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Generating Type 2 Trapezoidal Fuzzy membership function Using Genetic Tuning

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Computers, Materials & Continua 2022年第4期71卷 717-734页

作者： Siti Hajar Khairuddin Mohd Hilmi Hasan Emilia Akashah P.Akhir Manzoor Ahmed Hashmani Centre for Research in Data Science Department of Computer and Information SciencesUniversiti Teknologi PETRONASPerakMalaysia

Fuzzy inference system(FIS)is a process of fuzzy logic reasoning to produce the output based on fuzzified *** system starts with identifying input from data,applying the fuzziness to input using membership functions(MF),generating fuzzy rules for the fuzzy sets and obtaining the *** are several types of input MFs which can be introduced in FIS,commonly chosen based on the type of real data,sensitivity of certain rule implied and computational *** paper focuses on the construction of interval type 2(IT2)trapezoidal shape MF from fuzzy C Means(FCM)that is used for fuzzification process of mamdani *** the process,upper MF(UMF)and lower MF(LMF)of the MF need to be identified to get the range of the footprint of uncertainty(FOU).This paper proposes Genetic tuning process,which is a part of genetic algorithm(GA),to adjust parameters in order to improve the behavior of existing system,especially to enhance the accuracy of the system *** novel process is a hybrid approach which produces Genetic Fuzzy System(GFS)that helps to enhance fuzzy classification problems and *** approach provides a new method for the construction and tuning process of the IT2 MF,based on the FCM *** result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA *** is shown that the proposed approach is able to outperform the mentioned benchmarked *** work implies a wider range of IT2 MF types,constructed based on FCM outcomes,and an optimum generation of the FOU so that it can be implemented in practical applications such as prediction,analytics and rule-based solutions.

关键词： Fuzzy inference system membership function genetic tuning lateral adjustment trapezoidal MF fuzzy C means

Properties of Fuzzy Entropy Based on the Shape Change of membership function

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Journal of Donghua University(English Edition) 2007年第2期24卷 268-271页

作者：卿铭秦应兵 Department of Mathematics Southwest Jiaotong University

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 to that of the original one while elevation factor just acts as a propartional factor. These results should contribute to the analysis and design of a fuzzy system.

关键词： fuzzy entropy membership function entropy function triangular fuzzy number support interval

Describing Fuzzy membership function and Detecting the Outlier by Using Five Number Summary of Data

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American Journal of Computational Mathematics 2020年第3期10卷 410-424页

作者： Md. Farooq Hasan Md. Abdus Sobhan Department of Mathematics and Statistics Bangladesh University of Business and Technology Dhaka Bangladesh

One of the most important activities in data science is defining a membership function in fuzzy system. Although there are few ways to describe membership function like artificial neural networks, genetic algorithms etc.;they are very complex and time consuming. On the other hand, the presence of outlier in a data set produces deceptive results in the modeling. So it is important to detect and eliminate them to prevent their negative effect on the modeling. This paper describes a new and simple way of constructing fuzzy membership function by using five-number summary of a data set. Five states membership function can be created in this new method. At the same time, if there is any outlier in the data set, it can be detected with the help of this method. Usually box plot is used to identify the outliers of a data set. So along with the new approach, the box plot has also been drawn so that it is understood that the results obtained in the new method are accurate. Several real life examples and their analysis have been discussed with graph to demonstrate the potential of the proposed method. The results obtained show that the proposed method has given good results. In the case of outlier, the proposed method and the box plot method have shown similar results. Primary advantage of this new procedure is that it is not as expensive as neural networks, and genetic algorithms.

关键词： Fuzzy Set membership function Five Number Summary Outliers

New Methods of Fitting the membership function of Oceanic Water Masses

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Journal of Ocean University of China 2004年第1期3卷 1-9页

作者： LIFengqi XIEJun LIYao CollegeofEnvironmentalScienceandEngineering OceanUniversityofChinaQingdao266003P.R.China

After reviewing the analytical theories of T S curve, some methods of T S relationship, and fuzzy sets for studying water masses, new methods of fitting the membership function of oceanic water masses are presented based on the characteristics of T S curve family of oceanic water masses. The membership functions of oceanic Subsurface Water Mass with high salinity and Intermediate Water Mass with low salinity are fitted and discussed using the new methods. The proposed methods are useful in analyzing the mixing and modifying processes of these water masses, especially in tracing their sources. The principles and formulae of the new methods and examples are given.

关键词： water mass T-S curve fuzzy sets membership function the South China Sea (SCS) Bashi Channel (Luzon Strait)

Robust Fuzzy Association Rule Mining Based on Neighbors-Considered Clustering with Amended membership function

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Robust Fuzzy Association Rule Mining Based on Neighbors-Cons...

Design and experimental research on the sweet potato seedling transplanting mechanism of the planetary gear train with deformed elliptical gear transmission

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作者： Jinxian Wu Li Dai Weidong Zou Yuanqing Xia School of Automation Beijing Institute of Technology

Clustering based association rule mining algorithms usually deal with data sets by clustering numerical transactions into boolean ones then using the boolean method. However, the numerical data will often change slightly, which may be caused by errors in the data acquisition process or disturbance in the environment, as a result, the obtained association rules will change greatly. Therefore, the uncertainty in the association rule mining should be considered. In this paper, an improved fuzzy clustering based robust association rule mining algorithm（RFARM） is proposed, where a regularization term is added into the objective function in which each point considers its own k-nearest neighbors to offset small disturbance and we also derive the necessary conditions for the convergence to the local minimum. Meanwhile, fuzzy clustering methods with constraints produce ripple parts in membership functions, which cannot be explained in association rule mining. In order to solve this, we design a variant algorithm（RFARM*） that can perform and be understood better than the frequently-used methods. Experimental results have shown that the proposed methods are superior in the accuracy of association rules and the anti-noise capability.

关键词： Fuzzy association rule mining Data mining Fuzzy C Means membership function

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International Journal of Agricultural and Biological Engineering 2024年第3期17卷 91-99页

作者： Bingliang Ye Yuxuan Ye Haili Zhou Gaohong Yu Xiong Zhao Bin Deng Faculty of Mechanical Engineering Zhejiang Sci-Tech UniversityHangzhou 310018China Zhejiang Province Key Laboratory of Transplanting Equipment and Technology Hangzhou 310018China Key Laboratory of Agricultural Equipment for Hilly and Mountainous Areas in Southeastern China(Co-construction by Ministry and Province) Ministry of Agriculture and Rural AffairsHangzhou 310018China

Aiming at the lack of suitable machines for sweet potato seedling transplanting in China,and according to the agronomic requirements for the horizontal insertion method of sweet potato seedling,a new sweet potato seedling transplanting mechanism of planetary gear train was proposed based on the non-uniform transmission of deformed elliptical *** working principle of the transplanting mechanism was analyzed,and the kinematics modeling and analysis of the mechanism were carried *** study established the numerical objectives of the transplanting mechanism and applied the theory of membership function to establish a mathematical model for the parameter-guided optimization design of the transplanting *** parameter-guided optimization design software was developed to obtain a set of optimal mechanism parameters that satisfied the motion trajectory of sweet potato transplanting and the posture of the transplanting *** on the optimized parameters,the structure of the transplanting mechanism was designed,and a virtual prototype of the mechanism was created,whereby a virtual motion simulation of the transplanting mechanism was conducted to verify the correctness of the kinematics model and design of the *** high-speed photographic kinematics test of the mechanism prototype and sweet potato seedling transplanting tests were conducted to test the mechanism’s kinematic characteristics and transplanting *** test results show that the test trajectory of the mechanism and test posture of the transplanting arm are almost consistent with the theoretical and simulation trajectory,meeting the agronomic requirements of the horizontal insertion method of sweet potato seedling;And when the rotary speed of the mechanism are 20 r/min and 30 r/min,the average success ratios of sweet potato seedlings transplanting are 90%and 82%,respectively,which prove the application feasibility of the mechanism in the practical machines.

关键词： sweet potato seedling transplanter transplanting mechanism deformed elliptical gear transmission kinematics analysis membership function optimization design

Feature Selection Based on Adaptive Fuzzy membership functions

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自动化学报 2006年第4期32卷 496-503页

作者： XIE Yan-Tao SANG Nong ZHANG Tian-Xu Institute for Pattern Recognition and Artificial Intelligence Huazhong University of Science and Technology Wuhan 430074 Key Laboratory of Ministry of Education for Image Processing and Intelligent Control Huazhong University of Science and Technology Wuhan 430074

Neuro-fuzzy(NF)networks are adaptive fuzzy inference systems(FIS)and have been applied to feature selection by some ***,their rule number will grow exponentially as the data dimension *** the other hand,feature selection algorithms with artificial neural networks(ANN)usually require normalization of input data,which will probably change some characteristics of original data that are important for *** overcome the problems mentioned above,this paper combines the fuzzification layer of the neuro-fuzzy system with the multi-layer perceptron(MLP)to form a new artificial neural ***,fuzzification strategy and feature measurement based on membership space are proposed for feature selection. Finally,experiments with both natural and artificial data are carried out to compare with other methods,and the results approve the validity of the algorithm.

关键词： membership function feature selection architecture pruning artificial neural networks

Water quality evaluation of Haihe River with fuzzy similarity measure methods

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Journal of Environmental Sciences 2013年第10期25卷 2041-2046页

作者： Xiaojing Wang Zhihong Zou Hui Zou School of Economic and Management Beihang University Department of Applied Mathematics College of ScienceChina Agricultural University

Fuzzy similarity measures, which are used to judge the closeness of two fuzzy sets, are presented to evaluate the water quality of the Haihe River. Based on the membership functions and coefficient of variation as the weights, four fuzzy similarity measures （including Lattice similarity measure, Hamming similarity measure, Euclidean similarity measure and the max-min similarity measure） are used to classify the 299 samples into the proper water quality standard ranks. The results are compared with the traditional distance discriminant methods. The calculation of two traditional distance discriminant methods （both Euclidean distance and absolute value distance） is also based on the use of coefficients of variation as the weights. Without the Lattice similarity measure, for this method loses some information, the correct assignment of samples classified into the same water quality ranks is 75.92% with the other three similarity measures and two distance discriminant methods. This result shows the reliability of the five methods. Only considering the three similarity measures, there were only 1.01% of the samples that did not classify to the same ranks, while the corresponding ratio of the two distance discriminant methods was 5.69%. The results of leave-one-out cross validation show that more than 88% of the samples are classified to the proper ranks, which demonstrates that the similarity measures are suitable to evaluate the water quality of the Haihe River.

关键词： similarity measure distance discriminant coefficient of variation membership function

An adaptive attitude algorithm based on a current statistical model for maneuvering acceleration

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Chinese Journal of Aeronautics 2017年第1期30卷 426-433页

作者： Wang Menglong Wang Hua School of Astronautics Beihang University

A current statistical model for maneuvering acceleration using an adaptive extended Kalman filter（CS-MAEKF） algorithm is proposed to solve problems existing in conventional extended Kalman filters such as large estimation error and divergent tendencies in the presence of continuous maneuvering acceleration. A membership function is introduced in this algorithm to adaptively modify the upper and lower limits of loitering vehicles＇ maneuvering acceleration and for realtime adjustment of maneuvering acceleration variance. This allows the algorithm to have superior static and dynamic performance for loitering vehicles undergoing different maneuvers. Digital simulations and dynamic flight testing show that the yaw angle accuracy of the algorithm is 30% better than conventional algorithms, and pitch and roll angle calculation precision is improved by 60%.The mean square deviation of heading and attitude angle error during dynamic flight is less than3.05°. Experimental results show that CS-MAEKF meets the application requirements of miniature loitering vehicles.

关键词： Attitude and heading reference system Current statistical model Kalman filter Loitering vehicle Maneuvering acceleration membership function