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
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
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
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.
Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each...Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.展开更多
Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems....Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.展开更多
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 equ...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.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
Feature selection（FS） refers to the process of selecting those input attributes that are most predictive of a given outcome. Unlike other dimensionality reduction methods,feature selectors preserve the original mean...Feature selection（FS） refers to the process of selecting those input attributes that are most predictive of a given outcome. Unlike other dimensionality reduction methods,feature selectors preserve the original meaning of the features after reduction. The benefits of FS are twofold：it considerably decreases the running time of the induction algorithm,and increases the accuracy of the resulting model. This paper analyses the FS process in mammogram classification using fuzzy logic and rough set theory. Rough set and fuzzy logic based Quickreduct algorithms are applied for the FS from the features extracted using gray level co-occurence matrix（GLCM） constructed over the mammogram region. The predictive accuracy of the features is tested using NaiveBayes,Ripper,C4.5,and ant-miner algorithms. The results show that the ant-miner produces significant result comparing with others and the number of features selected using fuzzy-rough quick reduct algorithm is minimum,too.展开更多
This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rou...This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.展开更多
Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generaliz...Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.展开更多
Classical rough set has a limited processing capacity in fuzzy decision table. Combining fuzzy set with classical rough set,attribute reduction algorithm on fuzzy decision table is studied. First,new similarity degree...Classical rough set has a limited processing capacity in fuzzy decision table. Combining fuzzy set with classical rough set,attribute reduction algorithm on fuzzy decision table is studied. First,new similarity degree and new similarity category are defined. In the meantime,similarity category clusters which are divided by condition attribute are provided. And then,two theorems are presented. Subsequently,a new attribute reduction algorithm is proposed. Finally,the new attribute reduction algorithm is verified through a performance evaluation decision table of the self-repairing flight-control system. The result shows the proposed attribute reduction algorithm is able to deal with fuzzy decision table to a certain extent.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.
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.
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.
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Scheme evaluation and selection is an optimum selecting and sequencing problem with multi-objective and multi-level. It can’t follow single objective function or rule. Meanwhile,these objectives are coupled with each other and the attribution information is fuzzy also. It is necessary to find an effective evaluation method which can consider all conditions and restrictions. In this paper,AHP and rough set theory are applied to fuzzy optimization to determine important weight of each attribution. The rough set fuzzy optimum selection is used to eliminate the useless information. Autonomous underwater vehicle (AUV) is large-scale systems with many coupled design variables and objective functions. Their scheme evaluation and selection are very important,which relate to multiple factors,such as reliability; security,service time; the lifecycle,etc. Results of application in torpedo design indicate that this method is feasible.
基金The National Natural Science Foundation of China (No60474022)
文摘Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.
文摘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.
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.
文摘Feature selection（FS） refers to the process of selecting those input attributes that are most predictive of a given outcome. Unlike other dimensionality reduction methods,feature selectors preserve the original meaning of the features after reduction. The benefits of FS are twofold：it considerably decreases the running time of the induction algorithm,and increases the accuracy of the resulting model. This paper analyses the FS process in mammogram classification using fuzzy logic and rough set theory. Rough set and fuzzy logic based Quickreduct algorithms are applied for the FS from the features extracted using gray level co-occurence matrix（GLCM） constructed over the mammogram region. The predictive accuracy of the features is tested using NaiveBayes,Ripper,C4.5,and ant-miner algorithms. The results show that the ant-miner produces significant result comparing with others and the number of features selected using fuzzy-rough quick reduct algorithm is minimum,too.
基金Supported by Soft Science Research Project of Henan Province(122400450212)Supported by Foundation Lead-edge Technologies Research Project of Henan Province(122300410061)
文摘This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.
基金supported by the National Natural Science Foundation of China under Grant No.71571128the Humanities and Social Sciences Foundation of Ministry of Education of the People’s Republic of China(No.17XJA630003).
文摘Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment,the evaluation information of alternatives given by decision makers is often fuzzy and uncertain.As a generalization of intuitionistic fuzzy set(IFSs)and Pythagoras fuzzy set(PFSs),q-rung orthopair fuzzy set(q-ROFS)is more suitable for expressing fuzzy and uncertain information.But,in actual multiple attribute decision making(MADM)problems,the weights of DMs and attributes are always completely unknown or partly known,to date,the maximizing deviation method is a good tool to deal with such issues.Thus,combine the q-ROFS and conventional maximizing deviation method,we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper.Firstly,we briefly introduce the basic concept of q-rung orthopair fuzzy sets(q-ROFSs)and q-rung interval-valued orthopair fuzzy sets(q-RIVOFSs).Then,combine the maximizing deviation method with q-rung orthopair fuzzy information,we establish two new decision making models.On this basis,the proposed models are applied to MADM problems with q-rung orthopair fuzzy information.Compared with existing methods,the effectiveness and superiority of the new model are analyzed.This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers(q-ROFNs)and whose attributes are incomplete.
基金supported by the Foundation and Frontier Technologies Research Plan Projects of Henan Province of China under Grant No. 102300410266
文摘Classical rough set has a limited processing capacity in fuzzy decision table. Combining fuzzy set with classical rough set,attribute reduction algorithm on fuzzy decision table is studied. First,new similarity degree and new similarity category are defined. In the meantime,similarity category clusters which are divided by condition attribute are provided. And then,two theorems are presented. Subsequently,a new attribute reduction algorithm is proposed. Finally,the new attribute reduction algorithm is verified through a performance evaluation decision table of the self-repairing flight-control system. The result shows the proposed attribute reduction algorithm is able to deal with fuzzy decision table to a certain extent.
