This paper deals with the problem of attribute discernibility reduction and proposes some new concepts to rough set theory （RST） based on the discernibility matrix of Skowron, such as secondary core, regeneration ma...This paper deals with the problem of attribute discernibility reduction and proposes some new concepts to rough set theory （RST） based on the discernibility matrix of Skowron, such as secondary core, regeneration matrix and the degree of attribute discernibility （DAD）. This paper puts forward an attribute reduction algorithm based on maximum discernibility degree, which opens up an effective way of gaining minimum attribute reduction of decision table. The efficacy of this algorithm has been verified by practical application in a diagnostic system of loader, which substantially decreases information gathering requirement and lowers the overall cost with no loss of accuracy.展开更多
A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put...A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put forward a method for data classification. Namely, firstly, we use discernibility matrix and discernibility function to delete superfluous attributes in formation system and get a necessary attribute set. Secondly, we delete superfluous attribute values and get decision rules. Finally, we classify data by means of decision rules. The experiments show that data classification using this method is simpler in the structure, and can improve the efficiency of classification.展开更多
The attribute reduction algorithms of decision table based on discernible matrix are required to construct discernible matrix, which reduces efficiency of algorithms. In this paper, the relationship between attribute ...The attribute reduction algorithms of decision table based on discernible matrix are required to construct discernible matrix, which reduces efficiency of algorithms. In this paper, the relationship between attribute discernible matrix and its discernibility is first established for general information systems. Based on the idea that the equivalent discernible matrix has a same attribute reduction, existing matrices are modified and a formula of attribute discernibility associated with algebraic reduction for decision table is proposed. A heuristic attribute reduction algorithm based on attribute discernibility is presented. Experimental results indicate that the algorithm can more easily explore an optimal or sub-optimal reduction, and is efficient.展开更多
In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for...In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.展开更多
To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a ...To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.展开更多
The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specifi...The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specified by the principle of discernibility matrix; (2) ID3 can be partly, but not naturally, specified by the principle of discernibility matrix; and (3) The principle of discernibility matrix is employed to analyze Cendrowska sample set, and it shows the weaknesses of knowledge representation style of decision tree in theory.展开更多
By using two-directional S-rough sets, the concepts of （f, f）-interference generation and （f, f）- interference law generation of knowledge, F-interference generation and F-interference law generation of two-direct...By using two-directional S-rough sets, the concepts of （f, f）-interference generation and （f, f）- interference law generation of knowledge, F-interference generation and F-interference law generation of two-directional S-rough sets are proposed. Based on the concepts above, the relation theoreras between F-interference loss and F-interference degree, the relation theorems between F-interference loss law and F-interference degree law, the dis- cernibility theorems between F-interference and F-interference law are presented. At last, the recognition criterion of F-interference law and its application are given.展开更多
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 servic...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.展开更多
In order to increase the fault diagnosis efficiency and make the fault data mining be realized, the decision table containing numerical attributes must be discretized for further calculations. The discernibility matri...In order to increase the fault diagnosis efficiency and make the fault data mining be realized, the decision table containing numerical attributes must be discretized for further calculations. The discernibility matrix-based reduction method depends on whether the numerical attributes can be properly discretized or not.So a discretization algorithm based on particle swarm optimization(PSO) is proposed. Moreover, hybrid weights are adopted in the process of particles evolution. Comparative calculations for certain equipment are completed to demonstrate the effectiveness of the proposed algorithm. The results indicate that the proposed algorithm has better performance than other popular algorithms such as class-attribute interdependence maximization(CAIM)discretization method and entropy-based discretization method.展开更多
By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-inter...By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.展开更多
Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obta...Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.展开更多
It is well known that most of information systems are based on tolerance relation instead of the classical equivalence relation because of various factors in real-world. To acquire brief decision rules from the inform...It is well known that most of information systems are based on tolerance relation instead of the classical equivalence relation because of various factors in real-world. To acquire brief decision rules from the information systems, lower approximation reduction is needed. In this paper, the lower approximation reduction is proposed in inconsistent information systems based on tolerance relation. Moreover, the properties are discussed. Furthermore, judgment theorem and discernibility matrix are obtained, from which an approach to lower reductions can be provided in the complicated information systems.展开更多
Single-phase low current grounding faults areoften seen in power distribution system of coal mines.These faults are difficult to reliably identify.We propose a new method of single-phase ground fault protection based ...Single-phase low current grounding faults areoften seen in power distribution system of coal mines.These faults are difficult to reliably identify.We propose a new method of single-phase ground fault protection based upon a discernible matrix of the fractal dimension associated with line currents.The method builds on existing selective protection methods.Faulted feeders are distinguished using differences in the zero-sequence transient current fractal dimension.The current signals were first processed through a fast Fourier transform and then the characteristics of a faulted line were identified using a discernible matrix.The method of calculation is illustrated.The results show that the method involves simple calculations, is easy to do and is highly accurate.It is, therefore, suitable for distribution networks having different neutral grounding modes.展开更多
By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute dis...By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute disturbance of knowledge, the attribute disturbance degree of knowledge, and the disturbance coefficient of knowledge are given. By employing these concepts, the cardinal order theorem of the attribute disturbance knowledge, the unit circle theorem of the attribute disturbance knowledge, and the discernible theorem of the attribute disturbance knowledge are presented.展开更多
文摘This paper deals with the problem of attribute discernibility reduction and proposes some new concepts to rough set theory （RST） based on the discernibility matrix of Skowron, such as secondary core, regeneration matrix and the degree of attribute discernibility （DAD）. This paper puts forward an attribute reduction algorithm based on maximum discernibility degree, which opens up an effective way of gaining minimum attribute reduction of decision table. The efficacy of this algorithm has been verified by practical application in a diagnostic system of loader, which substantially decreases information gathering requirement and lowers the overall cost with no loss of accuracy.
基金Supported by the National Natural Science Foun-dation of China(60474022)
文摘A method for data classification will influence the efficiency of classification. Attributes reduction based on discernibility matrix and discernibility function in rough sets can use in data classification, so we put forward a method for data classification. Namely, firstly, we use discernibility matrix and discernibility function to delete superfluous attributes in formation system and get a necessary attribute set. Secondly, we delete superfluous attribute values and get decision rules. Finally, we classify data by means of decision rules. The experiments show that data classification using this method is simpler in the structure, and can improve the efficiency of classification.
文摘The attribute reduction algorithms of decision table based on discernible matrix are required to construct discernible matrix, which reduces efficiency of algorithms. In this paper, the relationship between attribute discernible matrix and its discernibility is first established for general information systems. Based on the idea that the equivalent discernible matrix has a same attribute reduction, existing matrices are modified and a formula of attribute discernibility associated with algebraic reduction for decision table is proposed. A heuristic attribute reduction algorithm based on attribute discernibility is presented. Experimental results indicate that the algorithm can more easily explore an optimal or sub-optimal reduction, and is efficient.
文摘In this paper, we present reduction algorithms based on the principle of Skowron's discernibility matrix - the ordered attributes method. The completeness of the algorithms for Pawlak reduct and the uniqueness for a given order of the attributes are proved. Since a discernibility matrix requires the size of the memory of U2, U is a universe of objects, it would be impossible to apply these algorithms directly to a massive object set. In order to solve the problem, a so-called quasi-discernibility matrix and two reduction algorithms are proposed. Although the proposed algorithms are incomplete for Pawlak reduct, their opimal paradigms ensure the completeness as long as they satisfy some conditions. Finally we consider the problem on the reduction of distributive object sets.
基金supported by the National Natural Science Foundation of China (61403184, 61105082)the ‘1311 Talent Plan’ of Nanjing University of Posts and Telecommunications (NY2013)+3 种基金the ‘Qinglan’ Project of Jiangsu Province (QL2016)the Natural Science Foundation of Nanjing University of Posts and Telecommunications (215149)the Priority Academic Program Development of Jiangsu Higher Education Institutions, (PAPD)the Major Program of the Natural Science Foundation of Jiangsu Province Education Commission (17KJA120001)
文摘To extract and express the knowledge hidden in information systems, discernibility matrix and its extensions were introduced and applied successfully in many real life applications. Binary discernibility matrix, as a representative approach, has many interesting superior properties and has been rapidly developed to find intuitive and easy to understand knowledge. However, at present, the binary discernibility matrix is mainly adopted in the complete information system. It is a challenging topic how to achieve the attribute reduction by using binary discernibility matrix in incomplete information system. A form of generalized binary discernibility matrix is further developed for a number of representative extended rough set models that deal with incomplete information systems. Some useful properties and criteria are introduced for judging the attribute core and attribute relative reduction. Thereafter, a new algorithm is formulated which supports attribute core and attribute relative reduction based on the generalized binary discernibility matrix. This algorithm is not only suitable for consistent information systems but also inconsistent information systems. The feasibility of the proposed methods was demonstrated by worked examples and experimental analysis.
基金This research is partly supported by the National '863' High-Tech Programme (No. 863-306-ZT06-07-1)and NKPSF (G1998030508).
文摘The principle of discernibility matrix serves as a tool to discuss and analyze two algorithms of traditional inductive machine learning, AQ11 and ID3. The results are: (1) AQ11 and its family can be completely specified by the principle of discernibility matrix; (2) ID3 can be partly, but not naturally, specified by the principle of discernibility matrix; and (3) The principle of discernibility matrix is employed to analyze Cendrowska sample set, and it shows the weaknesses of knowledge representation style of decision tree in theory.
基金supported partly by the Natural Science Foundation of Fujian Province,China(S0650031)the Science and Technology Foundation of Education Department of Fujian Province,China(JA05327)the Key Subject of Sanming University(ZDXK0604).
文摘By using two-directional S-rough sets, the concepts of （f, f）-interference generation and （f, f）- interference law generation of knowledge, F-interference generation and F-interference law generation of two-directional S-rough sets are proposed. Based on the concepts above, the relation theoreras between F-interference loss and F-interference degree, the relation theorems between F-interference loss law and F-interference degree law, the dis- cernibility theorems between F-interference and F-interference law are presented. At last, the recognition criterion of F-interference law and its application are given.
基金Projects(9140A0605,0409JB8102) supported by Weaponry Equipment Pre-Research Foundation of PLA Equipment Ministry of ChinaProject(2009JSJ11) supported by Pre-Research Foundation of PLA University of Science and Technology,China
文摘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.
基金the National Natural Science Foundation of China(No.51775090)the General Program of Civil Aviation Flight University of China(No.J2015-39)
文摘In order to increase the fault diagnosis efficiency and make the fault data mining be realized, the decision table containing numerical attributes must be discretized for further calculations. The discernibility matrix-based reduction method depends on whether the numerical attributes can be properly discretized or not.So a discretization algorithm based on particle swarm optimization(PSO) is proposed. Moreover, hybrid weights are adopted in the process of particles evolution. Comparative calculations for certain equipment are completed to demonstrate the effectiveness of the proposed algorithm. The results indicate that the proposed algorithm has better performance than other popular algorithms such as class-attribute interdependence maximization(CAIM)discretization method and entropy-based discretization method.
基金Science and Technology Foundations of the Education Committee of Fujian Province of China (No.JA09232, No.JA08236)Science and Technology Projects of Sanming University, China (No. HX201007/Z)
文摘By employing function S-rough sets,the concepts of f-interference generation and separation of law,and the F-interference generation and separation of S-rough laws were proposed. Base on the concepts above,the F-interference relation theorems,the F-interference discernibility theorem,the dependent separation theorem by interfereence,and the dependent separation principle by interference were presented; finally the application was given. By employing F-interference dependence and separation of S-rough laws,the changes of characteristic of dynamic systemic regularities could be recognized.
基金supported by the Foundation and Frontier Technologies Research Plan Projects of Henan Province of China under Grant No. 102300410266
文摘Based on equivalence relation,the classical rough set theory is unable to deal with incomplete information systems.In this case,an extended rough set model based on valued tolerance relation and prior probability obtained from incomplete information systems is firstly founded.As a part of the model,the corresponding discernibility matrix and an attribute reduction of incomplete information system are then proposed.Finally,the extended rough set model and the proposed attribute reduction algorithm are verified under an incomplete information system.
文摘It is well known that most of information systems are based on tolerance relation instead of the classical equivalence relation because of various factors in real-world. To acquire brief decision rules from the information systems, lower approximation reduction is needed. In this paper, the lower approximation reduction is proposed in inconsistent information systems based on tolerance relation. Moreover, the properties are discussed. Furthermore, judgment theorem and discernibility matrix are obtained, from which an approach to lower reductions can be provided in the complicated information systems.
基金Project 50504015 supported by the National Natural Science Foundation of Chinathe Youth Science and Technology Research Program of China University of Mining and Technology (0C060996)
文摘Single-phase low current grounding faults areoften seen in power distribution system of coal mines.These faults are difficult to reliably identify.We propose a new method of single-phase ground fault protection based upon a discernible matrix of the fractal dimension associated with line currents.The method builds on existing selective protection methods.Faulted feeders are distinguished using differences in the zero-sequence transient current fractal dimension.The current signals were first processed through a fast Fourier transform and then the characteristics of a faulted line were identified using a discernible matrix.The method of calculation is illustrated.The results show that the method involves simple calculations, is easy to do and is highly accurate.It is, therefore, suitable for distribution networks having different neutral grounding modes.
基金Foundation item： Supported by the Nature Science Foundation of Shandong Province（Y2007H02）
文摘By using the dynamic characteristic of one direction S-rough sets（one direction singular rough sets） and dual of one direction S-rough sets（dual of one direction singular rough sets）, the concepts of attribute disturbance of knowledge, the attribute disturbance degree of knowledge, and the disturbance coefficient of knowledge are given. By employing these concepts, the cardinal order theorem of the attribute disturbance knowledge, the unit circle theorem of the attribute disturbance knowledge, and the discernible theorem of the attribute disturbance knowledge are presented.
