Function S-Rough sets and its applications

Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.

Self-organizing Map Method Based on Real Rough Sets Space and Its Application of Pattern Recognition

This paper presents a real rough sets space and corresponding concepts of real lower and upper approximation sets which correspond to the real-valued attributes. Therefore, the real rough sets space can be investigated directly. A rhombus neighborhood for SOM is proposed, and the combination of SOM and rough sets theory is explored. According to the distance between the weight of winner node and the input vector in the real rough sets space, new weight learning rules are defined. The modified method makes the classification of the output of SOM clearer and the intervals of different classes larger. Finally, an example based on fault identification of an aircraft actuator is presented, The result of the simulation shows that this method is right and effective.

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.

Condition Monitoring and Fault Diagnosis Based on Rough Set Theory

In order to raise the efficiency,automatization and intelligentization of condition monitoring and fault diagnosis for complex equipment systems,rough set theory is used to the field. A feature reduction algorithm based on rough set theory is adopted to extract condition information in monitoring and diagnosis for an engine,so that the technology condition monitoring parameters are optimized. The decision tables for each fault source are built and the diagnosis rules rooting in rough set reduction is applied to carry through intelligent fault diagnosis. The cases studied show that rough set method in condition monitoring and fault diagnosis can lighten the work burden in feature selection and afford advantages for autonomic learning and decision during diagnosis.

AN INTRUSION DETECTION SYSTEM BASED ON EVIDENCE THEORY AND ROUGH SET THEORY

In this paper,we propose a novel Intrusion Detection System (IDS) architecture utilizing both the evidence theory and Rough Set Theory (RST). Evidence theory is an effective tool in dealing with uncertainty question. It relies on the expert knowledge to provide evidences,needing the evidences to be independent,and this make it difficult in application. To solve this problem,a hybrid system of rough sets and evidence theory is proposed. Firstly,simplification are made based on Variable Precision Rough Set (VPRS) conditional entropy. Thus,the Basic Belief Assignment (BBA) for all evidences can be calculated. Secondly,Dempster’s rule of combination is used,and a decision-making is given. In the proposed approach,the difficulties in acquiring the BBAs are solved,the correlativity among the evidences is reduced and the subjectivity of evidences is weakened. An illustrative example in an intrusion detection shows that the two theories combination is feasible and effective.

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.

Evaluation and Analysis of Battery Technologies Applied to Grid-Level Energy Storage Systems Based on Rough Set Theory

Interest in the development of grid-level energy storage systems has increased over the years.As one of the most popular energy storage technologies currently available,batteries offer a number of high-value opportunities due to their rapid responses,flexible installation,and excellent performances.However,because of the complexity,multifunctionality,and wide deployment of power grids,trade-offs in battery performance exist,especially when considering economics,environmental effects,and safety.Therefore,establishing a comprehensive assessment of battery technologies is an urgent undertaking.In this work,we present an analysis of rough sets to evaluate the integration of battery systems(e.g.,lead-acid batteries,lithium-ion batteries,nickel/metal-hydrogen batteries,zinc-air batteries,and Na-S batteries)into a power grid.Specifically,technological properties,economic significance,environmental effects,and safety of these battery systems are evaluated on the basis of rough set theory.In addition,some perspectives are provided to promote the development of battery technologies for grid-level energy storage.

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.

Multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory-based environmental risk evaluation for tailings reservoirs

Environmental risk assessment of tailings reservoir assessment system is complex and has many index factors.In order to accurately judge surrounding environmental risks of tailings reservoirs and determinate the corresponding prevention and control work,multi-hierarchical fuzzy judgment and nested dominance relation of rough set theory are implemented to evaluate them and find out the rules of this evaluation system with 14 representative cases.The methods of multi-hierarchical fuzzy evaluation can overall consider each influence factor of risk assessment system and their mutual impact,and the index weight based on the analytic hierarchy process is relatively reasonable.Rough set theory based on dominance relation reduces each index attribute from the top down,largely simplifies the complexity of the original evaluation system,and considers the preferential information in each index.Furthermore,grey correlation theory is applied to analysis of importance of each reducted condition attribute.The results demonstrate the feasibility of the proposed safety evaluation system and the application potential.

Use of Rough Sets Theory in Point Cluster and River Network Selection

In this paper, we applied the rough sets to the point cluster and river network selection. In order to meet the requirements of rough sets, first, we structuralize and quantify the spatial information of objects by convex hull, triangulated irregular network (TIN), Voronoi diagram, etc.;second, we manually assign decisional attributes to the information table according to conditional attributes. In doing so, the spatial information and attribute information are integrated together to evaluate the importance of points and rivers by rough sets theory. Finally, we select the point cluster and the river network in a progressive manner. The experimental results show that our method is valid and effective. In comparison with previous work, our method has the advantage to adaptively consider the spatial and attribute information at the same time without any a priori knowledge.

Research on the Development Trend and General Applications of the Fuzzy Rough Granularity Computing Theory

In this paper, we conduct research on the development trend and general applications of the fuzzy rough granular computing theory. Granular computing is a new concept of general information processing and computing paradigm which covers all the granularity the study of the theory, methods, techniques and the tools. In many areas are the basic ideas of granular computing, such as the interval analysis, rough set theory, clustering analysis and information retrieval, machine learning, database, etc. With the theory of domain known division of target concept and rule acquisition, in knowledge discovery, data mining and the pattern recognition is widely used. Under this basis, in this paper, we propose the fuzzy rough theory based computing paradigm that gains ideal performance.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

Extracting Decision Rules for Cooperative Team Air Combat Based on Rough Set Theory

In order to reduce redundant features in air combat information and to meet the requirements of real-time decision in combat, rough set theory is introduced to the tactical decision analysis in cooperative team air combat. An algorithm of attribute reduction for extracting key combat information and generating tactical rules from given air combat databases is presented. Then, considering the practical requirements of team combat, a method for reduction of attribute-values under single decision attribute is extended to the reduction under multi-decision attributes. Finally, the algorithm is verified with an example for tactical choices in team air combat. The results show that, the redundant attributes in air combat information can be reduced, and that the main combat attributes, i.e., the information about radar command and medium-range guided missile, can be obtained with the algorithm mentioned above, moreover, the minimal reduced strategy for tactical decision can be generated without losing the result of key information classification. The decision rules extracted agree with the real situation of team air combat.

Automatic web services classification based on rough set theory

With development of web services technology, the number of existing services in the internet is growing day by day. In order to achieve automatic and accurate services classification which can be beneficial for service related tasks, a rough set theory based method for services classification was proposed. First, the services descriptions were preprocessed and represented as vectors. Elicited by the discernibility matrices based attribute reduction in rough set theory and taking into account the characteristic of decision table of services classification, a method based on continuous discernibility matrices was proposed for dimensionality reduction. And finally, services classification was processed automatically. Through the experiment, the proposed method for services classification achieves approving classification result in all five testing categories. The experiment result shows that the proposed method is accurate and could be used in practical web services classification.

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.

Rough law generation and its separation-recognition

By using function S-rough sets（function singular rough sets）, this paper gives rough law generation and the theorem of rough law generation.Based on these results above, the paper proposes rough law separation, the theorem of rough law separation, the compound generation theorem of rough law bands, and the principle of rough law bands.In the end, an application of rough law separation in recognizing the risk law of profit is presented.

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.