To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy ap...To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.展开更多
A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a f...A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.展开更多
In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure op...In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.展开更多
In this paper, the numerical solution of the boundary value problem that is two-order fuzzy linear differential equations is discussed. Based on the generalized Hukuhara difference, the fuzzy differential equation is ...In this paper, the numerical solution of the boundary value problem that is two-order fuzzy linear differential equations is discussed. Based on the generalized Hukuhara difference, the fuzzy differential equation is converted into a fuzzy difference equation by means of decentralization. The numerical solution of the boundary value problem is obtained by calculating the fuzzy differential equation. Finally, an example is given to verify the effectiveness of the proposed method.展开更多
Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance prin...Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.展开更多
Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuri...Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuristic attribute reduction algorithms usually keep the positive region of a target set unchanged and ignore boundary region information. So, how to acquire knowledge from the boundary region of a target set in a multi-granulation space is an interesting issue. In this paper, a new concept, fuzziness of an approximation set of rough set is put forward firstly. Then the change rules of fuzziness in changing granularity spaces are analyzed. Finally, a new algorithm for attribute reduction based on the fuzziness of 0.5-approximation set is presented. Several experimental results show that the attribute reduction by the proposed method has relative better classification characteristics compared with various classification algorithms.展开更多
A stall diagnosis method based on the entropy feature extraction algorithm is developed in axial compressors.The reliability of the proposed method is determined and a parametric sensitivity analysis is experimentally...A stall diagnosis method based on the entropy feature extraction algorithm is developed in axial compressors.The reliability of the proposed method is determined and a parametric sensitivity analysis is experimentally conducted for two different types of compressor stall diagnoses.A collection of time‐resolved pressure sensors is mounted circumferentially and along the chord direction to measure the dynamic pressure on the casing.Results show that the stall and prestall precursor embedded in the dynamic pressures are identified through nonlinear feature perturbation extraction using the entropy feature extraction algorithm.Further analysis demonstrates that the prestall precursor with the peak entropy value is related to the unsteady tip leakage flow for the spike‐type stall diagnosis.The modal wave inception with increasing amplitude is identified by the considerable increase of the entropy value.The flow field in the tip region indicates that the modal wave corresponds to the flow separation in the suction side of the rotor blade.The warning time is 100–300 rotor revolutions for both types of stall diagnoses,which is beneficial for stall control in different axial compressors.Moreover,a parametric study of the embedding dimension m,similar tolerance n,similar radius r,and data length N in the fuzzy entropy method is conducted to determine the optimal parameter setting for stall diagnosis.The stall warning based on the entropy feature extraction algorithm provides a new stall diagnosis approach in the axial compressor with different stall types.This stall warning can also be adopted as an online stability monitoring index when using the concept of active stall control.展开更多
基金supported by the Natural Science Foundation of Shandong Province (Y2006A12)the Scientific Research Development Project of Shandong Provincial Education Department (J06P01)+2 种基金the Science and Technology Foundation of Universityof Jinan (XKY0808 XKY0703)the Doctoral Foundation of University of Jinan (B0633).
文摘To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.
基金the National Natural Science Foundation of China (60364001, 70461001)Hainan ProvincialNatural Science Foundation of China (80401).
文摘A new method for translating a fuzzy rough set to a fuzzy set is introduced and the fuzzy approximation of a fuzzy rough set is given. The properties of the fuzzy approximation of a fuzzy rough set are studied and a fuzzy entropy measure for fuzzy rough sets is proposed. This measure is consistent with similar considerations for ordinary fuzzy sets and is the result of the fuzzy approximation of fuzzy rough sets.
文摘In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.
文摘In this paper, the numerical solution of the boundary value problem that is two-order fuzzy linear differential equations is discussed. Based on the generalized Hukuhara difference, the fuzzy differential equation is converted into a fuzzy difference equation by means of decentralization. The numerical solution of the boundary value problem is obtained by calculating the fuzzy differential equation. Finally, an example is given to verify the effectiveness of the proposed method.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 60632050） and Postdoctoral Science Foundation of China （20100481149）.
文摘Though the dominance-based rough set approach has been applied to interval-valued information systems for knowledge discovery, the traditional dominance relation cannot be used to describe the degree of dominance principle in terms of pairs of objects. In this paper, a ranking method of interval-valued data is used to describe the degree of dominance in the interval-valued information system. Therefore, the fuzzy rough technique is employed to construct the rough approximations of upward and downward unions of decision classes, from which one can induce at least and at most decision rules with certainty factors from the interval-valued decision system. Some numerical examples are employed to substantiate the conceptual arguments.
基金supported by the National Natural Science Foundation of China (61472056, 61309014)
文摘Rough set theory is an important tool to solve uncertain problems. Attribute reduction, as one of the core issues of rough set theory, has been proven to be an effective method for knowledge acquisition. Most of heuristic attribute reduction algorithms usually keep the positive region of a target set unchanged and ignore boundary region information. So, how to acquire knowledge from the boundary region of a target set in a multi-granulation space is an interesting issue. In this paper, a new concept, fuzziness of an approximation set of rough set is put forward firstly. Then the change rules of fuzziness in changing granularity spaces are analyzed. Finally, a new algorithm for attribute reduction based on the fuzziness of 0.5-approximation set is presented. Several experimental results show that the attribute reduction by the proposed method has relative better classification characteristics compared with various classification algorithms.
基金National Natural Science Foundation of China,Grant/Award Number:51922098,51727810National Science and TechnologyMajor Project of China,Grant/Award Number:J2019‐II‐0020‐0041Special Fund for the Member of Youth Innovation Promotion Association of Chinese Academy of Sciences,Grant/Award Number:2018173。
文摘A stall diagnosis method based on the entropy feature extraction algorithm is developed in axial compressors.The reliability of the proposed method is determined and a parametric sensitivity analysis is experimentally conducted for two different types of compressor stall diagnoses.A collection of time‐resolved pressure sensors is mounted circumferentially and along the chord direction to measure the dynamic pressure on the casing.Results show that the stall and prestall precursor embedded in the dynamic pressures are identified through nonlinear feature perturbation extraction using the entropy feature extraction algorithm.Further analysis demonstrates that the prestall precursor with the peak entropy value is related to the unsteady tip leakage flow for the spike‐type stall diagnosis.The modal wave inception with increasing amplitude is identified by the considerable increase of the entropy value.The flow field in the tip region indicates that the modal wave corresponds to the flow separation in the suction side of the rotor blade.The warning time is 100–300 rotor revolutions for both types of stall diagnoses,which is beneficial for stall control in different axial compressors.Moreover,a parametric study of the embedding dimension m,similar tolerance n,similar radius r,and data length N in the fuzzy entropy method is conducted to determine the optimal parameter setting for stall diagnosis.The stall warning based on the entropy feature extraction algorithm provides a new stall diagnosis approach in the axial compressor with different stall types.This stall warning can also be adopted as an online stability monitoring index when using the concept of active stall control.
