In order to improve the efficiency of learning the triangular membership functions( TMFs) for mining fuzzy association rule( FAR) in dynamic database,a single-pass fuzzy c means( SPFCM)algorithm is combined with the r...In order to improve the efficiency of learning the triangular membership functions( TMFs) for mining fuzzy association rule( FAR) in dynamic database,a single-pass fuzzy c means( SPFCM)algorithm is combined with the real-coded CHC genetic model to incrementally learn the TMFs. The cluster centers resulting from SPFCM are regarded as the midpoint of TMFs. The population of CHC is generated randomly according to the cluster center and constraint conditions among TMFs. Then a new population for incremental learning is composed of the excellent chromosomes stored in the first genetic process and the chromosomes generated based on the cluster center adjusted by SPFCM. The experiments on real datasets show that the number of generations converging to the solution of the proposed approach is less than that of the existing batch learning approach. The quality of TMFs generated by the approach is comparable to that of the batch learning approach. Compared with the existing incremental learning strategy,the proposed approach is superior in terms of the quality of TMFs and time cost.展开更多
In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice ...In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, we derived explicit Fourier series expressions for systematic and dynamic computation of grade of membership in the overlap and non-overlap regions of triangular Fuzzy sets. In another paper, we extended the methodology to cover cases of cosine, exponential and Gaussian Fuzzy sets by presenting explicit Fourier series representation for encoding fuzziness in the overlap and non-overlap domains of Fuzzy sets. This current paper presents the development of a “Fuzzy Controller” device, which incorporates the formal mathematical representation for computing grade of membership of Gaussian and triangular Fuzzy sets. It is shown that triangular approximation of Gaussian membership function in Fuzzy control can lead to wrong linguistic classification which may have adverse effects on operational and control decisions. The development of the Fuzzy controller demonstrates that the proposed technique can indeed be incorporated in engineering systems for dynamic and systematic computation of grade of membership in the overlap and non-overlap regions of Fuzzy sets;and thus provides a basis for the design of embedded Fuzzy controller for mission critical applications.展开更多
Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, p...Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers (TFNs), the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets (TFSs) with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen's assertion that the entropy of resultant fuzzy set of elevation operation is directly proportional to that of the original one while elevation factor just acts as a proportional factor. These results should contribute to the analysis and design of a fuzzy system.展开更多
基金Supported by the National Natural Science Foundation of China(No.61301245,U1533104)
文摘In order to improve the efficiency of learning the triangular membership functions( TMFs) for mining fuzzy association rule( FAR) in dynamic database,a single-pass fuzzy c means( SPFCM)algorithm is combined with the real-coded CHC genetic model to incrementally learn the TMFs. The cluster centers resulting from SPFCM are regarded as the midpoint of TMFs. The population of CHC is generated randomly according to the cluster center and constraint conditions among TMFs. Then a new population for incremental learning is composed of the excellent chromosomes stored in the first genetic process and the chromosomes generated based on the cluster center adjusted by SPFCM. The experiments on real datasets show that the number of generations converging to the solution of the proposed approach is less than that of the existing batch learning approach. The quality of TMFs generated by the approach is comparable to that of the batch learning approach. Compared with the existing incremental learning strategy,the proposed approach is superior in terms of the quality of TMFs and time cost.
文摘In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, we derived explicit Fourier series expressions for systematic and dynamic computation of grade of membership in the overlap and non-overlap regions of triangular Fuzzy sets. In another paper, we extended the methodology to cover cases of cosine, exponential and Gaussian Fuzzy sets by presenting explicit Fourier series representation for encoding fuzziness in the overlap and non-overlap domains of Fuzzy sets. This current paper presents the development of a “Fuzzy Controller” device, which incorporates the formal mathematical representation for computing grade of membership of Gaussian and triangular Fuzzy sets. It is shown that triangular approximation of Gaussian membership function in Fuzzy control can lead to wrong linguistic classification which may have adverse effects on operational and control decisions. The development of the Fuzzy controller demonstrates that the proposed technique can indeed be incorporated in engineering systems for dynamic and systematic computation of grade of membership in the overlap and non-overlap regions of Fuzzy sets;and thus provides a basis for the design of embedded Fuzzy controller for mission critical applications.
基金The National Natural Science Foundation of China(No.60474022)
文摘Modification of a fuzzy partition often leads to the change of fuzziness of a fuzzy system. Researches on the change of fuzzy entropy of a fuzzy set, responding to shape alteration of membership function, therefore, play a significant role in analysis of the change of fuzziness of a fuzzy system because a fuzzy partition consists of a set of fuzzy sets which satisfy some special constraints. This paper has shown several results about entropy changes of a fuzzy set. First, the entropies of two same type of fuzzy sets have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Second, as for Triangular Fuzzy Numbers (TFNs), the entropies of any two TFNs which can not be always the same type, also, have a constant proportional relationship which depends on the ratio of the sizes of their support intervals. Hence, any two TFNs with the same sizes of support intervals have the same entropies. Third, concerning two Triangular Fuzzy Sets (TFSs) with same sizes of support intervals and different heights, the relationship of their entropies lies on their height. Finally, we point it out a mistake that Chen's assertion that the entropy of resultant fuzzy set of elevation operation is directly proportional to that of the original one while elevation factor just acts as a proportional factor. These results should contribute to the analysis and design of a fuzzy system.
