An improved optimisation framework for fuzzy time-series prediction

In this study, we propose a space search algorithm (SSA) and then introduce a hybrid optimization of ANFIS-based fuzzy models based on SSA and information granulation (IG). In comparison with “conventional” evolutionary algorithms (such as PSO), SSA leads not only to better search performance to find global optimization but is also more computationally effective. In the hybrid optimization of ANFIS-based fuzzy inference system, SSA is exploited to carry out the parametric optimization of the fuzzy model as well as to realize its structural optimization. IG realized with the aid of C-Means clustering helps determine the initial values of the apex parameters of the membership function of fuzzy model. The overall hybrid identification of ANFIS-based fuzzy models comes in the form of two optimization mechanisms: structure identification (such as the number of input variables to be used, a specific subset of input variables, the number of membership functions, and polynomial type) and parameter identification (viz. the apexes of membership function). The structure identification is developed by SSA and C-Means while the parameter estimation is realized via SSA and a standard least square method. The evaluation of the performance of the proposed model was carried out by using three representative numerical examples such as Non-linear function, gas furnace, and Mackey-Glass time series. A comparative study of SSA and PSO demonstrates that SSA leads to improved performance both in terms of the quality of the model and the computing time required. The proposed model is also contrasted with the quality of some “conventional” fuzzy models already encountered in the literature.

A new approach is presented to enhance fuzzy modeling using multidimensional fuzzy sets directly in the fuzzy model in place of decomposed fuzzy sets by projection. The antecedent fuzzy sets in the form of multivariable functions are represented in continuous form. This is accomplished by using a multi input and multi output neural network, which is in particular radial basis functions (RBF) network providing the required multivariable function approximation properties in a fuzzy model. The inputs of the network are fuzzy model inputs, outputs are the membership function values as to the multivariable fuzzy sets involved in the model. Thus, each output is restricted to one multivariable fuzzy set. The RBF network is trained according to the multidimensional fuzzy sets which are identified after fuzzy clustering of the data. Based on this, the linear model parameters are determined by the method of least squares in a straightforward manner. The transparency issues can be handled by means of projection process to have information about the shape and locations of the membership functions pertinent to each variable at the input. The accurate fuzzy modeling having been thus guaranteed the information on the linear model parameters are used to establish the multivariable fuzzy rules with their respective validity regions. The redundancy of the number of fuzzy sets can be circumvented by classical cluster merging algorithms available. In this approach, the fuzzy rules are determined from the local linear models, however in contrast with the conventional fuzzy modeling, the model outputs are determined by the multivariable fuzzy sets. To obtain regular sets, RBF network is trained by means of orthogonal least squares (OLS) method so that at the same time the convergence issues of general neural network training is eliminated.

Implementation issues related to evolving Takagi-Sugeno -Kang (TSK) fuzzy models of a nonlinear process are offered. The nonlinear process is the pendulum dynamics in the framework of the representative pendulum-crane systems, where the pendulum angle is the output variable of the TSK fuzzy models. An online identification algorithm (OIA) is given, which continuously evolves the rule bases and the parameters of the TSK fuzzy models, adds new rules with more summarization power and modifies the existing rules and parameters. The OIA includes an input selection algorithm and a Gravitational Search Algorithm that updates the parameters in the rule consequents. The evolving TSK fuzzy models are validated by experiments conducted on pendulum-crane laboratory equipment.

С.А. Глушенко - кандидат экономических наук, старший преподаватель кафедры информационных систем и прикладной информатики, Ростовский государственный экономический университет (РИНХ)Адрес: 344002, г. Ростов-на-Дону, ул. Большая Садовая, д. 69E-mail: gs-gears@yandex.ru В статье обосновывается важность применения оценки рисков при реализации системы обеспечения информационной безопасности. Рассматриваются наиболее распространенные методики оценки риска и предлагается использовать для этих целей теорию нечеткой логики. Описывается предложенная нечеткая продукционная модель (НПМ), в которой определены семь входных лингвистических переменных, характеризующих факторы риска, четыре выходных лингвистических переменных, характеризующих риски различных областей информационной безопасности, а также четыре базы правил. Отмечается, что НПМ является первым приближением для рассматриваемой предметной области и требует оптимизации с целью минимизации ошибки выходов модели. Рассматриваются наиболее распространенные методы оптимизации параметров нечетких моделей и обосновываются преимущества применения методов, основанных на использовании нейро-нечетких сетей (ННС). Описывается процесс преобразования элементов нечеткой модели, таких как блок фаззификации, блок базы правил и блок дефаззификации во фрагменты нейронной сети. Результатом данного процесса является нейро-нечеткая сеть, соответствующая нечеткой модели. Построение разработанной ННС осуществляется на основе системы нейро-нечеткого вывода (adaptive neuro-fuzzy inference system, ANFIS) посредством применения специализированного пакета Neuro-Fuzzy Designer программного средства MATLAB. Обучение модели было выполнено гибридным методом, который представляет собой комбинацию методов наименьших квадратов и обратного распространения ошибки. Результатом данного процесса является оптимизация (настройка) параметров функций принадлежности входных лингвистических переменных. Использованный подход нейро-нечеткого моделирования позволил получить более адекватную нечеткую продукционную модель, которая позволяет проводить лингвистический анализ рисков информационной безопасности организации. Полученные с ее помощью сведения позволяют ИТ-менеджерам определять приоритеты рисков и разрабатывать эффективные планы мероприятий по снижению влияния наиболее опасных угроз. [1] Исследование выполнено при финансовой поддержке РФФИ, в рамках научного проекта № 16-31-00285 «Методы и модели нечеткой логики в системах принятия решений управления рисками»

This paper aims to evaluate the performance of Electroencephalographic (EEG) emotion recognition system (EEG-ER) using source-temporal domain with Takagi- Sugeno-Kang (TSK) fuzzy model. Ten healthy subjects aged 5-6 years were participated in this study. Emotion elicitation procedure has done using the Radbound faces database (RafD). The selected emotions were happy, sad, and neutral and fear. The results were compared with wavelet coefficients (WC) as feature extraction method and Regularized Least Square (RLS) and Multi-Layer Perception (MLP) neural network classifiers from our previous work. Another comparison was done between affective model of Russell and RafD. The results show the efficiency of using source-temporal features in emotion recognition system hence there was a slight difference in accuracy among different classifier; MLP, RLS and TSK however MLP and TSK results were with high accurate and stable. Moreover Russell model which is based on positive-negative dimensions shows high accuracy than RafD model that has positive dimensions. The accuracy was around 97% using Russell model.

The concept of fuzzy instrumental variable and an approach for fuzzy identification of nonlinear discrete time systems were proposed. Convergence conditions for identification in a noisy environment in a fuzzy context were studied. Simulation results for off-line and on-line schemes evidence the good quality of this fuzzy instrumental variable approach for identification and function approximation with observation errors in input and output data.

In order to overcome the shortcoming of the solution may be trapped into the local minimization in the traditional TSK (Takagi-Sugeno-Kang) fuzzy inference training, this paper attempts to consider the TSK fuzzy system modeling approach based on the visual system principle and the Weber law. This approach not only utilizes the strong capability of identifying objects of human eyes, but also considers the distribution structure of the training data set in parameter regulation. In order to overcome the shortcoming of it adopting the gradient learning algorithm with slow convergence rate, a novel visual TSK fuzzy system model based on evolutional learning is proposed by introducing the particle swarm optimization algorithm. The main advantage of this method lies in its very good optimization, very strong noise immunity and very good interpretability. The new method is applied to long-term hydrological forecasting examples. The simulation results show that the method is feasible and effective, the new method not only inherits the advantages of traditional visual TSK fuzzy models but also has the better global convergence and accuracy than the traditional model.

In this paper, we propose a Takagi-Sugeno-Kang (TSK) fuzzy model for a four-Mecanum-wheel omni-directional mobile free-base (4MW-ODMFB) with system uncertainties and external disturbances based on the model given in [12], [13], and then design an adaptive sliding-mode control (ASMC) system for trajectory tracking of 4MW-ODMFB, which combines the techniques of adaptive control and sliding-mode control. By using Lyapunov method we prove that the ASMC system is global asymptotic stable. We also conduct simulation experiments in MATLAB environment to test our TSK fuzzy model and the ASMC method. All the simulation results demonstrate the effectiveness of the proposed TSK fuzzy model and the stability and robustness of ASMC system.

We introduce an optimization of fuzzy set-fuzzy systems based on IG (Information Granules). The proposed fuzzy model implements system structure and parameter identification by means of IG and GAs. The concept of information granulation was coped with to enhance the abilities of structural optimization of the fuzzy model. Granulation of information realized with C-Means clustering helps determine the initial parameters of the fuzzy model such as the initial apexes of the membership functions in the premise part and the initial values of polynomial functions in the consequence part of the fuzzy rules. The initial parameters are adjusted effectively with the help of the GAs and the standard least square method. To optimally identify the structure and the parameters of the fuzzy model we exploit GAs with successive tuning method to simultaneously search the structure and the parameters within one individual. We also consider the variant generation-based evolution to adjust the rate of identification of the structure and the parameters in successive tuning method. The proposed model is evaluated with the performance of the conventional fuzzy model.

The problem of classification for imbalanced datasets is frequently encountered in practical applications. The data to be classified in this problem are skewed, i.e., the samples of one class (the minority class) are much less than those of other classes (the majority class). When dealing with imbalanced datasets, most classifiers encounter a common limitation, that is, they often obtain better classification performances on the majority classes than those on the minority class. To alleviate the limitation, in this study, a fuzzy rule-based modeling approach using information granules is proposed. Information granules, as some entities derived and abstracted from data, can be used to describe and capture the characteristics (distribution and structure) of data from both majority and minority classes. Since the geometric characteristics of information granules depend on the distance measures used in the granulation process, the main idea of this study is to construct information granules on each class of imbalanced data using Minkowski distance measures and then to establish the classification models by using “If-Then” rules. The experimental results involving synthetic and publicly available datasets reflect that the proposed Minkowski distance-based method can produce information granules with a series of geometric shapes and construct granular models with satisfying classification performance for imbalanced datasets.

The paper describes an approach to generating optimal adaptive fuzzy neural models from I/O data. This approach combines structure and parameter identification of Takagi-Sugeno-Kang (TSK) fuzzy models. We propose to achieve structure determination via a combination of modified mountain clustering (MMC) algorithm, recursive least squares estimation (RLSE), and group method of data handling (GMDH). Parameter adjustment is achieved by training the initial TSK model using the algorithm of an adaptive network based fuzzy inference system (ANFIS), which employs backpropagation (BP) and RLSE. Further, a procedure for generating locally optimal model structures is suggested. The structure optimization procedure is composed of two phases: 1) locally optimal rule premise variables subsets (LOPVS) are identified using MMC, GMDH, and a search tree (ST); and 2) locally optimal numbers of model rules (LONOR) are determined using MMC/RLSE along with parallel simulation mean square error (PSMSE) as a performance index. The effectiveness of the proposed approach is verified by a variety of simulation examples. The examples include modeling of a nonlinear dynamical process from I/O data and modeling nonlinear components of dynamical plants, followed by tracking control based on a model reference adaptive scheme (MRAC). Simulation results show that this approach is fast and accurate and leads to several optimal models.

Electro-tactile based rehabilitation systems must be capable of self-tuning to suit the tactile preference of different users. However, tactile preference is difficult to assess in practice. We propose a Takagi-Sugeno-Kang (TSK) fuzzy logic modeling and control approach for the on-line assessment of tactile preference. The method relies on real-time measurements of voltage and power absorbed by the fingertip. Our results show that the fuzzy logic approach successfully models user tactile preference. We are currently developing an electro-tactile based Braille display (E-Braille) for assisting the Blind and Visually Impaired (BVI) that exploits our fuzzy model.

Entropy-based fuzzy clustering and fuzzy modeling

Granular computing is a method of studying human intelligent information processing, which has advantage of knowledge discovery. In this paper, we convert a classification problem of sample space into a classification problem of fuzzy clustering granular space and propose a random fuzzy clustering granular hyperplane classifier (RFCGHC) from the perspective of granular computing. Most classifiers are only used to process numerical data, RFCGHC can process not only non-numerical data, such as information granules, but also numerical data. The classic granulation method is generally serial granulation, which has high time complexity. We design a parallel distributed granulation method to enhance efficiency. First, a clustering algorithm with adaptive cluster center number is proposed, where the ratio of standard deviation between categories and standard deviation within categories is as evaluation criterion. The clusters and the optimal amount of cluster centers can be achieved by the method. On the basis of these, sample set can be divided into many subsets and each sample can be granulated by these cluster centers. Then, a fuzzy clustering granular space can be formed, where fuzzy clustering granules, fuzzy clustering granular vectors, and their operators can be defined. In order to get the optimal hyperplane in the fuzzy clustering granular space to classify these samples, we design a loss function and evaluate each category with probability by fuzzy clustering granular hyperplane. In solving the loss function, genetic algorithm based on fuzzy clustering granules is adopted. Experimental results and theoretical analysis show that RFCGHC has good performance.

In this paper, we propose a new design methodology of fuzzy-neural networks - fuzzy set-based polynomial neural networks (FSPNN) with symbolic genetic algorithms. Fuzzy set-based polynomial neural networks (FSPNN) are based on a fuzzy set-based polynomial neuron (FSPN) whose fuzzy rules include the information granules (about the real system) obtained through information granulation. The information granules are capable of show the specific characteristic of the system. We have developed a design methodology (genetic optimization using symbolic genetic algorithms) to find the optimal structure for fuzzy-neural networks that expanded from group method of data handling (GMDH). It is the number of input variables, the order of the polynomial, the number of membership functions, and a collection of the specific subset of input variables that are the parameters of FSPNN fixed by aid of symbolic genetic optimization that has search capability to find the optimal solution on the solution space. The augmented and genetically developed FPNN (gFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional FPNNs. The GA-based design procedure being applied at each layer of FPNN leads to the selection of the most suitable nodes (or FSPNs) available within the FPNN. Symbolic genetic algorithms are capable of reducing the solution space more than conventional genetic algorithms with binary genetype chromosomes. The performance of genetically optimized FSPNN (gFSPNN) with aid of symbolic genetic algorithms is quantified through experimentation where we use a number of modeling benchmarks data which are already experimented with in fuzzy or neurofuzzy modeling