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...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.展开更多
The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the defin...The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the definitions of several upper and lower covering approximation operators on the covering approximation space. Then, we study the properties of these operators. Finally, we propose the mutual relations between approximation operators and similar relations of the operator （ I ） based on the covering rough sets.展开更多
Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have no...Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have not any restrictions on the approximate description of the object,and they might form a covering of the universe. From this viewpoint,we establish a connection between these two theories. Specifically,we propose a complementary parameter for this purpose. With this parameter,the soft covering approximation space is established and the two theories are bridged. Furthermore,we study some relations between the covering and the soft covering approximation space and obtain some significant results. Finally,we define a notion of combine parameter which can help us to simplify the set of parameters and reduce the storage requirement of a soft covering approximation space.展开更多
The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integ...The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.展开更多
Data mining (also known as Knowledge Discovery in Databases - KDD) is defined as the nontrivial extraction of implicit, previously unknown, and potentially useful information from data. The aims and objectives of data...Data mining (also known as Knowledge Discovery in Databases - KDD) is defined as the nontrivial extraction of implicit, previously unknown, and potentially useful information from data. The aims and objectives of data mining are to discover knowledge of interest to user needs.Data mining is really a useful tool in many domains such as marketing, decision making, etc. However, some basic issues of data mining are ignored. What is data mining? What is the product of a data mining process? What are we doing in a data mining process? Is there any rule we should obey in a data mining process? In order to discover patterns and knowledge really interesting and actionable to the real world Zhang et al proposed a domain-driven human-machine-cooperated data mining process.Zhao and Yao proposed an interactive user-driven classification method using the granule network. In our work, we find that data mining is a kind of knowledge transforming process to transform knowledge from data format into symbol format. Thus, no new knowledge could be generated (born) in a data mining process. In a data mining process, knowledge is just transformed from data format, which is not understandable for human, into symbol format,which is understandable for human and easy to be used.It is similar to the process of translating a book from Chinese into English.In this translating process,the knowledge itself in the book should remain unchanged. What will be changed is the format of the knowledge only. That is, the knowledge in the English book should be kept the same as the knowledge in the Chinese one.Otherwise, there must be some mistakes in the translating proces, that is, we are transforming knowledge from one format into another format while not producing new knowledge in a data mining process. The knowledge is originally stored in data (data is a representation format of knowledge). Unfortunately, we can not read, understand, or use it, since we can not understand data. With this understanding of data mining, we proposed a data-driven knowledge acquisition method based on rough sets. It also improved the performance of classical knowledge acquisition methods. In fact, we also find that the domain-driven data mining and user-driven data mining do not conflict with our data-driven data mining. They could be integrated into domain-oriented data-driven data mining. It is just like the views of data base. Users with different views could look at different partial data of a data base. Thus, users with different tasks or objectives wish, or could discover different knowledge (partial knowledge) from the same data base. However, all these partial knowledge should be originally existed in the data base. So, a domain-oriented data-driven data mining method would help us to extract the knowledge which is really existed in a data base, and really interesting and actionable to the real world.展开更多
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 classif...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.展开更多
Submission Deadline： 10 December 2010Since the introduction of rough sets in 1982 by Professor Zdzislaw Pawlak, we have witnessed great advances in both theory and applications. In order to promote development of rou...Submission Deadline： 10 December 2010Since the introduction of rough sets in 1982 by Professor Zdzislaw Pawlak, we have witnessed great advances in both theory and applications. In order to promote development of rough sets, we are preparing a special issue on ＂Artificial Intelligence with Rough Sets＂ published by JEST （International）, Journal of Electronic Science and Technology, which is a refereed international journal focusing on IT area. The aim of this special issue is to present the current state of the research in this area, oriented towards both theoretical and applications aspects of rough sets.展开更多
In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief ...In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.展开更多
As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoreti...As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.展开更多
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...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.展开更多
By analyzing the questionnaires recollected from 74 different government departments in Chengdu, China, an evaluation model for scientific quality of civil servants was developed with the rough set theory. In the empi...By analyzing the questionnaires recollected from 74 different government departments in Chengdu, China, an evaluation model for scientific quality of civil servants was developed with the rough set theory. In the empirical study, a series of important rules were given to help to check and forecast the degree of the scientific quality of civil servants by using the reduction algorithm, and the total accuracy of prediction was 93.2%.展开更多
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 ...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.展开更多
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...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.展开更多
A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performa...A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performance of global convergence. In addition, the numbers of rules and the initial weights and structure of fuzzy neural networks are difficult to determine. Here rough sets are introduced to decide the numbers of rules and original weights. Finally, experiment results show the algorithm may get better effect than the BP algorithm.展开更多
This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed ...This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.展开更多
Solving complex problems by multi-agent systems in distributed environments requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Granular Comput...Solving complex problems by multi-agent systems in distributed environments requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Granular Computing(GC). We discuss the Rough-Granular Computing(RGC) approach to modeling of computations in complex adaptive systems and multiagent systems as well as for approximate reasoning about the behavior of such systems. The RGC methods have been successfully applied for solving complex problems in areas such as identification of objects or behavioral patterns by autonomous systems, web mining, and sensor fusion.展开更多
Rough set theory is used to treat the data of vehicle transmission system faults. The minimum fault feature vector can be obtained by calculating the importance and dependency of each attribute. Real time diagnosis, ...Rough set theory is used to treat the data of vehicle transmission system faults. The minimum fault feature vector can be obtained by calculating the importance and dependency of each attribute. Real time diagnosis, as a result, can be actualized. Ultimate decision making can be done by analyzing the consistency of decision information. The result shows that rough set theory is useful and possesses its unique merits in this field.展开更多
This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
Aiming at the disadvantages of BP model in artificial neural networks applied to intelligent fault diagnosis, neural network fault diagnosis optimization method with rough sets and genetic algorithms are presented. Th...Aiming at the disadvantages of BP model in artificial neural networks applied to intelligent fault diagnosis, neural network fault diagnosis optimization method with rough sets and genetic algorithms are presented. The neural network nodes of the input layer can be calculated and simplified through rough sets theory; The neural network nodes of the middle layer are designed through genetic algorithms training; the neural network bottom-up weights and bias are obtained finally through the combination of genetic algorithms and BP algorithms. The analysis in this paper illustrates that the optimization method can improve the performance of the neural network fault diagnosis method greatly.展开更多
In this paper,we propose a Rough Set assisted Meta-Learning method on how to select the most-suited machine-learning algorithms with minimal effort for a new given dataset. A k-Nearest Neighbor (k-NN) algorithm is use...In this paper,we propose a Rough Set assisted Meta-Learning method on how to select the most-suited machine-learning algorithms with minimal effort for a new given dataset. A k-Nearest Neighbor (k-NN) algorithm is used to recognize the most similar datasets that have been performed by all of the candidate algorithms.By matching the most similar datasets we found,the corresponding performance of the candidate algorithms is used to generate recommendation to the user.The performance derives from a multi-criteria evaluation measure-ARR,which contains both accuracy and time.Furthermore,after applying Rough Set theory,we can find the redundant properties of the dataset.Thus,we can speed up the ranking process and increase the accuracy by using the reduct of the meta attributes.展开更多
文摘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.
基金The National Natural Science Foundation of China(No.60474022)
文摘The coveting rough sets theory is a generalization of traditional rough set theory, and can also describe information with incompleteness and fuzziness in information systems. In this paper, we first provide the definitions of several upper and lower covering approximation operators on the covering approximation space. Then, we study the properties of these operators. Finally, we propose the mutual relations between approximation operators and similar relations of the operator （ I ） based on the covering rough sets.
基金supported by National Natural Science Foundation of China under Grant No. 60873077/F020107the Science Research Project of Zhangzhou Normal University under Grant No. SK09002
文摘Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have not any restrictions on the approximate description of the object,and they might form a covering of the universe. From this viewpoint,we establish a connection between these two theories. Specifically,we propose a complementary parameter for this purpose. With this parameter,the soft covering approximation space is established and the two theories are bridged. Furthermore,we study some relations between the covering and the soft covering approximation space and obtain some significant results. Finally,we define a notion of combine parameter which can help us to simplify the set of parameters and reduce the storage requirement of a soft covering approximation space.
基金Supported by the Natural Science Foundation of Shandong Province（ZR2010AL019） Supported by the Education Science Foundation of Shandong Province（2010JZ123）
文摘The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.
文摘Data mining (also known as Knowledge Discovery in Databases - KDD) is defined as the nontrivial extraction of implicit, previously unknown, and potentially useful information from data. The aims and objectives of data mining are to discover knowledge of interest to user needs.Data mining is really a useful tool in many domains such as marketing, decision making, etc. However, some basic issues of data mining are ignored. What is data mining? What is the product of a data mining process? What are we doing in a data mining process? Is there any rule we should obey in a data mining process? In order to discover patterns and knowledge really interesting and actionable to the real world Zhang et al proposed a domain-driven human-machine-cooperated data mining process.Zhao and Yao proposed an interactive user-driven classification method using the granule network. In our work, we find that data mining is a kind of knowledge transforming process to transform knowledge from data format into symbol format. Thus, no new knowledge could be generated (born) in a data mining process. In a data mining process, knowledge is just transformed from data format, which is not understandable for human, into symbol format,which is understandable for human and easy to be used.It is similar to the process of translating a book from Chinese into English.In this translating process,the knowledge itself in the book should remain unchanged. What will be changed is the format of the knowledge only. That is, the knowledge in the English book should be kept the same as the knowledge in the Chinese one.Otherwise, there must be some mistakes in the translating proces, that is, we are transforming knowledge from one format into another format while not producing new knowledge in a data mining process. The knowledge is originally stored in data (data is a representation format of knowledge). Unfortunately, we can not read, understand, or use it, since we can not understand data. With this understanding of data mining, we proposed a data-driven knowledge acquisition method based on rough sets. It also improved the performance of classical knowledge acquisition methods. In fact, we also find that the domain-driven data mining and user-driven data mining do not conflict with our data-driven data mining. They could be integrated into domain-oriented data-driven data mining. It is just like the views of data base. Users with different views could look at different partial data of a data base. Thus, users with different tasks or objectives wish, or could discover different knowledge (partial knowledge) from the same data base. However, all these partial knowledge should be originally existed in the data base. So, a domain-oriented data-driven data mining method would help us to extract the knowledge which is really existed in a data base, and really interesting and actionable to the real world.
文摘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.
文摘Submission Deadline： 10 December 2010Since the introduction of rough sets in 1982 by Professor Zdzislaw Pawlak, we have witnessed great advances in both theory and applications. In order to promote development of rough sets, we are preparing a special issue on ＂Artificial Intelligence with Rough Sets＂ published by JEST （International）, Journal of Electronic Science and Technology, which is a refereed international journal focusing on IT area. The aim of this special issue is to present the current state of the research in this area, oriented towards both theoretical and applications aspects of rough sets.
基金NationalNaturalScienceFoundationofChina (No .60373078)
文摘In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.
基金NationalNaturalScienceFoundationof China underGrant No .60173054
文摘As a new mathematical theory, Rough sets have been applied to processing imprecise, uncertain and incomplete data. It has been fruitful in finite and non-empty set. Rough sets, however, are only served as the theoretic tool to discretize the real function. As far as the real function research is concerned, the research to define rough sets in the real function is infrequent. In this paper, we exploit a new method to extend the rough set in normed linear space, in which we establish a rough set,put forward an upper and lower approximation definition, and make a preliminary research on the property of the rough set.A new tool is provided to study the approximation solutions of differential equation and functional variation in normed linear space. This research is significant in that it extends the application of rough sets to a new field.
基金Supported by the NSF of Henan Province(082300410040)Supported by the NSF of Zhumadian City(087006)
文摘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.
基金Doctoral Fund of Ministry of Educationof China (No20060613019)
文摘By analyzing the questionnaires recollected from 74 different government departments in Chengdu, China, an evaluation model for scientific quality of civil servants was developed with the rough set theory. In the empirical study, a series of important rules were given to help to check and forecast the degree of the scientific quality of civil servants by using the reduction algorithm, and the total accuracy of prediction was 93.2%.
文摘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.
文摘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.
文摘A rough set based fuzzy neural network algorithm is proposed to solve the problem of pattern recognition. The least square algorithm (LSA) is used in the learning process of fuzzy neural network to obtain the performance of global convergence. In addition, the numbers of rules and the initial weights and structure of fuzzy neural networks are difficult to determine. Here rough sets are introduced to decide the numbers of rules and original weights. Finally, experiment results show the algorithm may get better effect than the BP algorithm.
基金Supported by the National Natural Science Foundation of China（60875034）
文摘This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.
基金The grant3 T11C 00226 from Min istroyf ScientifiRcesearchand InformationTechnologyoftheRepublicofPoland.
文摘Solving complex problems by multi-agent systems in distributed environments requires new approximate reasoning methods based on new computing paradigms. One such recently emerging computing paradigm is Granular Computing(GC). We discuss the Rough-Granular Computing(RGC) approach to modeling of computations in complex adaptive systems and multiagent systems as well as for approximate reasoning about the behavior of such systems. The RGC methods have been successfully applied for solving complex problems in areas such as identification of objects or behavioral patterns by autonomous systems, web mining, and sensor fusion.
文摘Rough set theory is used to treat the data of vehicle transmission system faults. The minimum fault feature vector can be obtained by calculating the importance and dependency of each attribute. Real time diagnosis, as a result, can be actualized. Ultimate decision making can be done by analyzing the consistency of decision information. The result shows that rough set theory is useful and possesses its unique merits in this field.
基金Supported by the National Natural Science Foundation of China (No. 69803007)
文摘This paper gives the definition of λ-cut sets and studies the structure of fuzzy rough sets. Based on the concept of rough sets, this paper proposes the representation theorem of fuzzy rough sets.
文摘Aiming at the disadvantages of BP model in artificial neural networks applied to intelligent fault diagnosis, neural network fault diagnosis optimization method with rough sets and genetic algorithms are presented. The neural network nodes of the input layer can be calculated and simplified through rough sets theory; The neural network nodes of the middle layer are designed through genetic algorithms training; the neural network bottom-up weights and bias are obtained finally through the combination of genetic algorithms and BP algorithms. The analysis in this paper illustrates that the optimization method can improve the performance of the neural network fault diagnosis method greatly.
文摘In this paper,we propose a Rough Set assisted Meta-Learning method on how to select the most-suited machine-learning algorithms with minimal effort for a new given dataset. A k-Nearest Neighbor (k-NN) algorithm is used to recognize the most similar datasets that have been performed by all of the candidate algorithms.By matching the most similar datasets we found,the corresponding performance of the candidate algorithms is used to generate recommendation to the user.The performance derives from a multi-criteria evaluation measure-ARR,which contains both accuracy and time.Furthermore,after applying Rough Set theory,we can find the redundant properties of the dataset.Thus,we can speed up the ranking process and increase the accuracy by using the reduct of the meta attributes.
