On Development of Fuzzy Controller: The Case of Gaussian and Triangular Membership Functions

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.

Fuzzy logic controller design with unevenly-distributed membership function for high performance chamber cooling system

Fuzzy logic controller adopting unevenly-distributed membership function was presented with the purpose of enhancing performance of the temperature control precision and robustness for the chamber cooling system.Histogram equalization and noise detection were performed to modify the evenly-distributed membership functions of error and error change rate into unevenly-distributed membership functions.Then,the experimental results with evenly and unevenly distributed membership functions were compared under the same outside environment conditions.The experimental results show that the steady-state error is reduced around 40% and the noise disturbance is rejected successfully even though noise range is 60% of the control precision range.The control precision is improved by reducing the steady-state error and the robustness is enhanced by rejecting noise disturbance through the fuzzy logic controller with unevenly-distributed membership function.Moreover,the system energy efficiency and lifetime of electronic expansion valve(EEV) installed in chamber cooling system are improved by adopting the unevenly-distributed membership function.

Optimization of Membership Function for Fuzzy Control Based on Genetic Algorithm and Its Applications

In this paper, a simple and practicable algorithm for optimization of membership function (MF) is proposed. As it is known that MF is very important in the fuzzy control. Unfortunately, to find, especially to optimize MF is always rather complex even difficult. So, to study and develop an effectual aglorithm for MF optimization is a good topic. Allow for the inner advantages of genetic algorithm (GA), it is adopted in the algorithm .The principle and executive procdeure are first presented. Then it is applied in the fuzzy control system of a typical plant. Results of real time run show that the control strategy is encouraging, and the developed algorithm is practicable.

A modeling approach for fuzzy programming with echelon form membership functions

In order to solve fuzzy mathematical programming with soft constraints,the initial models must first be converted into crisp models.Membership functions are employed to describe the fuzzy right-hand side parameters needed to achieve this conversion.In some cases,echelon form membership functions(EFMFs)are required to depict the actual fuzzy situation.However,due to their discrete properties,fuzzy programming problems with such membership functions cannot be modeled by traditional methods.Motivated by these challenges,this paper introduces a novel absolute value representation modeling approach to formulate fuzzy programming using EFMFs.This approach can translate a discrete model to a continuous one which can then be easily solved.Finally,by means of a numerical example,the effectiveness of our new approach is demonstrated.

Generating Type 2 Trapezoidal Fuzzy Membership Function Using Genetic Tuning

Fuzzy inference system(FIS)is a process of fuzzy logic reasoning to produce the output based on fuzzified inputs.The 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 output.There 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 limits.This 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 FIS.In 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 model.This novel process is a hybrid approach which produces Genetic Fuzzy System(GFS)that helps to enhance fuzzy classification problems and performance.The approach provides a new method for the construction and tuning process of the IT2 MF,based on the FCM outcomes.The result is compared to Gaussian shape IT2 MF and trapezoid IT2 MF generated by the classic GA method.It is shown that the proposed approach is able to outperform the mentioned benchmarked approaches.The 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.

Energy Price Forecasting Through Novel Fuzzy Type-1 Membership Functions

Electricity price forecasting is a subset of energy and power forecasting that focuses on projecting commercial electricity market present and future prices.Electricity price forecasting have been a critical input to energy corporations’strategic decision-making systems over the last 15 years.Many strategies have been utilized for price forecasting in the past,however Artificial Intelligence Techniques(Fuzzy Logic and ANN)have proven to be more efficient than traditional techniques(Regression and Time Series).Fuzzy logic is an approach that uses membership functions(MF)and fuzzy inference model to forecast future electricity prices.Fuzzy c-means(FCM)is one of the popular clustering approach for generating fuzzy membership functions.However,the fuzzy c-means algorithm is limited to producing only one type of MFs,Gaussian MF.The generation of various fuzzy membership functions is critical since it allows for more efficient and optimal problem solutions.As a result,for the best and most improved results for electricity price forecasting,an approach to generate multiple type-1 fuzzy MFs using FCM algorithm is required.Therefore,the objective of this paper is to propose an approach for generating type-1 fuzzy triangular and trapezoidal MFs using FCM algorithm to overcome the limitations of the FCM algorithm.The approach is used to compute and improve forecasting accuracy for electricity prices,where Australian Energy Market Operator(AEMO)data is used.The results show that the proposed approach of using FCM to generate type-1 fuzzy MFs is effective and can be adopted.

New Approaches to the Prognosis and Diagnosis of Breast Cancer Using Fuzzy Expert Systems

Breast cancer remains a significant global health challenge, necessitating effective early detection and prognosis to enhance patient outcomes. Current diagnostic methods, including mammography and MRI, suffer from limitations such as uncertainty and imprecise data, leading to late-stage diagnoses. To address this, various expert systems have been developed, but many rely on type-1 fuzzy logic and lack mobile-based applications for data collection and feedback to healthcare practitioners. This research investigates the development of an Enhanced Mobile-based Fuzzy Expert system (EMFES) for breast cancer pre-growth prognosis. The study explores the use of type-2 fuzzy logic to enhance accuracy and model uncertainty effectively. Additionally, it evaluates the advantages of employing the python programming language over java for implementation and considers specific risk factors for data collection. The research aims to dynamically generate fuzzy rules, adapting to evolving breast cancer research and patient data. Key research questions focus on the comparative effectiveness of type-2 fuzzy logic, the handling of uncertainty and imprecise data, the integration of mobile-based features, the choice of programming language, and the creation of dynamic fuzzy rules. Furthermore, the study examines the differences between the Mamdani Inference System and the Sugeno Fuzzy Inference method and explores challenges and opportunities in deploying the EMFES on mobile devices. The research identifies a critical gap in existing breast cancer diagnostic systems, emphasizing the need for a comprehensive, mobile-enabled, and adaptable solution by developing an EMFES that leverages Type-2 fuzzy logic, the Sugeno Inference Algorithm, Python Programming, and dynamic fuzzy rule generation. This study seeks to enhance early breast cancer detection and ultimately reduce breast cancer-related mortality.

Asymptotically Necessary and Sufficient Quadratic Stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality

Asymptotically necessary and sufficient quadratic stability conditions of Takagi-Sugeno (T-S) fuzzy systems are obtained by utilizing staircase membership functions and a basic inequality. The information of the membership functions is incorporated in the stability analysis by approximating the original continuous membership functions with staircase membership functions. The stability of the T-S fuzzy systems was investigated based on a quadratic Lyapunov function. The asymptotically necessary and sufficient stability conditions in terms of linear matrix inequalities were derived using a basic inequality. A fuzzy controller was also designed based on the stability results. The derivation process of the stability results is straightforward and easy to understand. Case studies confirmed the validity of the obtained stability results.

Describing Fuzzy Membership Function and Detecting the Outlier by Using Five Number Summary of Data

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.

Properties of Fuzzy Entropy Based on the Shape Change of Membership Function

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.

Fuzzy smooth support vector machine with different smooth functions

Smooth support vector machine （SSVM） changs the normal support vector machine （SVM） into the unconstrained op- timization by using the smooth sigmoid function. The method can be solved under the Broyden-Fletcher-Goldfarb-Shanno （BFGS） algorithm and the Newdon-Armijio （NA） algorithm easily, however the accuracy of sigmoid function is not as good as that of polyno- mial smooth function. Furthermore, the method cannot reduce the influence of outliers or noise in dataset. A fuzzy smooth support vector machine （FSSVM） with fuzzy membership and polynomial smooth functions is introduced into the SVM. The fuzzy member- ship considers the contribution rate of each sample to the optimal separating hyperplane and makes the optimization problem more accurate at the inflection point. Those changes play a positive role on trials. The results of the experiments show that those FSSVMs can obtain a better accuracy and consume the shorter time than SSVM and lagrange support vector machine （LSVM）.

Fuzzy Set-Membership Filtering for Discrete-Time Nonlinear Systems

In this article,the problem of state estimation is addressed for discrete-time nonlinear systems subject to additive unknown-but-bounded noises by using fuzzy set-membership filtering.First,an improved T-S fuzzy model is introduced to achieve highly accurate approximation via an affine model under each fuzzy rule.Then,compared to traditional prediction-based ones,two types of fuzzy set-membership filters are proposed to effectively improve filtering performance,where the structure of both filters consists of two parts:prediction and filtering.Under the locally Lipschitz continuous condition of membership functions,unknown membership values in the estimation error system can be treated as multiplicative noises with respect to the estimation error.Real-time recursive algorithms are given to find the minimal ellipsoid containing the true state.Finally,the proposed optimization approaches are validated via numerical simulations of a one-dimensional and a three-dimensional discrete-time nonlinear systems.

New Methods of Fitting the Membership Function of Oceanic Water Masses

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.

Incremental learning of the triangular membership functions based on single-pass FCM and CHC genetic model

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.

INVESTIGATION ON MAKING MEMBERSHIP FUNCTION OF WATER MASS FROM MIXING MODIFIED PROCESS

A water mass in the sea area under investigation is defined as a fuzzy subset in the discourse universe. Possible forms of membership function of water masses in the mixing modified process are discussed with the mixing theory for conservative concentration of sea water. It may provide bases for making membership functions. Results in this paper may be extended and applied to shallow water. Examples and discussion are given in this paper.

Research on Method R_w for Discrete Membership Functions

In this paper, a number of concepts related to continuous membership function (CMFs) advanced in [2] are extended to discrete membership functions (DMFs) in the light of the characteristics of DMFs so that fuzzy reasoning method R. based upon CMFs suits the case of DMFs.

Output Linearization of Single-Input Single-Output Fuzzy System to Improve Accuracy and Performance

For fuzzy systems to be implemented effectively,the fuzzy membership function(MF)is essential.A fuzzy system(FS)that implements precise input and output MFs is presented to enhance the performance and accuracy of single-input single-output(SISO)FSs and introduce the most applicable input and output MFs protocol to linearize the fuzzy system’s output.Utilizing a variety of non-linear techniques,a SISO FS is simulated.The results of FS experiments conducted in comparable conditions are then compared.The simulated results and the results of the experimental setup agree fairly well.The findings of the suggested model demonstrate that the relative error is abated to a sufficient range(≤±10%)and that the mean absolute percentage error(MPAE)is reduced by around 66.2%.The proposed strategy to reduceMAPE using an FS improves the system’s performance and control accuracy.By using the best input and output MFs protocol,the energy and financial efficiency of every SISO FS can be improved with very little tuning of MFs.The proposed fuzzy system performed far better than other modern days approaches available in the literature.

50份加工型辣椒DH系苗期耐低温弱光综合评价

以前期利用花药培养技术创制的50份加工型辣椒DH系为试验材料,以SPAD值、F_(v)/F_(m)、根系直径、茎叶干质量、根系干质量、整株干质量和根冠比7个指标的耐低温弱光指数为评价指标,采用模糊隶属函数和聚类分析法对其进行耐低温弱光综合评价。结果表明:50份DH系的耐低温弱光模糊隶属函数综合指数范围在0.20~0.76之间,聚类分析可将其分为两大类,根据耐低温弱光指数特点和模糊隶属函数综合指数可确定第Ⅱ类有7份DH系为耐低温弱光材料,即H201605-8、H201604-4-1、H201612-4-1、H201605-7、H201612-4、H201605-34和H201604-18。50份加工型辣椒DH系间耐低温弱光性差异较大,可作为相关机理研究的试验材料;筛选出的7份耐低温弱光DH系为培育适合设施栽培的优良辣椒新品种提供了材料基础,也为定向培育抗非生物逆境辣椒种质新材料提供了参考。

基于优化赋权模型预测控制的风储协调策略研究

风储系统多目标之间存在难以协调控制的问题,权重系数的选择对多目标控制效果具有显著影响。首先,构建以储能充放平衡、并网波动最小和储能输出最小的风储系统多目标函数,考虑各子目标权重系数对风储系统的影响,提出一种改进鲸鱼算法(IWOA)优化模型预测控制(MPC)的风储协调运行方法,采用组合隶属度函数进行满意度评价,得到混合储能最优总控制量和权重系数。然后,采用集合经验模式分解(ICEEMDAN)算法对混合储能总控制量进行分解,利用Pearson相关系数对分解分量进行重构,实现混合储能功率的分配。最后,以新疆某风电场数据进行仿真,验证所提优化模型的有效性和功率分配策略的合理性。