Optimal Number Of Fuzzy Rules Research Articles

Bayesian inference using an adaptive neuro-fuzzy inference system

For most Bayesian inference problems that are of interest, solving for the model parameter posterior probability distribution remains to be the main challenge. A typical technique entails using Markov chain Monte Carlo (MCMC), in order to obtain an approximation of the posterior distribution. However, one drawback of MCMC is that it usually requires solving the forward problem multiple times, which could be infeasible, if the forward model is computationally expensive. In this paper, a computationally cheap surrogate model is developed using the adaptive neuro-fuzzy inference system with a fuzzy c-means initialization (ANFIS-FCM). The optimal number of fuzzy rules is chosen via a proposed algorithm based on the pairing frequency clustering validity index. The effectiveness of the ANFIS-FCM model is tested on inferring reaction rate parameters in a 3-node network toy problem, which mimics idealized combustion reaction networks. Using multiple error measures, it is shown that the developed ANFIS-FCM model is capable of constructing accurate surrogate models at a minimal computational cost.

A hybrid neuro-fuzzy power prediction system for wind energy generation

Abstract Wind energy generation is expected to increase in future electric grids. The generated wind power has an intermittent nature which may affect power system stability and increase the risk of blackouts. Therefore, a prediction system for wind power generation is essential for optimum operation of a power system with a significant share of wind energy conversion systems. In this paper, a hybrid neuro-fuzzy wind power prediction system is proposed. A wireless sensor network (WSN) is used to measure and transmit the required parameters for the prediction model at the operator centre. Those parameters are the major factors affecting wind farm output power, namely air temperature, wind speed, air density and air pressure. Considering all these factors will increase the prediction accuracy of the proposed model. The proposed prediction model is designed and tested using fuzzy rules with adaptive network. To decide the optimal number of fuzzy rules, the clustering of the data using modified Fuzzy C-Means (FCM) is used to implement hybrid optimization method. The prediction model is tested using four subsets of data divided into four seasons of year. The proposed prediction model is implemented using Matlab. Analysis of results shows that the proposed model has good prediction accuracy and provides a useful qualitative description of the prediction system.

Fuzzy classification knowledge base construction based on trend rules and inverse inference

In this paper, an approach to fuzzy classification rules construction within the framework of fuzzy relation equations is proposed. At the same time, the system of fuzzy trend rules serves as a carrier of expert information and generator of rules - solutions of fuzzy relation equations. The system of fuzzy classification rules can be rearranged as a set of linguistic solutions of fuzzy relation equations using the composite system of fuzzy terms, e.g. “significant rise”, “essential drop” etc., where causes and effects significance measures are described by fuzzy quantifiers. The problem of inverse logical inference, which lies in restoring the coordinates of the maximum of the fuzzy input terms membership functions for each output class is reduced to solving the system of fuzzy relation equations using a genetic algorithm. The proposed approach allows to avoid the alternative rule selection. The aim of the rule selection methods is to reduce the system complexity by removing inefficient and redundant rules and improve the system accuracy by introducing alternative rules into the final rule base. Using expert knowledge cannot guarantee the optimal cooperation activity among rules. The rule selection problem is still relevant since there is currently no single methodical standard for the optimal structural adjustment of fuzzy classification knowledge bases. Solving fuzzy relation equations using the genetic algorithm ensures the optimal number of fuzzy rules for each output term and optimal form of the membership functions of the fuzzy input terms for each linguistic solution. Consecutive solution of the optimization problems provides complexity reduction of the problem of fuzzy classification knowledge bases generation.

Fuzzy-Neural Networks Based on Subtractive Clustering and its Applications in Soft Sensor

A soft sensor modeling method is presented in this paper，it selects optimal fuzzy rules by tuning the radius of a subtractive cluster center to generate a T-S fuzzy model. The radius of a cluster center is adjusted to select optimal number of fuzzy rules, to acquire a fuzzy model with perfect generalization capability. Then, the parameter is fine-tuned by means of a hybrid gradient descent (GD) and least-squares estimation (LSE) approach. Finally, the method is used to model a PDU Naphtha’s Dry Point, simulation results show that it can determine the optimal model quickly and achieve satisfactory prediction precision.

Hybrid-controlled neurofuzzy networks analysis resulting in genetic regulatory networks reconstruction.

Reverse engineering of gene regulatory networks (GRNs) is the process of estimating genetic interactions of a cellular system from gene expression data. In this paper, we propose a novel hybrid systematic algorithm based on neurofuzzy network for reconstructing GRNs from observational gene expression data when only a medium-small number of measurements are available. The approach uses fuzzy logic to transform gene expression values into qualitative descriptors that can be evaluated by using a set of defined rules. The algorithm uses neurofuzzy network to model genes effects on other genes followed by four stages of decision making to extract gene interactions. One of the main features of the proposed algorithm is that an optimal number of fuzzy rules can be easily and rapidly extracted without overparameterizing. Data analysis and simulation are conducted on microarray expression profiles of S. cerevisiae cell cycle and demonstrate that the proposed algorithm not only selects the patterns of the time series gene expression data accurately, but also provides models with better reconstruction accuracy when compared with four published algorithms: DBNs, VBEM, time delay ARACNE, and PF subjected to LASSO. The accuracy of the proposed approach is evaluated in terms of recall and F-score for the network reconstruction task.

A New Approach to Dynamic Fuzzy Modeling of Genetic Regulatory Networks

In this paper, the dynamic fuzzy modeling approach is applied for modeling genetic regulatory networks from gene expression data. The parameters of the dynamic fuzzy model and the optimal number of fuzzy rules for the fuzzy gene network can be obtained via the proposed modeling approach from the measured gene expression data. One of the main features of the proposed approach is that the prior qualitative knowledge on the network structure can be easily incorporated in the proposed identification algorithm, so that the faster learning convergence of the algorithm can be achieved. Two sets of data, one the synthetic data, and the other the experimental SOS DNA repair network data with structural knowledge, have been used to validate the proposed modeling approach. It is shown that the proposed approach is effective in modeling genetic regulatory networks.

Evolving Fuzzy Modeling for MANETs Using Lightweight Online Unsupervised Learning

The study presents a methodology for evolving fuzzy modeling tasks in Mobile Ad hoc Networks (MANETs) based on distributed data-driven fuzzy clustering and reasoning. The fuzzy clustering is exploited for the purpose of learning fuzzy inference rules online. That calls for one-pass Lightweight Evolving Fuzzy Clustering Method (LEFCM) suitable for deploying on mobile devices with constrained resources in MANETs. There is no standard method to determine the optimal number of fuzzy rules and most of the fuzzy systems still apply the trial and error method, unsuitable for online modeling tasks. The proposed methodology addresses the issues of uncertainties, simplicity and speed to run in non-intrusive way. It estimates online the number of clusters and their centers in the input data space, accordingly the fuzzy rules, by online adaptation of the LEFCM threshold value that affects the number of clusters. Adaptation is based on the combination of geometrical and statistical analyses, as well as on incorporating a multidimensional fuzzy membership degree into the clustering process. The proposed LEFCM is proven by using traditional cluster validity indexes and tested on real data sets.

An improved Takagi-Sugeno fuzzy model with multidimensional fuzzy sets

In this study, we propose fuzzy modeling algorithm to improve Takagi-Sugeno fuzzy model. This algorithm initially finds desirable number of rules at once, in advance, and then identifies the premise and consequent parameters separately by fixing number determined. The proposed algorithm consists of three stages: determination of the optimal number of fuzzy rules, coarse tuning of parameters and fine tuning of these parameters. To find the optimal number of rules, the new cluster validity algorithm that is based on the validity criterion V sv adapted to the usage of FCRM-like clustering, is proposed. In coarse tuning, by using the mentioned clustering algorithm for input-output data and the projection scheme, the consequent and premise parameters are coarsely defined. In fine tuning, the gradient descent (GD) method is used to precisely adjust parameters of fuzzy model but unlike other similar modeling algorithms, the premise parameters are adjusted with respect to multidimensional membership function in premise part of rule. Finally, two examples are given to demonstrate the validity of suggested modeling algorithm and show its excellent predictive performance.

Rule-base self-generation and simplification for data-driven fuzzy models

Data-driven fuzzy modeling has been used in a wide variety of applications. However, in fuzzy rule-based models acquired from numerical data, redundancy often exists in the form of redundant rules or similar fuzzy sets. This results in unnecessary structural complexity and decreases the interpretability of the system. In this paper, a rule-base self-extraction and simplification method is proposed to establish interpretable fuzzy models from numerical data. A fuzzy clustering technique associated with the proposed fuzzy partition validity index is used to extract the initial fuzzy rule-base and find out the optimal number of fuzzy rules. To reduce the complexity of fuzzy models while keeping good model accuracy, some approximate similarity measures are presented and a parameter fine-tuning mechanism is introduced to improve the accuracy of the simplified model. Using the proposed similarity measures, the redundant fuzzy rules are removed and similar fuzzy sets are merged to create a common fuzzy set in the rule base. The simplified rule base is computationally efficient and linguistically interpretable. The approach has been successfully applied to fuzzy models of non-linear function approximation, dynamical system modeling and mechanical property prediction for hot-rolled steels.

Sensor monitoring using a fuzzy neural network with an automatic structure constructor

The performance of fuzzy neural networks applied to sensor monitoring strongly depends on the selection of input signals. A large number of input signals may be involved to estimate an output signal for failure detection. However, as the number of input signals increases, the required training time increases exponentially and the uncertainty of the model increases significantly due to the irrelevant and/or the redundant inputs. In this paper, a fuzzy neural network with an optimal structure constructor has been successfully developed to achieve a reliable and efficient sensor monitoring system. A fuzzy neural network is used to estimate an output signal from the selected input signals. Correlation analysis and genetic algorithm (GA) are combined for automatic input selection. In addition, the optimal number of fuzzy rules is accomplished automatically by the GA integrated along with the automatic input selection. The status of sensor health is determined by applying sequential probability ratio test to the residuals between the measured signals and the estimated signals. The proposed sensor monitoring system has been validated by using a variety of sensor signals acquired from Yonggwang units 3 and 4 pressurized water reactors.

Takagi-Sugeno fuzzy modeling incorporating input variables selection

Fuzzy models, especially Takagi-Sugeno (T-S) fuzzy models, have received particular attention in the area of nonlinear modeling due to their capability to approximate any nonlinear behavior. Based only on measured data without any prior knowledge, there is no systematic way to obtain a T-S fuzzy model with a simple structure and sufficient accuracy. The main idea discussed in this paper is to reduce the complexity of T-S fuzzy models by estimating an optimal number of fuzzy rules and selecting relevant inputs as antecedent variables independently of the selection of consequent regressors. A systematic procedure is proposed here and illustrated on static and dynamical nonlinear systems.

HIERARCHICAL CLUSTERING FOR FUZZY MODELING OF MATERIALS PROPERTY PREDICTION

A simple and effective fuzzy clustering approach is presented for fuzzy modeling from industrial data. In this approach, fuzzy clustering is implemented in two phases: data compression by a self-organizing network, and fuzzy partitioning via fuzzy c-means clustering associated with a proposed cluster validity measure. The approach is used to extract fuzzy models from data and find out the optimal number of fuzzy rules. The simulation results show that the proposed approach has good clustering performance with noise-contaminated data and high-dimensional industrial data.

Neural-Fuzzy Modeling for Tensile Strength Prediction of Heat-Treated Alloy Steels

To utilise process data to build empirical models capable of predicting mcchanical test results for steels after heat treatment process, a neural-fuzzy modelling approach is presented in this paper and has been used to construct models for tensile strength prediction. The proposed fuzzy modelling approach consists of several stages: initial rule-base generation, fuzzy model-based input selection, rule-base optimisation and parameter learning. To find the optimal number of fuzzy rules, a modified fuzzy c-means clustering approach is used for model structure identification. Based on the model structure identification, the parameters both in the membership functions of antecedent part and linear weights in consequent part of the rules are optimised by an adaptive back-propagation algorithm. Simulation results show that the predicted tensile strength has good agreement with the experimental data via the obtained fuzzy model with only a few rules.

Input selection and partition validation for fuzzy modelling using neural network

A simple and effective method for selecting significant input variables and determining optimal number of fuzzy rules when building a fuzzy model from data is proposed. In contrast to the existing clustering-based methods, in this approach both input selecting and partition validating are determined on the basis of a class of sub-clusters created by a self-organising network instead of on the data. The important input variables which independently and significantly influence the system output can be extracted by a fuzzy neural network. On the other hand, the optimal number of fuzzy rules can be determined separately via the fuzzy c-means algorithm with a modified fuzzy entropy as the criterion of cluster validation. The simulation results show that the proposed method can provide good model structures for fuzzy modelling and has high computing efficiency.

Intelligent Multisensor State Information Fusion with a Stochastic, Fuzzy, Neural Network

The intelligent multisensor state information fusion based on a new stochastic, fuzzy, neural network is investigated. This network carries out the parameter and structure learning to obtain the optimal fuzzy membership functions and the optimal number of fuzzy rules of stochastic dynamic systems. The state information fusion with radar and infrared sensors based on the network is simulated in an uncertain environment. The numerical results show that the proposed intelligent method is effective and superior to fuzzy neural network based method