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
With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and re...With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.展开更多
Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value j...Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.展开更多
In computer aided geometric design （CAGD）, B′ezier-like bases receive more andmore considerations as new modeling tools in recent years. But those existing B′ezier-like basesare all defined over the rectangular do...In computer aided geometric design （CAGD）, B′ezier-like bases receive more andmore considerations as new modeling tools in recent years. But those existing B′ezier-like basesare all defined over the rectangular domain. In this paper, we extend the algebraic trigono-metric B′ezier-like basis of order 4 to the triangular domain. The new basis functions definedover the triangular domain are proved to fulfill non-negativity, partition of unity, symmetry,boundary representation, linear independence and so on. We also prove some properties of thecorresponding B′ezier-like surfaces. Finally, some applications of the proposed basis are shown.展开更多
The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordina...The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains： a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.展开更多
In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can sa...In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.展开更多
The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained ...The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.展开更多
A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several inter...A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.展开更多
Scattering of SH-waves on the triangular hill joined by semi-cylindrical canyon in half-space is studied using the method of complex function and moving coordinates. The model being studied is divided into two domains...Scattering of SH-waves on the triangular hill joined by semi-cylindrical canyon in half-space is studied using the method of complex function and moving coordinates. The model being studied is divided into two domains. The wave functions satisfying the required condition at each wedge are constructed in each equation. The equations are solved with Fourier expansion. Numerical results are provided to discuss the influence of scattering of SH-waves.展开更多
Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the consta...Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.展开更多
变革性研究是科技新范式或新领域产生的前导,识别变革性研究对科研管理和科技前瞻具有重要意义。现有研究较少考虑不同引文关联对目标文献价值判断的影响,为此,本文提出一种融合引文功能和三角引用结构的变革性研究识别方法。根据不同...变革性研究是科技新范式或新领域产生的前导,识别变革性研究对科研管理和科技前瞻具有重要意义。现有研究较少考虑不同引文关联对目标文献价值判断的影响,为此,本文提出一种融合引文功能和三角引用结构的变革性研究识别方法。根据不同引文功能组合获取目标文献及其前序、后序文献间的三角引用结构,提取文献间的巩固或颠覆关系,据此构建目标文献的自我中心巩固-颠覆引用(ego-centric consolidation-disruption citation,ECCD)网络,以ECCD网络结构特征与文本内容特征为输入,构建图注意力神经网络模型,识别兼具高学术影响力和专家认定颠覆性的变革性研究。在PMCOA(PubMed Central Open Access Subset)数据集上的实证分析发现,变革性研究识别任务的最佳F1值为0.3926,优于其他基线模型。模型参数的可解释性分析显示,本文基于引文功能识别的颠覆性引用关系在高学术影响力研究和变革性研究识别任务中具有重要作用。展开更多
This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on ther...This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems.The controller parameters were tuned using the Integral Time Absolute Error(ITAE)objective function,which was also evaluated alongside other objective functions(IAE,ISE,and ITSE)to ensure high precision in frequency stabilization.To validate the effectiveness of the triangular membership function,comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions.Performance metrics,including ITAE,settling time,overshoot,and undershoot of frequency deviation,as well as tie-line power deviation,were evaluated.Robustness was established through a comprehensive sensitivity analysis with T_(G),T_(T),andT_(R) parameter variations(±50%),a non-linearity analysis incorporating Generation Rate Constraint(GRC)and Governor Deadband(GDB),a random Step Load Perturbation(SLP)over 0–100 s,and also Stability analysis of the proposed scheme is conducted using multiple approaches,including frequency-domain analysis,Lyapunov stability theory,and eigenvalue analysis.Additionally,the system incorporating thermal,hydro,and gas turbines,along with advanced components like CES and HVDC links,was analysed.Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm(MGOA),Honey Badger Algorithm(HBA),Particle Swarm Optimization(PSO),Artificial Bee Colony(ABC),and Spider Monkey Optimization(SMO)algorithms.Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives,exhibiting superior performance across all evaluated metrics.This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.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.
文摘With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
文摘Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.
基金Supported by the National Natural Science Foundation of China( 60933008,60970079)
文摘In computer aided geometric design （CAGD）, B′ezier-like bases receive more andmore considerations as new modeling tools in recent years. But those existing B′ezier-like basesare all defined over the rectangular domain. In this paper, we extend the algebraic trigono-metric B′ezier-like basis of order 4 to the triangular domain. The new basis functions definedover the triangular domain are proved to fulfill non-negativity, partition of unity, symmetry,boundary representation, linear independence and so on. We also prove some properties of thecorresponding B′ezier-like surfaces. Finally, some applications of the proposed basis are shown.
文摘The influence of local landforms on ground motion is an important problem. The antiplane response of a scalene triangular hill to incident SH waves is studied in this paper by using a complex function, moving coordinates and auxiliary functions. First, the model is divided into two domains： a scalene triangular hill with a semi-circular bottom; and a half space with a semi-circular canyon. Wave functions that satisfy the zero-stress condition at the triangular wedges and at the horizontal surface are constructed in both domains. Then, considering the displacement continuity and stress equilibrium, algebraic equations are established. Finally, numerical examples are provided to illustrate the influence of the geometry of the hill and the characteristics of the incident waves on the ground motions.
文摘In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.
文摘The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.
文摘A family of Said-Bézier type generalized Ball （SBGB） bases and surfaces with a parameter H over triangular domain is introduced,which unifies Bézier surface and Said-Ball surface and includes several intermediate surfaces. To convert different bases and surfaces,the dual functionals of bases are presented. As an application of dual functionals,the subdivision formulas for surfaces are established.
文摘Scattering of SH-waves on the triangular hill joined by semi-cylindrical canyon in half-space is studied using the method of complex function and moving coordinates. The model being studied is divided into two domains. The wave functions satisfying the required condition at each wedge are constructed in each equation. The equations are solved with Fourier expansion. Numerical results are provided to discuss the influence of scattering of SH-waves.
文摘Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.
文摘变革性研究是科技新范式或新领域产生的前导,识别变革性研究对科研管理和科技前瞻具有重要意义。现有研究较少考虑不同引文关联对目标文献价值判断的影响,为此,本文提出一种融合引文功能和三角引用结构的变革性研究识别方法。根据不同引文功能组合获取目标文献及其前序、后序文献间的三角引用结构,提取文献间的巩固或颠覆关系,据此构建目标文献的自我中心巩固-颠覆引用(ego-centric consolidation-disruption citation,ECCD)网络,以ECCD网络结构特征与文本内容特征为输入,构建图注意力神经网络模型,识别兼具高学术影响力和专家认定颠覆性的变革性研究。在PMCOA(PubMed Central Open Access Subset)数据集上的实证分析发现,变革性研究识别任务的最佳F1值为0.3926,优于其他基线模型。模型参数的可解释性分析显示,本文基于引文功能识别的颠覆性引用关系在高学术影响力研究和变革性研究识别任务中具有重要作用。
文摘This study develops a GWO-optimized cascaded fuzzy-PID controller with triangular membership functions for load frequency control in interconnected power systems.The controller’s effectiveness is demonstrated on thermal–thermal and hybrid thermal–hydro–gas power systems.The controller parameters were tuned using the Integral Time Absolute Error(ITAE)objective function,which was also evaluated alongside other objective functions(IAE,ISE,and ITSE)to ensure high precision in frequency stabilization.To validate the effectiveness of the triangular membership function,comparisons were made with fuzzy-PID controllers employing trapezoidal and Gaussian membership functions.Performance metrics,including ITAE,settling time,overshoot,and undershoot of frequency deviation,as well as tie-line power deviation,were evaluated.Robustness was established through a comprehensive sensitivity analysis with T_(G),T_(T),andT_(R) parameter variations(±50%),a non-linearity analysis incorporating Generation Rate Constraint(GRC)and Governor Deadband(GDB),a random Step Load Perturbation(SLP)over 0–100 s,and also Stability analysis of the proposed scheme is conducted using multiple approaches,including frequency-domain analysis,Lyapunov stability theory,and eigenvalue analysis.Additionally,the system incorporating thermal,hydro,and gas turbines,along with advanced components like CES and HVDC links,was analysed.Comparisons were conducted against controllers optimized using Modified Grasshopper Optimization Algorithm(MGOA),Honey Badger Algorithm(HBA),Particle Swarm Optimization(PSO),Artificial Bee Colony(ABC),and Spider Monkey Optimization(SMO)algorithms.Results demonstrate that the GWO-based fuzzy-PID controller outperforms the alternatives,exhibiting superior performance across all evaluated metrics.This highlights the potential of the proposed approach as a robust solution for load frequency control in complex and dynamic power systems.
