S-rough sets and knowledge separation

The conceptions of the knowledge screen generated by S-rough sets are given: f- screen and - screen , and then puts forward - filter theorem, - filter theorem of knowledge. At last, the applications of knowledge separation are given according to - screen and - screen.

Research on knowledge acquisition method about the IF/THEN rules based on rough set theory

The basic principles of IF/THEN rules in rough set theory are analyzed first, and then the automatic process of knowledge acquisition is given. The numerical data is qualitatively processed by the classification of membership functions and membership degrees to get the normative decision table. The regular method of relations and the reduction algorithm of attributes are studied. The reduced relations are presented by the multi-representvalue method and its algorithm is offered. The whole knowledge acquisition process has high degree of automation and the extracted knowledge is true and reliable.

IMPROVED ACCURACY AND ROUGHNESS MEASURES FOR ROUGH SETS

Accuracy and roughness, proposed by Pawlak(1982), might draw a conclusion inconsistent with our intuition in some cases. This letter analyzes the limitations in these measures and proposes improved accuracy and roughness measures based on information theory.

Transformation and entropy for fuzzy rough sets

A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.

S-rough sets and the discovery of F-hiding knowledge

Singular rough sets （S-rough sets） have three classes of forms： one-directional S-rough sets, dual of onedirectional S-rough sets, and two-directional S-rough sets. Dynamic, hereditary, mnemonic, and hiding properties are the basic characteristics of S-rough sets. By using the S-rough sets, the concepts of f-hiding knowledge, F-hiding knowledge, hiding degree, and hiding dependence degree are given. Then, both the hiding theorem and the hiding dependence theorem of hiding knowledge are proposed. Finally, an application of hiding knowledge is discussed.

Fault Diagnosis of a Rotary Machine Based on Information Entropy and Rough Set

There exists some discord or contradiction of information during the process of fault diagnosis for rotary machine. But the traditional methods used in fault diagnosis can not dispose of the information. A model of fault diagnosis for a rotary machine based on information entropy theory and rough set theory is presented in this paper. The model has clear mathematical definition and can dispose both complete unification information and complete inconsistent information of vibration faults. By using the model, decision rules of six typical vibration faults of a steam turbine and electric generating set are deduced from experiment samples. Finally, the decision rules are validated by selected samples and good identification results are acquired.

Applying rough sets in word segmentation disambiguation based on maximum entropy model

To solve the complicated feature extraction and long distance dependency problem in Word Segmentation Disambiguation （WSD）, this paper proposes to apply rough sets ill WSD based on the Maximum Entropy model. Firstly, rough set theory is applied to extract the complicated features and long distance features, even frnm noise or inconsistent corpus. Secondly, these features are added into the Maximum Entropy model, and consequently, the feature weights can be assigned according to the performance of the whole disambiguation mnltel. Finally, tile semantic lexicou is adopted to build class-hased rough set teatures to overcome data spareness. The experiment indicated that our method performed better than previous models, which got top rank in WSD in 863 Evaluation in 2003. This system ranked first and second respcetively in MSR and PKU open test in the Second International Chinese Word Segmentation Bankeoff held in 2005.

NEW METHOD FOR MEASURING FUZZINESS IN ROUGH SETS

A method with the fuzzy entropy for measuring fuzziness to fuzzy problem in rough sets is proposed. A new sort of the fuzzy entropy is given. The calculating formula and the equivalent expression method with the fuzzy entropy in rough sets based on equivalence relation are provided, and the properties of the fuzzy entropy are proved. The fuzzy entropy based on equivalent relation is extended to generalize the fuzzy entropy based on general binary relation, and the calculating formula and the equivalent expression of the generalized fuzzy entropy are also given. Finally, an example illustrates the way for getting the fuzzy entropy. Results show that the fuzzy entropy can conveniently measure the fuzziness in rough sets.

基于Rough Set理论的典型振动故障诊断

在分析旋转机械振动特点和Rough Set理论的基础上,针对传统的频谱分析方法对质量不平衡、动静碰摩、支座松动等3种典型故障识别效率低的缺点,提出了一个基于Rough Set的振动故障诊断模型.该模型根据故障和能量的映射关系,分别在时域、频域、时-频域中定义4种信息熵作为条件属性,推导了3种典型振动的决策规则,实现了对振动信号中不一致信息的处理.通过汽轮发电机组振动实验对上述方法进行了验证.结果表明,该模型能够很好地识别这3种典型故障.

基于Rough Set的数据预处理

RoughSet理论是一种新的处理不精确,不完全与不相容知识的数学工具。数据预处理是数据挖掘中必不可少的步骤,处理的结果对下一步数据挖掘有直接影响。论文利用RoughSet一些特性对KDD99中的数据集进行处理,并且针对数据集的特点实现了对其进行数据离散化、属性约简等处理。通过这些处理过程为下一步的数据挖掘打下了基础。

一种新的集合理论Vague Rough sets

将不确定理论Vague集合和Rough集合相结合,提出一种新的集合理论VagueRoughsets.并讨论了其不确定性性质,如模糊度粗糙度等。

A Decision Model Based on Grey Rough Sets Integration with Incomplete Information

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.

Half-global discretization algorithm based on rough set theory

It is being widely studied how to extract knowledge from a decision table based on rough set theory. The novel problem is how to discretize a decision table having continuous attribute. In order to obtain more reasonable discretization results, a discretization algorithm is proposed, which arranges half-global discretization based on the correlational coefficient of each continuous attribute while considering the uniqueness of rough set theory. When choosing heuristic information, stability is combined with rough entropy. In terms of stability, the possibility of classifying objects belonging to certain sub-interval of a given attribute into neighbor sub-intervals is minimized. By doing this, rational discrete intervals can be determined. Rough entropy is employed to decide the optimal cut-points while guaranteeing the consistency of the decision table after discretization. Thought of this algorithm is elaborated through Iris data and then some experiments by comparing outcomes of four discritized datasets are also given, which are calculated by the proposed algorithm and four other typical algorithras for discritization respectively. After that, classification rules are deduced and summarized through rough set based classifiers. Results show that the proposed discretization algorithm is able to generate optimal classification accuracy while minimizing the number of discrete intervals. It displays superiority especially when dealing with a decision table having a large attribute number.

Improved Rough Set Algorithms for Optimal Attribute Reduct

Feature selection（FS） aims to determine a minimal feature（attribute） subset from a problem domain while retaining a suitably high accuracy in representing the original features. Rough set theory（RST） has been used as such a tool with much success. RST enables the discovery of data dependencies and the reduction of the number of attributes contained in a dataset using the data alone,requiring no additional information. This paper describes the fundamental ideas behind RST-based approaches,reviews related FS methods built on these ideas,and analyses more frequently used RST-based traditional FS algorithms such as Quickreduct algorithm,entropy based reduct algorithm,and relative reduct algorithm. It is found that some of the drawbacks in the existing algorithms and our proposed improved algorithms can overcome these drawbacks. The experimental analyses have been carried out in order to achieve the efficiency of the proposed algorithms.

An information-based rough set approach to critical engineering factor identification

In order to analyze the main critical engineering factors, an information-based rough set approach that considers conditional information entropy as a measurement of information has been developed. An algorithm for continuous attribute discretization based on conditional information entropy and an algorithm for rule extraction considering the supports of rules are proposed. The initial decision system is established by collecting enough monitoring data. Then, the continuous attributes are discretized, and the condition attributes are reduced. Finally, the rules that indicate the action law of the main factors are extracted and the results are explained. By applying this approach to a crack in an arch gravity dam, it can be concluded that the water level and the temperature are the main factors affecting the crack opening, and there is a negative correlation between the crack opening and the temperature. This conclusion corresponds with the observation that cracks in most concrete dams are influenced mainly by water level and temperature, and the influence of temperature is more evident.

Emergency Decision-Making Based on q-Rung Orthopair Fuzzy Rough Aggregation Information

With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.

基于信息熵与Rough集理论的城市信息系统知识依赖度分析

以城市信息化空间数据处理为研究背景,基于信息熵与Rough集理论解决信息系统中信息不确定、数据量大的困难。从Rough集的基本概念出发,给出决策表的知识表达系统,探讨了信息熵处理知识依赖度的方法。最后通过运用该方法对城市空间数据决策表的实例进行属性值依赖关系的确定。

基于Rough熵的决策表约简算法研究

知识约简是Rough集理论研究中的核心内容之一,已证明求决策表的最小约简是NP-hard问题,解决办法一般是采用启发式算法.本文分析了信息熵在Rough集理论中的应用,利用Rough熵定义了决策表中条件属性的相对重要度,讨论了其性质,在此基础上提出了一种用于计算决策表中的相对约简的启发式算法.

Information Measures of Roughness of Knowledge and Rough Sets for Incomplete Information Systems

In this paper we address information measures of roughness of knowledge and rough sets for incomplete information systems. The definition of rough entropy of knowledge and its important properties are given. In particular, the relationship between rough entropy of knowledge and the Hartley measure of uncertainty is established. We show that rough entropy of know1edge decreases monotonously as granularity of information become smaller. This gives an information interpretation for roughness of knowledge. Based on rough entropy of knowledge and roughness of rough set. a definition of rough entropy of rough set is proposed, and we show that rough entropy of rough set decreases monotonousIy as granularity of information become smaller. This gives more accurate measure for roughness of rough set.

基于ROUGH集的决策树测试属性选择方法

测试属性的选择直接影响到决策树中结点的个数甚至是深度,因此如何选择测试属性是研究的一个热点。本文主要介绍了粗集理论的方法。通过比较我们会发现,在单变量决策树的构造上,粗集理论中属性重要性的方法计算量较小,而多变量决策树充分考虑了条件属性间的相关性,因此通过求解信息系统的相对核从而减少决策树结点的个数。