Function Approximation with Complex Neuro-Fuzzy System Using Complex Fuzzy Sets �C A New Approach

A new neuro-fuzzy computing paradigm using complex fuzzy sets is proposed in this paper. The novel computing paradigm is applied to the problem of function approximation to test its nonlinear mapping ability. A complex fuzzy set (CFS) is an extension of traditional type-1 fuzzy set whose membership is within the unit real-valued interval. For a CFS, the membership is extended to complex-valued state within the unit disc of the complex plane. For self-adaption of the proposed complex neuro-fuzzy system (CNFS), the Particle Swarm Optimization (PSO) algorithm and Recursive Least Squares Estimator (RLSE) algorithm are used in a hybrid way to adjust the free parameters of the CNFS. With the novel PSO-RLSE hybrid learning method, the CNFS parameters can be converged efficiently and quickly. By the PSO-RLSE method for the CNFS, fast learning convergence is observed and great performance in accuracy is shown. In the experimental results, the CNFS shows much better performance than its traditional neuro-fuzzy counterpart and other compared approaches. Excellent performance by the proposed approach has been shown.     

Approximation accuracy of some neuro-fuzzy approaches

Many methods have been proposed in the literature for designing fuzzy systems from input-output data (the so-called neuro-fuzzy methods), but very little was done to analyze the performance of the methods from a rigorous mathematical point of view. In this paper, we establish approximation bounds for two of these methods - the table lookup scheme proposed by Wang et al. (1992) and the clustering method studied by Wang (1993, 1997). We derive detailed formulas of the error bounds between the nonlinear function to be approximated and the fuzzy systems designed using the methods based on input-output data. These error bounds show explicitly how the parameters in the two methods influence their approximation capability. We also propose modified versions for the two methods such that the designed fuzzy systems are well-defined over the whole input domain     

Interval type-2 neuro-fuzzy system with implication-based inference mechanism

Neuro-fuzzy systems have been proved to be an efficient tool for modelling real life systems. They are precise and have ability to generalise knowledge from presented data. Neuro-fuzzy systems use fuzzy sets – most commonly type-1 fuzzy sets. Type-2 fuzzy sets model uncertainties better than type-1 fuzzy sets because of their fuzzy membership function. Unfortunately computational complexity of type reduction in general type-2 systems is high enough to hinder their practical application. This burden can be alleviated by application of interval type-2 fuzzy sets. The paper presents an interval type-2 neuro-fuzzy system with interval type-2 fuzzy sets both in premises (Gaussian interval type-2 fuzzy sets with uncertain fuzziness) and consequences (trapezoid interval type-2 fuzzy set). The inference mechanism is based on the interval type-2 fuzzy Łukasiewicz, Reichenbach, Kleene-Dienes, or Brouwer–Gödel implications. The paper is accompanied by numerical examples. The system can elaborate models with lower error rate than type-1 neuro-fuzzy system with implication-based inference mechanism. The system outperforms some known type-2 neuro-fuzzy systems.     

Wavelet feature selection based neural networks with application to the text independent speaker identification

A wavelet packets feature selection derived by using neuro-fuzzy evaluation index for speaker identification is described. The concept of a flexible membership function incorporating weighed distance is introduced in the evaluation index to make the modeling of clusters more appropriate. Experimental evaluation of the systems performance was conducted on three speech databases. Our results have shown that this feature selection introduced better performance than the wavelet features with respect to the percentages of recognition.     

Parallel Interval Type-2 Subsethood Neural Fuzzy Inference System

Neuro-fuzzy models are being increasingly employed in the domains like weather forecasting, stock market prediction, computational finance, control, planning, physics, economics and management, to name a few. These models enable one to predict system behavior in a more human-like manner than their crisp counterparts. In the present work, an interval type-2 neuro-fuzzy evolutionary subsethood based model has been proposed for its use in finding solutions to some well-known problems reported in the literature such as regression analysis, data mining and research problems relevant to expert and intelligent systems. A novel subsethood based interval type-2 fuzzy inference system, named as Interval Type-2 Subsethood Neural Fuzzy Inference System (IT2SuNFIS) is proposed in the present work. Mathematical modeling and empirical studies clearly bring out the efficacy of this model in a wide variety of practical problems such as Truck backer-upper control, Mackey–Glass time-series prediction, Narazaki–Ralescu and bell function approximation. The simulation results demonstrate intelligent decision making capability of the proposed system based on the available data. The major contribution of this work lies in identifying subsethood as an efficient measure for finding correlation in interval type-2 fuzzy sets and applying this concept to a wide variety of problems pertaining to expert and intelligent systems. Subsethood between two type-2 fuzzy sets is different from the commonly used sup-star methods. In the proposed model, this measure assists in providing better contrast between dissimilar objects. This method, coupled with the uncertainty handling capacity of type-2 fuzzy logic system, results in better trainability and improved performance of the system. The integration of subsethood with type-2 fuzzy logic system is a novel idea with several advantages, which is reported for the first time in this paper.     

Tuning of a neuro-fuzzy controller by genetic algorithm

Due to their powerful optimization property, genetic algorithms (GAs) are currently being investigated for the development of adaptive or self-tuning fuzzy logic control systems. This paper presents a neuro-fuzzy logic controller (NFLC) where all of its parameters can be tuned simultaneously by GA. The structure of the controller is based on the radial basis function neural network (RBF) with Gaussian membership functions. The NFLC tuned by GA can somewhat eliminate laborious design steps such as manual tuning of the membership functions and selection of the fuzzy rules. The GA implementation incorporates dynamic crossover and mutation probabilistic rates for faster convergence. A flexible position coding strategy of the NFLC parameters is also implemented to obtain near optimal solutions. The performance of the proposed controller is compared with a conventional fuzzy controller and a PID controller tuned by GA. Simulation results show that the proposed controller offers encouraging advantages and has better performance.     

A PSO-aided neuro-fuzzy classifier employing linguistic hedge concepts

The present paper proposes the development of an adaptive neuro-fuzzy classifier which employs two relatively less explored and comparatively new problem solving domains in fuzzy systems. The relatively less explored field is the domain of the fuzzy linguistic hedges which has been employed here to define the flexible shapes of the fuzzy membership functions (MFs). To achieve finer and finer adaptation, and hence control, over the fuzzy MFs, each MF is composed of several piecewise MF sections and the shape of each such MF section is varied by applying a fuzzy linguistic operator on it. The system employs a Takagi–Sugeno based neuro-fuzzy system where the rule consequences are described by zero order elements. This proposed linguistic hedge based neuro-fuzzy classifier (LHBNFC) employs a relatively new field in the area of combinatorial metaheuristics, called particle swarm optimization (PSO), for its efficient learning. PSO has been employed in this scheme to simultaneously tune the shape of the fuzzy MFs as well as the rule consequences for the entire fuzzy rule base. The performance of the proposed system is demonstrated by implementing it for two classical benchmark data sets: (i) the iris data and (ii) the thyroid data. Performance comparison vis-à-vis other available algorithms shows the effectiveness of our proposed algorithm.     

A neuro-fuzzy system for chemical agent detection

The authors previously introduced a fuzzy version of Kohonen's well-known self-organizing map neural network model. In this novel neuro-fuzzy system, the neurons of Kohonen's original model are replaced by fuzzy rules. Each fuzzy rule is composed of fuzzy sets and an output singleton. Since the fuzzy self-organizing map is a modified version of Kohonen's original model, the self-organizing map and the learning vector quantization learning laws can be used to tune the neuro-fuzzy system. Originally, the fuzzy self-organizing map was intended to be used as an unknown function approximator, while Kohonen's self-organizing map is primarily used as a neural classifier. In this paper, the authors show how the fuzzy self-organizing map can also be used as a neuro-fuzzy classifier. Simulation results show that, in chemical agent detection, the fuzzy self-organizing map not only gives better classification results than Kohonen's model, but it also has smaller number of fuzzy rules than the corresponding neurons required by Kohonen's self-organizing map     

Neuro-fuzzy modelling of suspended sediment load: The need for a sound comparison with established methods

This paper questions the correctness of two bias-corrected sediment rating curve models that were used to compare and contrast traditional counterparts against state-of-the-art computational tools in a recent article on “Adaptive neuro-fuzzy computing technique for suspended sediment estimation” by Kisi et al. (2009). Mathematical and graphical procedures are used to demonstrate substantial and unexplained shortcomings in the reported equations. The superior performance of more advanced computational methods – such as neural network and neuro-fuzzy system solutions in the reported scenario – is thus brought into question.     

Efficient DE-based symbiotic cultural algorithm for neuro-fuzzy system design

This study proposes a differential-evolution-based symbiotic cultural algorithm (DESCA) for the implementation of neuro-fuzzy systems (NFS) to solve nonlinear control system problems. DESCA adopts symbiotic evolution to decompose a fuzzy system into multiple fuzzy rules as multiple subpopulations. In addition, DESCA randomly selects fuzzy rules from different subpopulations that combine into a complete solution whose performance is be evaluated. Moreover, DESCA uses various mutation strategies of differential evolution as five knowledge sources in the belief space. These knowledge sources influence the population space in the cultural algorithm and can be used as models to guide the feasible search space. Finally, the proposed algorithm is applied to various simulations. The results demonstrate the effectiveness of this approach.     

Complexity reduction and interpretability improvement for fuzzy rule systems based on simple interpretability measures and indices by bi-objective evolutionary rule selection

The aim of this paper is to develop a general post-processing methodology to reduce the complexity of data-driven linguistic fuzzy models, in order to reach simpler fuzzy models preserving enough accuracy and better fuzzy linguistic performance with respect to their initial values. This post-processing approach is based on rule selection via the formulation of a bi-objective problem with one objective focusing on accuracy and the other on interpretability. The latter is defined via the aggregation of several interpretability measures, based on the concepts of similarity and complexity of fuzzy systems and rules. In this way, a measure of the fuzzy model interpretability is given. Two neuro-fuzzy systems for providing initial fuzzy models, Fuzzy Adaptive System ART based and Neuro-Fuzzy Function Approximation and several case studies, data sets from KEEL Project Repository, are used to check this approach. Both fuzzy and neuro-fuzzy systems generate Mamdani-type fuzzy rule-based systems, each with its own particularities and complexities from the point of view of the fuzzy sets and the rule generation. Based on these systems and data sets, several fuzzy models are generated to check the performance of the proposal under different restrictions of complexity and fuzziness.     

Neuro-fuzzy control based on the NEFCON-model: recent developments

 Fuzzy systems are currently being used in a wide field of industrial and scientific applications. Since the design and especially the optimization process of fuzzy systems can be very time consuming, it is convenient to have algorithms which construct and optimize them automatically. One popular approach is to combine fuzzy systems with learning techniques derived from neural networks. Such approaches are usually called neuro-fuzzy systems. In this paper we present our view of neuro-fuzzy systems and an implementation in the area of control theory: the NEFCON-Model. This model is able to learn and optimize the rule base of a Mamdani like fuzzy controller online by a reinforcement learning algorithm that uses a fuzzy error measure. Therefore, we also describe some methods to determine a fuzzy error measure for a dynamic system. In addition we present some implementations of the model and an application example. The presented implementations are available free of charge for non-commercial purposes.     

Soft computing-based expert systems to predict energy consumption and stability margin in turning gaits of six-legged robots

Turning gaits are the most general and very important ones for omni-directional walking of a six-legged robot. Soft computing-based expert systems have been developed in the present work to predict specific energy consumption and stability margin of turning gait of a six-legged robot. Besides back-propagation neural network, three approaches based on adaptive neuro-fuzzy inference system have been developed and their performances are compared with each other. Genetic algorithm-tuned multiple adaptive neuro-fuzzy inference systems are found to perform better than other approaches. This could be due to a more exhaustive search conducted by the genetic algorithm in place of back-propagation algorithm and the use of two separate adaptive neuro-fuzzy inference systems for two different outputs.     

An effective hybrid approach of desirability,fuzzy logic,ANFIS and LAPO algorithm for optimizing compliant mechanism

This paper proposes an efficient hybrid approach for solving multi-objective optimization design of a compliant mechanism. The approach is developed by integrating desirability function approach, fuzzy logic system, adaptive neuro-fuzzy inference system, and Lightning attachment procedure optimization. Box–Behnken design is used to form a numerically experimental matrix. First, a refinement of design variables is conducted through analysis of variance and Taguchi approach in terms of considerably eliminating space of design variables and computation efforts. Next, desirability of two objective functions is computed and transferred into the fuzzy logic system. The output of fuzzy logic system is regarded as single combined objective function. Subsequently, a modeling for fuzzy output is developed via adaptive neuro-fuzzy inference system. Then, LAPO algorithm is adopted for solving the optimization problem. By investigating three different numerical examples, performance of the proposed approach is validated. Numerical results revealed that the proposed approach has a computational accuracy better than that of Taguchi-based fuzzy logic reasoning. Finally, case study 1 is chosen as an optimal solution for the mechanism. Furthermore, the effectiveness of proposed approach is greater than that of the Jaya algorithm and TLBO algorithm through Wilcoxon signed rank test and Friedman test. The proposed approach can be used for related engineering fields.

     

Neuro-fuzzy position control of demining tele-operation system based on RNN modeling

The paper considers the neuro-fuzzy position control of multi-finger robot hand in tele-operation system—an active master–slave hand system (MSHS) for demining. Recently, fuzzy control systems utilizing artificial intelligent techniques are also being actively investigated in robotic area. Neural network with their powerful learning capability are being sought as the basis for many adaptive control systems where on-line adaptation can be implemented. Fuzzy logic on the other hand has been proved to be rather popular in many control system applications providing a rule-base like structure. In this paper, the design and optimization process of fuzzy position controller is supported by learning techniques derived from neural network where a radial basis function (RBF) neural network is implemented to learn fuzzy rules and membership functions with predictor of recurrent neural network (RNN) model. The results of experiment show that based on the predictive capability of RNN model neuro-fuzzy controller with good adaptation and robustness capability can be designed.     

A neuro-fuzzy approach to gear system monitoring

The detection of the onset of damage in gear systems is of great importance to industry. In this paper, a new neuro-fuzzy diagnostic system is developed, whereby the strengths of three robust signal processing techniques are integrated. The adopted techniques are: the continuous wavelet transform (amplitude) and beta kurtosis based on the overall residual signal, and the phase modulation by employing the signal average. Three reference functions are proposed as post-processing techniques to enhance the feature characteristics in a way that increases the accuracy of fault detection. Monitoring indexes are derived to facilitate the automatic diagnoses. A constrained-gradient-reliability algorithm is developed to train the fuzzy membership function parameters and rule weights, while the required fuzzy completeness is retained. The system output is set to different monitoring levels by using an optimization procedure to facilitate the decision-making process. The test results demonstrate that the novel neuro-fuzzy system, because of its adaptability and robustness, significantly improves the diagnostic accuracy. It outperforms other related classifiers, such as those based on fuzzy logic and neuro-fuzzy schemes, which adopt different types of rule weights and employ different training algorithms.     

Data mining in forecasting PVT correlations of crude oil systems based on Type1 fuzzy logic inference systems

Pressure–volume–temperature properties are very important in the reservoir engineering computations. There are many empirical approaches for predicting various PVT properties based on empirical correlations and statistical regression models. Last decade, researchers utilized neural networks to develop more accurate PVT correlations. These achievements of neural networks open the door to data mining techniques to play a major role in oil and gas industry. Unfortunately, the developed neural networks correlations are often limited, and global correlations are usually less accurate compared to local correlations. Recently, adaptive neuro-fuzzy inference systems have been proposed as a new intelligence framework for both prediction and classification based on fuzzy clustering optimization criterion and ranking. This paper proposes neuro-fuzzy inference systems for estimating PVT properties of crude oil systems. This new framework is an efficient hybrid intelligence machine learning scheme for modeling the kind of uncertainty associated with vagueness and imprecision. We briefly describe the learning steps and the use of the Takagi Sugeno and Kang model and Gustafson–Kessel clustering algorithm with K-detected clusters from the given database. It has featured in a wide range of medical, power control system, and business journals, often with promising results. A comparative study will be carried out to compare their performance of this new framework with the most popular modeling techniques, such as neural networks, nonlinear regression, and the empirical correlations algorithms. The results show that the performance of neuro-fuzzy systems is accurate, reliable, and outperform most of the existing forecasting techniques. Future work can be achieved by using neuro-fuzzy systems for clustering the 3D seismic data, identification of lithofacies types, and other reservoir characterization.     

基于数据融合的自适应神经网络模糊控制系统设计

基于数据融合的思想，提出一种非线性系统的自适应神经网络模糊控制器的设计方法。该方法利用数据融合技术降低了模糊控制器的输入维数，简化了模糊控制器的设计。用自适应神经模糊推理系统的神经网络自学习功能完成模糊控制器的设计。仿真结果表明，自适应神经网络模糊控制系统性能优于采用普通的模糊控制器的情况，为数据融合与智能系统技术在非线性系统中的应用作了有益的探索.     

Tool wear monitoring using neuro-fuzzy techniques: a comparative study in a turning process

Tool wear detection is a key issue for tool condition monitoring. The maximization of useful tool life is frequently related with the optimization of machining processes. This paper presents two model-based approaches for tool wear monitoring on the basis of neuro-fuzzy techniques. The use of a neuro-fuzzy hybridization to design a tool wear monitoring system is aiming at exploiting the synergy of neural networks and fuzzy logic, by combining human reasoning with learning and connectionist structure. The turning process that is a well-known machining process is selected for this case study. A four-input (i.e., time, cutting forces, vibrations and acoustic emissions signals) single-output (tool wear rate) model is designed and implemented on the basis of three neuro-fuzzy approaches (inductive, transductive and evolving neuro-fuzzy systems). The tool wear model is then used for monitoring the turning process. The comparative study demonstrates that the transductive neuro-fuzzy model provides better error-based performance indices for detecting tool wear than the inductive neuro-fuzzy model and than the evolving neuro-fuzzy model.     

A modified gradient-based neuro-fuzzy learning algorithm and its convergence

Neuro-fuzzy approach is known to provide an adaptive method to generate or tune fuzzy rules for fuzzy systems. In this paper, a modified gradient-based neuro-fuzzy learning algorithm is proposed for zero-order Takagi-Sugeno inference systems. This modified algorithm, compared with conventional gradient-based neuro-fuzzy learning algorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. Some weak and strong convergence results for this algorithm are proved, indicating that the gradient of the error function goes to zero and the fuzzy parameter sequence goes to a fixed value, respectively. A constant learning rate is used. Some conditions for the constant learning rate to guarantee the convergence are specified. Numerical examples are provided to support the theoretical findings.