期刊：
International Journal of Fuzzy Systems,2021年23(3):833-848 ISSN：1562-2479
通讯作者：
Long, Zuqiang
作者机构：
[Wang, Guijun] Tianjin Normal Univ, Sch Math Sci, Tianjin 300387, Peoples R China.;[Wang, Hongzhi] Tonghua Normal Univ, Coll Math, Tonghua 134002, Jilin, Peoples R China.;[Long, Zuqiang] Hengyang Normal Univ, Coll Phys & Elect Engn, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Long, Zuqiang] H;Hengyang Normal Univ, Coll Phys & Elect Engn, Hengyang 421008, Hunan, Peoples R China.
关键词：
Piecewise linear function (PLF);Subdivision number;\( \hat{\mu }_{p} \)-integrable function;K p-norm;Mamdani fuzzy system;Approximation
摘要：
The core of fuzzy system is to bypass the establishment of a definite mathematical model to carry out logical reasoning and intelligent calculation for fuzzy information; its main method is to process data information and language information based on a set of IF-THEN rules. Although it does not depend on accurate mathematical model, it has the ability of logical reasoning, numerical calculation and non-linear function approximation. In this paper, the analytic expression of the piecewise linear function (PLF) is first introduced by the determinant of coefficient matrix of linear equations in hyperplane, and an new Kp-norm is proposed by the K-quasi-subtraction operator. Secondly, it is proved that PLFs can approximate to a
$$ \hat{\mu }_{p} $$
-integrable function in Kp-norm by real analysis method, and the Mamdani fuzzy system can also approximate to a PLF, and then an analytic representation of the upper bound of a subdivision number is given. Finally, using the three-point inequality of Kp-norm it is verified that Mamdani fuzzy system can approximate a
$$ \hat{\mu }_{p} $$
-integrable function to arbitrary accuracy, and the approximation of the Mamdani fuzzy system to a class of integrable function is confirmed by t-hypothesis test method in statistics.
作者机构：
[Li, Long; Long, Zuqiang] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Qiao, Zhijun] Univ Texas Rio Grande Valley, Dept Math, Edinburg, TX 78539 USA.
通讯机构：
[Li, Long] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
摘要：
In this paper, a smoothing algorithm with constant learning rate is presented for training two kinds of fuzzy neural networks (FNNs): max-product and max-min FNNs. Some weak and strong convergence results for the algorithm are provided with the error function monotonically decreasing, its gradient going to zero, and weight sequence tending to a fixed value during the iteration. Furthermore, conditions for the constant learning rate are specified to guarantee the convergence. Finally, three numerical examples are given to illustrate the feasibility and efficiency of the algorithm and to support the theoretical findings.
摘要：
Interval type-2 fuzzy controllers have received attention because of their potential in handling uncertainties better than type-1 (T1) fuzzy controllers. However, directly deriving the analytical structure of interval type-2 fuzzy controllers is a great challenge due to the iterative computation of Karnik–Mendel algorithm and similar ones. Analytical structure is necessary for the analysis and design of control systems (e.g. stability analysis). In this study, a novel technique is proposed for deriving the analytical structure of interval type-2 fuzzy controllers based on the configurations of the triangle interval type-2 input fuzzy sets, T1 output fuzzy singletons, product AND operators, Karnik–Mendel center-of-set type reducer, and centroid defuzzifier. Input space is partitioned into a group of input combinations (ICs), which are produced by superposing input ICs and case ICs, to obtain an analytical structure. Input ICs are evaluated by the upper/lower membership functions and case ICs using the equation of the terminating condition of Karnik–Mendel algorithm. An explicit analytical expression is obtained on any IC because each IC has the same membership functions and switch points. Finally, two examples are used to verify the validity of our method.
关键词：
Daily water demand forecasting;Deep belief networks;CDBNN model;Chaotic theory
摘要：
The prediction of daily water demands is a crucial part of the effective functioning of the water supply system. This work proposed that a continuous deep belief neural network (CDBNN) model based on the chaotic theory should be implemented to predict the daily water demand time series in Zhuzhou, China. CDBNN should initially be used to predict the urban water demand time series. First, the power spectrum and the largest Lyapunov exponent is used to determine the chaotic characteristic of the daily water demand time series. Second, C-C method is utilized to reconstruct the water demand time series' phase space. Lastly, the forecasting model should be produced with the continuous deep belief network and neural network algorithms implemented for feature learning and regression, respectively, and the CDBNN input established by the best embedding dimension of the reconstructed phase space. The proposed method is contrasted with the support vector regression, generalized regression neural networks and feed forward neural networks, and they are accepted with the identical dataset. The predictive performance of the models is examined using normalized root-mean-square error (NRMSE), correlation coefficient (COR), and mean absolute percentage error (MAPE). The results suggest that the hybrid model has the smallest NRMSE and MAPE values, and the largest COR.
作者机构：
[龙祖强; 许岳兵; 李龙] College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, Hunan, 421002, China;[龙祖强] Department of Computers and Electronic Engineering, Wayne State University, Detroit, MI, 48202, United States
通讯机构：
College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang, Hunan, China
期刊：
International Journal of Control and Automation,2016年9(1):33-46 ISSN：2005-4297
通讯作者：
Long, Zuqiang(zuqianglong@126.com)
作者机构：
[Long, Zuqiang] Dept. of Physics and Electronics Information Science, Hengyang Normal University, Hengyang, China;[Li, Long] Dept. of Mathematics and Computational Science, Hengyang Normal University, Hengyang, China;[Xu, Yuebing] College of Electrical and Information Engineering, Hunan University, Changsha, China
通讯机构：
Dept. of Physics and Electronics Information Science, Hengyang Normal University, Hengyang, China
关键词：
Expert Rules;Flash Evaporator;Fuzzy Control;Fuzzy Systems;Phosphoric Slurry;Variable Universes of Discourse
期刊：
International Journal on Smart Sensing and Intelligent Systems,2014年7(3):1114-1133 ISSN：1178-5608
通讯作者：
Long, Zuqiang(zuqianglong@126.com)
作者机构：
[Long, Zuqiang; Du, Shehui; Xu, Yuebing] Department of Physics and Electronics Information Science, Hengyang Normal University, Hengyang 421008, China;[Yuan, Yan] School of Information Science and Engineering, Central South University, Changsha 410083, China
通讯机构：
Department of Physics and Electronics Information Science, Hengyang Normal University, China
关键词：
Approximation error;CNC-lathe;Contraction-expansion factor;Fuzzy controller;Fuzzy system;Positioning of work pieces;Servo system;Variable universe of discourse
摘要：
A novel fuzzy controller is proposed here to improve the positioning precision of servo system of CNC lathes. To utilize the high-accuracy potential of the VUD fuzzy controller, a grating-ruler was used as a sensor to measure the displacement of work pieces. Designing the VUD fuzzy controller involved five steps, i.e., setting up universes of discourse and parameters, selecting membership functions, designing a differential circuit, constructing a base of fuzzy rules, and defining a set of contraction-expansion factors. The method of lookup table was applied to construct the base of fuzzy rules via four typical input instructions, and the method of maximum strength to settle the conflicting rules properly. The experimental results show that the VUD fuzzy controller can be effective in controlling the position of work pieces.
