Research on the Information Fusion Method of Oil Diagnosis and Vibration Diagnosis Based on the Rough Sets Theory

The improved method has been presented for knowledge reduction in rough sets （R-S） theory, when R-S is used to model the information expression of oil and vibration diagnosis. Therefore, the typical fault simulation tests of rolling bearings have been made, and the application method of R-S has been also analysed in this paper. The diagnosis model of holding rack fault in rolling bearing was presented based on the improved reduction method. It is suited to information fusion to combine information when oil analysis and vibration analysis are combined for fault diagnosis.

New judging model of fuzzy cluster optimal dividing based on rough sets theory

To investigate the judging problem of optimal dividing matrix among several fuzzy dividing matrices in fuzzy dividing space, correspondingly, which is determined by the various choices of cluster samples in the totality sample space, two algorithms are proposed on the basis of the data analysis method in rough sets theory： information system discrete algorithm （algorithm 1） and samples representatives judging algorithm （algorithm 2）. On the principle of the farthest distance, algorithm 1 transforms continuous data into discrete form which could be transacted by rough sets theory. Taking the approximate precision as a criterion, algorithm 2 chooses the sample space with a good representative. Hence, the clustering sample set in inducing and computing optimal dividing matrix can be achieved. Several theorems are proposed to provide strict theoretic foundations for the execution of the algorithm model. An applied example based on the new algorithm model is given, whose result verifies the feasibility of this new algorithm model.

Granularity of Knowledge Computed by Genetic Algorithms Based on Rough Sets Theory

Rough set philosophy hinges on the granularity of data, which is used to build all its basic concepts, like approximations, dependencies, reduction etc. Genetic Algorithms provides a general frame to optimize problem solution of complex system without depending on the domain of problem.It is robust to many kinds of problems.The paper combines Genetic Algorithms and rough sets theory to compute granular of knowledge through an example of information table. The combination enable us to compute granular of knowledge effectively.It is also useful for computer auto-computing and information processing.

Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.

New Image Recognition Method Based on Rough-Sets and Fuzzy Theory

A new image recognition method based on fuzzy rough sets theory is proposed, and its implementation discussed. The performance of this method as applied to ferrography image recognition is evaluated. It is shown that the new method gives better results than fuzzy or rough sets method when used alone.

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.

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.

Autonomous Clustering Using Rough Set Theory

This paper proposes a clustering technique that minimizes the need for subjective human intervention and is based on elements of rough set theory （RST）. The proposed algorithm is unified in its approach to clustering and makes use of both local and global data properties to obtain clustering solutions. It handles single-type and mixed attribute data sets with ease. The results from three data sets of single and mixed attribute types are used to illustrate the technique and establish its efficiency.

Seismic vulnerability assessment of urban buildings using the rough set theory and weighted linear combination

Seismic vulnerability assessment of urban buildings is among the most crucial procedures to post-disaster response and recovery of infrastructure systems.The present study proceeds to estimate the seismic vulnerability of urban buildings and proposes a new framework training on the two objectives.First,a comprehensive interpretation of the effective parameters of this phenomenon including physical and human factors is done.Second,the Rough Set theory is used to reduce the integration uncertainties,as there are numerous quantitative and qualitative data.Both objectives were conducted on seven distinct earthquake scenarios with different intensities based on distance from the fault line and the epicenter.The proposed method was implemented by measuring seismic vulnerability for the seven specified seismic scenarios.The final results indicated that among the entire studied buildings,71.5%were highly vulnerable as concerning the highest earthquake scenario(intensity=7 MM and acceleration calculated based on the epicenter),while in the lowest earthquake scenario(intensity=5 MM),the percentage of vulnerable buildings decreased to approximately 57%.Also,the findings proved that the distance from the fault line rather than the earthquake center(epicenter)has a significant effect on the seismic vulnerability of urban buildings.The model was evaluated by comparing the results with the weighted linear combination(WLC)method.The accuracy of the proposed model was substantiated according to evaluation reports.Vulnerability assessment based on the distance from the epicenter and its comparison with the distance from the fault shows significant reliable results.

Matrix-based method for solving decision domains of neighbourhood multigranulation decision-theoretic rough sets

It is more and more important to analyse and process complex data for gaining more valuable knowledge and making more accurate decisions.The multigranulation decision theory based on conditional probability and cost loss has the advantage of processing decision-making problems from multi-levels and multi-angles,and the neighbourhood rough set model(NRS)can facilitate the analysis and processing of numerical or mixed type data,and can address the limitation of multigranulation decision-theoretic rough sets(MG-DTRS),which is not easy to cope with complex data.Based on the in-depth study of hybrid-valued decision systems and MG-DTRS models,this study analysed neigh-bourhood MG-DTRS(NMG-DTRS)deeply by fusing MG-DTRS and NRS;a matrix-based approach for approximation sets of NMG-DTRS model was proposed on the basis of the matrix representations of concepts;the positive,boundary and negative domains were constructed from the matrix perspective,and the concept of positive decision recognition rate was introduced.Furthermore,the authors explored the related properties of NMG-DTRS model,and designed and described the corresponding solving algorithms in detail.Finally,some experimental results that were employed not only verified the effectiveness and feasibility of the proposed algorithm,but also showed the relationship between the decision recognition rate and the granularity and threshold.

Two Hybrid Methods Based on Rough Set Theory for Network Intrusion Detection

In this paper,we propose two intrusion detection methods which combine rough set theory and Fuzzy C-Means for network intrusion detection.The first step consists of feature selection which is based on rough set theory.The next phase is clustering by using Fuzzy C-Means.Rough set theory is an efficient tool for further reducing redundancy.Fuzzy C-Means allows the objects to belong to several clusters simultaneously,with different degrees of membership.To evaluate the performance of the introduced approaches,we apply them to the international Knowledge Discovery and Data mining intrusion detection dataset.In the experimentations,we compare the performance of two rough set theory based hybrid methods for network intrusion detection.Experimental results illustrate that our algorithms are accurate models for handling complex attack patterns in large network.And these two methods can increase the efficiency and reduce the dataset by looking for overlapping categories.

Evaluation of Parameters Importance in Cloud Service Selection Using Rough Sets

With the rapid development of the cloud computing technology, it has matured enough for a lot of individuals and organizations to move their work into the cloud. Correspondingly, a variety of cloud services are emerging. It is a key issue to assess the cloud services in order to help the cloud users select the most suitable cloud service and the cloud providers offer this service with the highest quality. The criteria parameters defining the cloud services are complex which lead to cloud service deviation. In this paper, we propose an assessment method of parameters importance in cloud services using rough set theory. The method can effectively compute the importance of cloud services parameters and sort them. On the one hand, the calculation can be used as the credible reference when users choose their appropriate cloud services. On the other hand, it can help cloud service providers to meet user requirements and enhance the user experience. The simulation results show the effectiveness of the method and its relevance in the cloud context.

Rough Set Theory over Fuzzy Lattices

Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.

Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.

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.

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.

Axis Problem of Rough 3-Valued Algebras

The collection of all the rough sets of an approximation space has been given several algebraic interpretations, including Stone algebras, regular double Stone algebras, semi-simple Nelson algebras, pre-rough algebras and 3-valued Lukasiewicz algebras. A 3-valued Lukasiewicz algebra is a Stone algebra, a regular double Stone algebra, a semi-simple Nelson algebra, a pre-rough algebra. Thus, we call the algebra constructed by the collection of rough sets of an approximation space a rough 3-valued Lukasiewicz algebra.In this paper,the rough 3-valued Lukasiewicz algebras, which are a special kind of 3-valued Lukasiewicz algebras, are studied. Whether the rough 3-valued Lukasiewicz algebra is a axled 3-valued Lukasiewicz algebra is examined.

Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

FAULT DIAGNOSIS OF ROTATING MACHINERY USING KNOWLEDGE-BASED FUZZY NEURAL NETWORK

A novel knowledge-based fuzzy neural network （KBFNN） for fault diagnosis is presented. Crude rules were extracted and the corresponding dependent factors and antecedent coverage factors were calculated firstly from the diagnostic sample based on rough sets theory. Then the number of rules was used to construct partially the structure of a fuzzy neural network and those factors were implemented as initial weights, with fuzzy output parameters being optimized by genetic algorithm. Such fuzzy neural network was called KBFNN. This KBFNN was utilized to identify typical faults of rotating machinery. Diagnostic results show that it has those merits of shorter training time and higher right diagnostic level compared to general fuzzy neural networks.