A New Method for Constructing Decision Tree Based on Rough Sets Theory

Decision trees induction algorithms have been used for classification in a wide range of application domains. In the process of constructing a tree, the criteria of selecting test attributes will influence the classification accuracy of the tree.In this paper,the degree of dependency of decision attribute to condition attribute,based on rough set theory,is used as a heuristic for selecting the attribute that will best separate the samples into individual classes.The result of an example shows that compared with the entropy-based approach,our approach is a better way to select nodes for constructing decision trees.

Core Competitiveness Evaluation of Financial Institution with Rough Sets and Gray Correlation Analysis

The comprehensive evaluation method of enterprise core competitiveness is proposed by combining rough sets and gray correlation theories. Firstly,the initial index is screened through rough set attribute reduction algorithm,and the evaluation weight of each index is obtained through the rough set theory. Then,based on the gray correlation theory, an evaluation model is built for empirical analysis. The 30 financial institutions on the Yangtze River Delta are examined from the theoretical and empirical perspective.The result demonstrates not only the feasibility of rough set attribute reduction algorithm in the core competitiveness index system of the financial institution,but also the accuracy of the combination of these two methods in the comprehensive evaluation of corporate core competitiveness.

Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Rough Set Processing Model for Fuzzy Decision Tables with Weights

The classical rough set can not show the fuzziness and the importance of objects in decision procedure because it uses definite form to express each object. In order to solve this problem,this paper firstly introduces a special decision table in which each object has a membership degree to show its fuzziness and has been assigned a weight to show its importance in decision procedure. Then,the special decision table is studied and the relevant rough set model is provided. In the meantime,relevant definitions and theorems are proposed. On the above basis,an attribute reduction algorithm is presented. Finally,feasibility of the relevant rough set model and the presented attribute reduction algorithm are verified by an example.

Variable precision rough set for multiple decision attribute analysis

A variable precision rough set (VPRS) model is used to solve the multi-attribute decision analysis (MADA) problem with multiple conflicting decision attributes and multiple condition attributes. By introducing confidence measures and a β-reduct, the VPRS model can rationally solve the conflicting decision analysis problem with multiple decision attributes and multiple condition attributes. For illustration, a medical diagnosis example is utilized to show the feasibility of the VPRS model in solving the MADA problem with multiple decision attributes and multiple condition attributes. Empirical results show that the decision rule with the highest confidence measures will be used as the final decision rules in the MADA problem with multiple conflicting decision attributes and multiple condition attributes if there are some conflicts among decision rules resulting from multiple decision attributes. The confidence-measure-based VPRS model can effectively solve the conflicts of decision rules from multiple decision attributes and thus a class of MADA problem with multiple conflicting decision attributes and multiple condition attributes are solved.

Fast assignment reduction in inconsistent incomplete decision systems

This paper focuses on fast algorithm for computing the assignment reduct in inconsistent incomplete decision systems. It is quite inconvenient to judge the assignment reduct directly ac-cording to its definition. We propose the judgment theorem for the assignment reduct in the inconsistent incomplete decision system, which greatly simplifies judging this type reduct. On such basis, we derive a novel attribute significance measure and construct the fast assignment reduction algorithm （F-ARA）, intended for com-puting the assignment reduct in inconsistent incomplete decision systems. Final y, we make a comparison between F-ARA and the discernibility matrix-based method by experiments on 13 Univer-sity of California at Irvine （UCI） datasets, and the experimental results prove that F-ARA is efficient and feasible.

Risk Analysis Technique on Inconsistent Interview Big Data Based on Rough Set Approach

Rough set theory is relativly new to area of soft computing to handle the uncertain big data efficiently. It also provides a powerful way to calculate the importance degree of vague and uncertain big data to help in decision making. Risk assessment is very important for safe and reliable investment. Risk management involves assessing the risk sources and designing strategies and procedures to mitigate those risks to an acceptable level. In this paper, we emphasize on classification of different types of risk factors and find a simple and effective way to calculate the risk exposure.. The study uses rough set method to classify and judge the safety attributes related to investment policy. The method which based on intelligent knowledge accusation provides an innovative way for risk analysis. From this approach, we are able to calculate the significance of each factor and relative risk exposure based on the original data without assigning the weight subjectively.

Support vector machine ensemble using rough sets theory

A support vector machine （SVM） ensemble classifier is proposed. Performance of SVM trained in an input space eonsisting of all the information from many sources is not always good. The strategy that the original input space is partitioned into several input subspaces usually works for improving the performance. Different from conventional partition methods, the partition method used in this paper, rough sets theory based attribute reduction, allows the input subspaces partially overlapped. These input subspaces can offer complementary information about hidden data patterns. In every subspace, an SVM sub-classifier is learned. With the information fusion techniques, those SVM sub-classifiers with better performance are selected and combined to construct an SVM ensemble. The proposed method is applied to decision-making of medical diagnosis. Comparison of performance between our method and several other popular ensemble methods is done. Experimental results demonstrate that our proposed approach can make full use of the information contained in data and improve the decision-making performance.

Attribute Reduction in Decision Systems Based on Relation Matrix

This paper proposes,from the viewpoint of relation matrix,a new algorithm of attribute reduction for decision systems.Two new and relative reasonable indices are first defined to measure significance of the attributes in decision systems and then a heuristic algorithm of attribute reduction is formulated.Moreover,the time complexity of the algorithm is analyzed and it is proved to be complete.Some numerical experiments are also conducted to access the performance of the presented algorithm and the results demonstrate that it is not only effective but also efficient.

A Survey of Software Packages Used for Rough Set Analysis

Soft computing is a combination of methods that complement each other when dealing with ambiguous real life decision systems. Rough Set Theory (RST) is a technique used in soft computing that enhances the idea of classical sets to deal with incomplete knowledge and provides a mechanism for concept approximation. It uses reducts to isolate key attributes affecting outcomes in decision systems. The paper summarizes two algorithms for reduct calculation. Moreover, to automate the application of RST, different software packages are available. The paper provides a survey of packages that are most frequently used to perform data analysis based on Rough Sets. For benefit of researchers, a comparison of based on functionalities of those software is also provided.

一种基于Rough Set理论的属性约简及规则提取方法

该文针对RoughSet理论中属性约简和值约简这两个重要问题进行了研究，提出了一种借助于可辨识矩阵（discernibilitymatrix）和数学逻辑运算得到最佳属性约简的新方法．同时，借助该矩阵还可以方便地构造基于RoushSet理论的多变量决策树．另外，对目前广泛采用的一种值约简策略进行了改进，最终使得到的规则进一步简化．

基于Rough Set的综合评价方法研究

目前诸多的综合评价方法在权重设置和单因素评价矩阵确定等方面的局限性制约了人们对评价对象的科学认识。论文根据RoughSet理论,提出了基于RoughSet的综合评价方法,旨在消除权重设置的主观性,有效削减指标体系规模。文章最后通过实例,验证该方法的实用性、可行性。

一种基于Rough Set的启发式属性约简算法

属性约简的目的在于减少条件属性中不必要属性的数目,是知识发现中的关键问题之一。本文提出了一种改进的基于Rough集的启发式算法(IMSA),定义了新的启发函数(WSH)。这个函数考虑了所有隐藏规则集的质量,并且考虑了相关规则集的权重。在算法本身的时间复杂度没有增加的前提下,能够解决MSA算法遇到多个相同MSH值时无法处理的情况。实验分析表明,该算法是有效的。

基于Rough Sets-C4.5的故障征兆提取与判别

针对原始信息系统往往存在大量重复样本和冗余属性,从而影响实际故障诊断的精度和速度这一问题,介绍了一种基于粗糙集和决策树C4.5算法相融合的故障诊断模型,用于设备的精确和快速故障诊断.利用粗糙集具有较强的处理不确定和不完备信息的能力,对原始样本集进行离散化及约简处理;同时,利用决策树C4.5算法对约简后的决策表进行快速学习并形成树状故障分类器.以实例介绍了利用该模型进行故障诊断的完整过程.

基于Rough Set的属性值约简算法研究

从逻辑的角度分析了属性值约简的本质及过程,在此基础上构造辨识矩阵,提出了一种基于Roughset的属性值约简新算法,并对此进行了证明。该算法比以往的算法更简便、直观,易于编程实现,也更易从本质上理解属性值约简的实质及过程,并且算法不破坏决策系统中的不一致规则所蕴含的信息量。实例分析表明该算法是有效可行的。

基于Rough Set的最简决策树确定算法的研究

决策树是一种有效用于分类的数据采掘方法,有确定性和非确定性决策树。传统的方法是通过信息熵的计算去生成决策树,计算量大。目前有人用RS方法去计算信息熵,但存在局限性。该文将指出其局限性,并给出了一种有效的属性选择算法,确定了最简确定性和非确定性决策树的判别准则及其通用生成算法。

基于Rough Set理论的商务决策支持系统知识发现的研究

针对商务决策支持系统中存在信息不确定、冗余数据量大的问题,提出了一种基于Rough Set理论的提取最小规则算法。该算法的核心是改进的分明矩阵属性约简和启发式的属性值约简。通过算法对原始数据表中的冗余属性和属性值进行约简,得到了决策表和最小决策规则。最后,对商务决策支持系统的实例进行数据约简,挖掘其中的隐含知识,获取了有价值的决策信息。

Lower Approximation Reduction in Ordered Information System with Fuzzy Decision

Attribute reduction is one of the most important problems in rough set theory. This paper introduces the concept of lower approximation reduction in ordered information systems with fuzzy decision. Moreover, the judgment theorem and discernable matrix are obtained, in which case an approach to attribute reduction in ordered information system with fuzzy decision is constructed. As an application of lower approximation reduction, some examples are applied to examine the validity of works obtained in our works..

基于Rough Set的一种决策树的确定算法

决策树是一种有效用于分类的数据采掘方法 ,通常是通过信息熵的计算去选择分枝属性 ,计算量大而复杂。文章利用粗集理论中相对正域的概念 ,找到另一种信息熵的等效表示方法 ,只要通过简单的集合运算 ,便可对协调和非协调决策表得到相应的确定和非确定性决策树 。

A Rough Set Based Optimization Method for Elderly Evaluation

In order to improve the efficiency of elderly evaluation, an optimization method based on rough set is proposed. Compared with the traditional rough set attribute reduction, the redundant evaluation items are eliminated by items’ correlation. It avoids a big overhead of calculating the core of rough sets that have many attributes. A novel rule reduction method is proposed based on reliability and coverage, in order to solve the problem of rarely appeared rules and conflict rules in traditional rough set. A sorting algorithm based on coverage is used to optimize the traditional flat evaluation questionnaire model with a hierarchical order. By these optimizations, the number of items that need to evaluate is greatly reduced. The proposed approach is deployed in an elderly service company named Lime family. Real-life result shows that the method can reduce more than 40% items with over 90% accuracy prediction rate. Compared with decision tree and the method based on expert knowledge in reduction rate and accuracy rate, the method has same performance in one index, and 20% improvement on average in the other one.