Simulation of Haloxylon Ammodendron Stand Basic Diameter Structure Based on Fuzzy Distribution Function

Based on the investigation data of 12 Haloxylon ammodendron plots in the south edge of Gurbantunggut Desert, Fuzzy distribution was introduced into the study of Haloxylon ammodendron base diameter structure fitting according to the consistency between the characteristics of Fuzzy distribution function and the distribution series of cumulative percentage of stand base diameter, and the fitting precision and effect of Fuzzy distribution function were discussed. The root mean square error RMSE and determination coefficient R2 values showed that Fuzzy-Γ1, Fuzzy-Γ2, Fuzzy-Γ3, Fuzzy-Γ4 had good fitting performance, among which Fuzzy-Γ1 had relatively high fitting precision, and its parameters were closely related to stand age and density, Fuzzy-Γ2 distribution function was the second, and Fuzzy-Γ4 distribution function had the worst fitting effect. By introducing a parameter c from the similarity of four distribution function formulas, a generalized Fuzzy distribution function Fuzzy-Γ5 is obtained. This function shows the highest fitting accuracy. Most of the values of parameter c are near 1 or 2, which shows that the diameter distribution is mainly approximate to Fuzzy-Γ1 and Fuzzy-Γ2.

Spherical Functions on Fuzzy Lie Group

Let G be a locally compact Lie group and its Lie algebra. We consider a fuzzy analogue of G, denoted by called a fuzzy Lie group. Spherical functions on are constructed and a version of the existence result of the Helgason-spherical function on G is then established on .

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）.

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.

FUZZY APPROACHING SET AND FUZZYAPPROACHING FUNCTIONAL MAPPING

By establishing the concepts of fuzzy approaching set and fuzzy approaching functional mapping and making research on them, a new method for time series prediction is introduced.

Delayed recognition: recent developments and a proposal to study this phenomenon as a fuzzy concept

Purpose： New developments in the study of delayed recognition are discussed.Design/methodology/approach： Based on these new developments a method is proposed to characterize delayed recognition as a fuzzy concept.Findings： A benchmark value of 0.333 corresponding with linear growth is obtained. Moreover, a case is discovered in which an expert found delayed recognition several years before citation analysis could discover this phenomenon. Research limitations： As all citation studies also this one is database dependent.Practical implications： Delayed recognition is turned into a fuzzy concept.Originality/value： The article presents a new way of studying delayed recognition.

Global Optimization Method Using SLE and Adaptive RBF Based on Fuzzy Clustering

High fidelity analysis models,which are beneficial to improving the design quality,have been more and more widely utilized in the modern engineering design optimization problems.However,the high fidelity analysis models are so computationally expensive that the time required in design optimization is usually unacceptable.In order to improve the efficiency of optimization involving high fidelity analysis models,the optimization efficiency can be upgraded through applying surrogates to approximate the computationally expensive models,which can greately reduce the computation time.An efficient heuristic global optimization method using adaptive radial basis function（RBF） based on fuzzy clustering（ARFC） is proposed.In this method,a novel algorithm of maximin Latin hypercube design using successive local enumeration（SLE） is employed to obtain sample points with good performance in both space-filling and projective uniformity properties,which does a great deal of good to metamodels accuracy.RBF method is adopted for constructing the metamodels,and with the increasing the number of sample points the approximation accuracy of RBF is gradually enhanced.The fuzzy c-means clustering method is applied to identify the reduced attractive regions in the original design space.The numerical benchmark examples are used for validating the performance of ARFC.The results demonstrates that for most application examples the global optima are effectively obtained and comparison with adaptive response surface method（ARSM） proves that the proposed method can intuitively capture promising design regions and can efficiently identify the global or near-global design optimum.This method improves the efficiency and global convergence of the optimization problems,and gives a new optimization strategy for engineering design optimization problems involving computationally expensive models.

AN OPTIMAL FUZZY APPROXIMATOR

In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means

Derivatives and differentials for multiplicative intuitionistic fuzzy information

By using the unsymmetrical scale instead of the symmetrical scale,the multiplicative intuitionistic fuzzy sets(MIFSs) reflect our intuition more objectively.Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number(MIFN)and is based on the unbalanced scale(i.e.,Saaty’s 1-9 scale).In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively,in this paper,we firstly propose two new basic operational laws for MIFNs,which are the subtraction law and the division law.Secondly,we describe the change values of MIFNs when considering them as variables,classify these change values based on the basic operational laws for MIFNs,and depict the convergences of sequences of MIFNs by the subtraction and division laws.Finally,we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities,derivatives and differentials,and also give their application in selecting the configuration of a computer.

Novel Active Contour Model for Image Segmentation Based on Local Fuzzy Gaussian Distribution Fitting

A novel active contour model is proposed, which incorporates local information distributions in a fuzzy energy function to effectively deal with the intensity inhomogeneity. Moreover, the proposed model is convex with respect to the variable which is used for extracting the contour. This makes the model independent on the initial condition and suitable for an automatic segmentation. Furthermore, the energy function is minimized in a computationally efficient way by calculating the fuzzy energy alterations directly. Experiments are carried out to prove the performance of the proposed model over some existing methods. The obtained results confirm the efficiency of the method.

Research on trend prediction of component stock in fuzzy time series based on deep forest

With the continuous development of machine learning and the increasing complexity of financial data analysis,it is more popular to use models in the field of machine learning to solve the hot and difficult problems in the financial industry.To improve the effectiveness of stock trend prediction and solve the problems in time series data processing,this paper combines the fuzzy affiliation function with stock-related technical indicators to obtain nominal data that can widely reflect the constituent stocks in the case of time series changes by analysing the S&P 500 index.Meanwhile,in order to optimise the current machine learning algorithm in which the setting and adjustment of hyperparameters rely too much on empirical knowledge,this paper combines the deep forest model to train the stock data separately.The experimental results show that(1)the accuracy of the extreme random forest and the accuracy of the multi-grain cascade forest are both higher than that of the gated recurrent unit(GRU)model when the un-fuzzy index-adjusted dataset is used as features for input,(2)the accuracy of the extreme random forest and the accuracy of the multigranular cascade forest are improved by using the fuzzy index-adjusted dataset as features for input,(3)the accuracy of the fuzzy index-adjusted dataset as features for inputting the extreme random forest is improved by 18.89% compared to that of the un-fuzzy index-adjusted dataset as features for inputting the extreme random forest and(4)the average accuracy of the fuzzy index-adjusted dataset as features for inputting multi-grain cascade forest increased by 5.67%.

Maximum power point tracking of a photovoltaic energy system using neural fuzzy techniques

In order to improve the output efficiency of a photovoltaic （PV） energy system, the real-time maximum power point （MPP） of the PV array should be tracked closely. The non-linear and time-variant characteristics of the photovoltaic array and the non-linear and non-minimum phase characteristics of a boost converter make it difficult to track the MPP as in traditional control strategies. A neural fuzzy controller （NFC） in conjunction with the reasoning capability of fuzzy logical systems and the learning capability of neural networks is proposed to track the MPP in this paper. A gradient estimator based on a radial basis function neural network is developed to provide the reference information to the NFC. With a derived learning algorithm, the parameters of the NFC are updated adaptively. Experimental results show that, compared with the fuzzy logic control algorithm, the proposed control algorithm provides much better tracking performance.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.

Application of Fuzzy QFD to Aircraft Top Hierarchy Design

In this paper, based on the Quality Function Deployment ( QFD) method, theFuzzy Quality Function Deployment (FQFD) theory and the step-by-step hierarchy structure in aircrafttop decision design are studied. The fuzzy model for computing competitive factor in evaluation ispresented. The decision of key technologies for improving the performance and affordability of afixed-wing aircraft is studied using the model, and the result proves the feasibility of this model.

Intuitionistic Fuzzy α-Generalized Closed Sets in Terms of Minimal Structure Spaces

In this paper, we introduce the notion of intuitionistic fuzzy α-generalized closed sets in intuitionistic fuzzy minimal structure spaces and investigate some of their properties. Further, we introduce and study the concept of intuitionistic fuzzy α-generalized minimal continuous functions.

An Ontology Based Multilayer Perceptron for Object Detection

In object detection,spatial knowledge assisted systems are effective.Object detection is a main and challenging issue to analyze object-related information.Several existing object detection techniques were developed to consider the object detection problem as a classification problem to perform feature selection and classification.But these techniques still face,less computational efficiency and high time consumption.This paper resolves the above limitations using the Fuzzy Tversky index Ontology-based Multi-Layer Perception method which improves the accuracy of object detection with minimum time.The proposed method uses a multilayer forfinding the similarity score.A fuzzy membership function is used to validate the score for predicting the burned and non-burned zone.Experimental assessment is performed with different factors such as classification rate,time complexity,error rate,space complexity,and precision by using the forestfire dataset.The results show that this novel technique can help to improve the classification rate and reduce the time and space complexity as well as error rate than the conventional methods.

Novel moderate transformation of fuzzy membership function into basic belief assignment

In information fusion,the uncertain information from different sources might be modeled with different theoretical frameworks.When one needs to fuse the uncertain information represented by different uncertainty theories,constructing the transformation between different frameworks is crucial.Various transformations of a Fuzzy Membership Function(FMF)into a Basic Belief Assignment(BBA)have been proposed,where the transformations based on uncertainty maximization and minimization can determine the BBA without preselecting the focal elements.However,these two transformations that based on uncertainty optimization emphasize the extreme cases of uncertainty.To avoid extreme attitudinal bias,a trade-off or moderate BBA with the uncertainty degree between the minimal and maximal ones is more preferred.In this paper,two moderate transformations of an FMF into a trade-off BBA are proposed.One is the weighted average based transformation and the other is the optimization-based transformation with weighting mechanism,where the weighting factor can be user-specified or determined with some prior information.The rationality and effectiveness of our transformations are verified through numerical examples and classification examples.

A Novel Control Algorithm for Interaction Between Surface Waves and A Permeable Floating Structure

An analytical solution is undertaken to describe the wave-induced flow field and the surge motion of a permeable platform structure with fuzzy controllers in an oceanic environment.In the design procedure of the controller,a parallel distributed compensation（PDC） scheme is utilized to construct a global fuzzy logic controller by blending all local state feedback controllers.A stability analysis is carried out for a real structure system by using Lyapunov method.The corresponding boundary value problems are then incorporated into scattering and radiation problems.They are analytically solved,based on separation of variables,to obtain series solutions in terms of the harmonic incident wave motion and surge motion.The dependence of the wave-induced flow field and its resonant frequency on wave characteristics and structure properties including platform width,thickness and mass has been thus drawn with a parametric approach.From which mathematical models are applied for the wave-induced displacement of the surge motion.A nonlinearly inverted pendulum system is employed to demonstrate that the controller tuned by swarm intelligence method can not only stabilize the nonlinear system,but has the robustness against external disturbance.

Analytic design of information granulation-based fuzzy radial basis function neural networks with the aid of multiobjective particle swarm optimization

Purpose–The purpose of this paper is to consider the concept of Fuzzy Radial Basis Function Neural Networks with Information Granulation(IG-FRBFNN)and their optimization realized by means of the Multiobjective Particle Swarm Optimization(MOPSO).Design/methodology/approach–In fuzzy modeling,complexity,interpretability(or simplicity)as well as accuracy of the obtained model are essential design criteria.Since the performance of the IG-RBFNN model is directly affected by some parameters,such as the fuzzification coefficient used in the FCM,the number of rules and the orders of the polynomials in the consequent parts of the rules,the authors carry out both structural as well as parametric optimization of the network.A multi-objective Particle Swarm Optimization using Crowding Distance(MOPSO-CD)as well as O/WLS learning-based optimization are exploited to carry out the structural and parametric optimization of the model,respectively,while the optimization is of multiobjective character as it is aimed at the simultaneous minimization of complexity and maximization of accuracy.Findings–The performance of the proposed model is illustrated with the aid of three examples.The proposed optimization method leads to an accurate and highly interpretable fuzzy model.Originality/value–A MOPSO-CD as well as O/WLS learning-based optimization are exploited,respectively,to carry out the structural and parametric optimization of the model.As a result,the proposed methodology is interesting for designing an accurate and highly interpretable fuzzy model.

基于灰色模糊综合评判的高压断路器状态评估

针对高压断路器状态评估因素具有模糊性和灰色性的特点,将灰色模糊理论应用到高压断路器的状态评估中。基于试点工程,建立考虑高压断路器运行机理的递阶层次评估模型;采用层次分析法计算各层次评估因素权重集的模部,结合信息充裕程度及专家经验,确定相应评估因素权重集的灰部;综合定性分析与定量分析,以隶属度描述评估因素与状态等级间的模糊关系,并引入点灰度描述模糊关系的不可信程度,建立灰色模糊判别矩阵,进而对高压断路器运行状态进行综合评估。实际算例表明,所提模型能够客观有效地评估高压断路器的状态。