEEE Trans. Fuzzy Syst. 4(3) (1996) 238) into our methods to adjust the confidence of each classification rule. For classification generalization ability, the simulation results from the iris data demonstrate that the proposed method may effectively derive fuzzy classification rules from training samples.     

Attribute selection with fuzzy decision reducts

Rough set theory provides a methodology for data analysis based on the approximation of concepts in information systems. It revolves around the notion of discernibility: the ability to distinguish between objects, based on their attribute values. It allows to infer data dependencies that are useful in the fields of feature selection and decision model construction. In many cases, however, it is more natural, and more effective, to consider a gradual notion of discernibility. Therefore, within the context of fuzzy rough set theory, we present a generalization of the classical rough set framework for data-based attribute selection and reduction using fuzzy tolerance relations. The paper unifies existing work in this direction, and introduces the concept of fuzzy decision reducts, dependent on an increasing attribute subset measure. Experimental results demonstrate the potential of fuzzy decision reducts to discover shorter attribute subsets, leading to decision models with a better coverage and with comparable, or even higher accuracy.     

结合粗糙集和模糊聚类方法的属性约简算法

本文针对粗糙集理论的属性约简算法进行了研究。结合模糊聚类方法，提出了一个新的属性约简算法，用户可以根据实际决策需要和领域知识更改阈值λ，从而得到用户满意的属性约简结果。最后利用该文的算法给出了一个实例的约筒结果。     

On fuzzy approximation operators in attribute reduction with fuzzy rough sets

Generally speaking, there are four fuzzy approximation operators defined on a general triangular norm (t-norm) framework in fuzzy rough sets. Different types of t-norms specify various approximation operators. One issue whether and how the different fuzzy approximation operators affect the result of attribute reduction is then arisen. This paper addresses this issue from the theoretical viewpoint by reviewing attribute reduction with fuzzy rough sets and then describing and proving some theorems which demonstrate the effects of the fuzzy approximation operators on the results of attribute reduction. First, we review some notions of attribute reduction with fuzzy rough sets, such as positive region, dependency degree and attribute reduction. We then present and prove some theorems which describe how and to what degree fuzzy approximation operators impact the performance of attribute reduction. Finally, we report some experimental simulation results which demonstrate the effectiveness and correctness of the theoretical contributions. One main contribution in this paper is that we have described and proven that each attribute reduction obtained using one type of fuzzy lower approximation operator always contains one reduction obtained using the other type of fuzzy lower approximation operator.     

Fuzzy data envelopment analysis and its application to location problems

In this paper, fuzzy DEA (data envelopment analysis) models are proposed for evaluating the efficiencies of objects with fuzzy input and output data. The obtained efficiencies are also fuzzy numbers that reflect the inherent ambiguity in evaluation problems under uncertainty. An aggregation model for integrating fuzzy attribute values is provided in order to rank objects objectively. Using the proposed method, a case study involving a restaurant location problem is analyzed in detail. Rent of establishment, traffic amount, level of security, consumer consumption level and competition level are identified as the primary factors in determining an ideal location for a Japanese-style rotisserie restaurant. Based on field investigation, the uncertain information on primary factors is represented by fuzzy numbers. Using the fuzzy aggregation model, the best location of restaurant is determined. The case study shows that fuzzy DEA models can be quite useful for solving business problems under uncertainty.     

Rough set theory for the interval-valued fuzzy information systems

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341-356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2-3) (1990) 191-209] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets. This paper deals with an interval-valued fuzzy information system by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory and discusses the basic rough set theory for the interval-valued fuzzy information systems. In this paper we firstly define the rough approximation of an interval-valued fuzzy set on the universe U in the classical Pawlak approximation space and the generalized approximation space respectively, i.e., the space on which the interval-valued rough fuzzy set model is built. Secondly several interesting properties of the approximation operators are examined, and the interrelationships of the interval-valued rough fuzzy set models in the classical Pawlak approximation space and the generalized approximation space are investigated. Thirdly we discuss the attribute reduction of the interval-valued fuzzy information systems. Finally, the methods of the knowledge discovery for the interval-valued fuzzy information systems are presented with an example.     

模糊决策粗糙集代价敏感属性约简研究

针对决策中普遍存在的代价问题,在模糊理论和决策粗糙集的基础上,对其代价敏感属性约简方法进行了研究。在模糊决策粗糙集属性约简中引入了包含误分类代价和测试代价的总代价。因此约简的目标不再只是考虑正域的大小,而是寻找使得总代价最小的最优属性子集。提出了一种模糊决策粗糙集代价敏感属性约简(COSAR)算法,该算法采用启发式方法搜索最优属性子集。给出了算法的步骤,并将该算法与已有的模糊粗决策粗糙集属性快速约简(QuickReduct)算法进行了性能对比。实验结果表明,COSAR算法比QuickReduct算法具有更强的属性约简能力、更低的分类总代价、更短的运行时间,且随着测试样本的增加,分类总代价差值也越来越大。