Improved structure optimization for fuzzy-neural networks

Fuzzy-neural-network-based inference systems are well-known universal approximators which can produce linguistically interpretable results. Unfortunately, their dimensionality can be extremely high due to an excessive number of inputs and rules, which raises the need for overall structure optimization. In the literature, various input selection methods are available, but they are applied separately from rule selection, often without considering the fuzzy structure. This paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously. First, a method is developed to select the most significant rules, along with a refinement stage to remove unnecessary correlations. An improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model, leading to a balanced tradeoff between interpretability and accuracy. Simulation results confirm the efficacy of the proposed method.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

An Efficient LS-SVM-Based Method for Fuzzy System Construction

This paper proposes an efficient learning mechanism to build fuzzy rule-based systems through the construction of sparse least-squares support vector machines (LS-SVMs). In addition to the significantly reduced computational complexity in model training, the resultant LS-SVM-based fuzzy system is sparser while offers satisfactory generalization capability over unseen data. It is well known that the LS-SVMs have their computational advantage over conventional SVMs in the model training process; however, the model sparseness is lost, which is the main drawback of LS-SVMs. This is an open problem for the LS-SVMs. To tackle the nonsparseness issue, a new regression alternative to the Lagrangian solution for the LS-SVM is first presented. A novel efficient learning mechanism is then proposed in this paper to extract a sparse set of support vectors for generating fuzzy IF-THEN rules. This novel mechanism works in a stepwise subset selection manner, including a forward expansion phase and a backward exclusion phase in each selection step. The implementation of the algorithm is computationally very efficient due to the introduction of a few key techniques to avoid the matrix inverse operations to accelerate the training process. The computational efficiency is also confirmed by detailed computational complexity analysis. As a result, the proposed approach is not only able to achieve the sparseness of the resultant LS-SVM-based fuzzy systems but significantly reduces the amount of computational effort in model training as well. Three experimental examples are presented to demonstrate the effectiveness and efficiency of the proposed learning mechanism and the sparseness of the obtained LS-SVM-based fuzzy systems, in comparison with other SVM-based learning techniques.

Privacy-Protected Facial Biometric Verification via Fuzzy Forest Learning

Although visual surveillance has emerged as an effective technolody for public security, privacy has become an issue of great concern in the transmission and distribution of surveillance videos. For example, personal facial images should not be browsed without permission. To cope with this issue, face image scrambling has emerged as a simple solution for privacyrelated applications. Consequently, online facial biometric verification needs to be carried out in the scrambled domain thus bringing a new challenge to face classification. In this paper, we investigate face verification issues in the scrambled domain and propose a novel scheme to handle this challenge. In our proposed method, to make feature extraction from scrambled face images robust, a biased random subspace sampling scheme is applied to construct fuzzy decision trees from randomly selected features, and fuzzy forest decision using fuzzy memberships is then obtained from combining all fuzzy tree decisions. In our experiment, we first estimated the optimal parameters for the construction of the random forest, and then applied the optimized model to the benchmark tests using three publically available face datasets. The experimental results validated that our proposed scheme can robustly cope with the challenging tests in the scrambled domain, and achieved an improved accuracy over all tests, making our method a promising candidate for the emerging privacy-related facial biometric applications.

Fuzzy Ensembles for Embedding Adaptive Behaviours in Semi-Autonomous Avatars in 3D Virtual Worlds

Semi-autonomous avatars should be both realistic and believable. The goal is to learn from and reproduce the behaviours of the user-controlled input to enable semi-autonomous avatars to plausibly interact with their human-controlled counterparts. A powerful tool for embedding autonomous behaviour is learning by imitation. Hence, in this paper an ensemble of fuzzy inference systems cluster the user input data to identify natural groupings within the data to describe the users movement and actions in a more abstract way. Multiple clustering algorithms are investigated along with a neuro-fuzzy classifier; and an ensemble of fuzzy systems are evaluated.

Estimating fuzzy membership functions parameters by the levenberg-marquardt algorithm

In previous papers from the authors fuzzy model identification methods were discussed. The bacterial algorithm for extracting fuzzy rule base from a training set was presented. The Levenberg-Marquardt algorithm was also proposed for determining membership functions in fuzzy systems. In this paper the Levenberg-Marquardt technique is improved to optimise the membership functions in the fuzzy rules without Ruspini-partition. The class of membership functions investigated is the trapezoidal one as it is general enough and widely used. The method can be easily extended to arbitrary piecewise linear functions as well.

B-spline and neuro-fuzzy models design with function and derivative equalities

The design of neuro-fuzzy models is still a complex problem, as it involves not only the determination of the model parameters, but also its structure. Of special importance is the incorporation of a priori information in the design process. In this paper two known design algorithms for B-spline models will be updated to account for function and derivatives equality restrictions, which are important when the neural model is used for performing single or multi-objective optimization on-line.

Training neuro-fuzzy models using evolution based algorithms

The normal design process for neural networks or fuzzy systems involve two different phases: the determination of the best topology, which can be seen as a system identification problem, and the determination of its parameters, which can be envisaged as a parameter estimation problem. This latter issue, the determination of the model parameters (linear weights and interior knots) is the simplest task and is usually solved using gradient or hybrid schemes. The former issue, the topology determination, is an extremely complex task, especially if dealing with real-world problems.

Design of neuro-fuzzy models by evolutionary and gradient-based algorithms

All systems found in nature exhibit, with different degrees, a nonlinear behavior. To emulate this behavior, classical systems identification techniques use, typically, linear models, for mathematical simplicity. Models inspired by biological principles (artificial neural networks) and linguistically motivated (fuzzy systems), due to their universal approximation property, are becoming alternatives to classical mathematical models. In systems identification, the design of this type of models is an iterative process, requiring, among other steps, the need to identify the model structure, as well as the estimation of the model parameters. This thesis addresses the applicability of gradient-basis algorithms for the parameter estimation phase, and the use of evolutionary algorithms for model structure selection, for the design of neuro-fuzzy systems, i.e., models that offer the transparency property found in fuzzy systems, but use, for their design, algorithms introduced in the context of neural networks. A new methodology, based on the minimization of the integral of the error, and exploiting the parameter separability property typically found in neuro-fuzzy systems, is proposed for parameter estimation. A recent evolutionary technique (bacterial algorithms), based on the natural phenomenon of microbial evolution, is combined with genetic programming, and the resulting algorithm, bacterial programming, advocated for structure determination. Different versions of this evolutionary technique are combined with gradient-based algorithms, solving problems found in fuzzy and neuro-fuzzy design, namely incorporation of a-priori knowledge, gradient algorithms initialization and model complexity reduction.

A Fuzzy-Wavelet Neural Network Model for the Detection of Meat Spoilage using an Electronic Nose

Food product safety is one of the most promising areas for the application of electronic noses. The performance of a portable electronic nose has been evaluated in monitoring the spoilage of beef fillet stored aerobically at different storage temperatures (0, 4, 8, 12, 16 and 20°C). This paper proposes a fuzzy-wavelet neural network model which incorporates a clustering pre-processing stage for the definition of fuzzy rules. The dual purpose of the proposed modeling approach is not only to classify beef samples in the respective quality class (i.e. fresh, semi-fresh and spoiled), but also to predict their associated microbiological population directly from volatile compounds fingerprints. Comparison results indicated that the proposed modeling scheme could be considered as a valuable detection methodology in food microbiology

Prescribed burning impact on forest soil properties – a fuzzy boolean nets approach

The Portuguese northern forests are often and severely affected by wildfires during the Summer season. These occurrences significantly affect and negatively impact all ecosystems, namely soil, fauna and flora. In order to reduce the occurrences of natural wildfires, some measures to control the availability of fuel mass are regularly implemented. Those preventive actions concern mainly prescribed burnings and vegetation pruning. This work reports on the impact of a prescribed burning on several forest soil properties, namely pH, soil moisture, organic matter content and iron content, by monitoring the soil self-recovery capabilities during a one year span. The experiments were carried out in soil cover over a natural site of Andaluzitic schist, in Gramelas, Caminha, Portugal, which was kept intact from prescribed burnings during a period of four years. Soil samples were collected from five plots at three different layers (0–3, 3–6 and 6–18) 1 day before prescribed fire and at regular intervals after the prescribed fire. This paper presents an approach where Fuzzy Boolean Nets (FBN) and Fuzzy reasoning are used to extract qualitative knowledge regarding the effect of prescribed fire burning on soil properties. FBN were chosen due to the scarcity on available quantitative data. The results showed that soil properties were affected by prescribed burning practice and were unable to recover their initial values after one year.

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

An evolving possibilistic fuzzy modeling approach for value-at-risk estimation

Market risk exposure plays a key role for nancial institutions risk management. A possible measure for this exposure is to evaluate losses likely to incurwhen the price of the portfolio's assets declines using Value-at-Risk (VaR) estimates, one of the most prominent measure of nancial downside market risk. This paper suggests an evolving possibilistic fuzzy modeling approach for VaR estimation. The approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based modeling, which employs memberships and typicalities to update clusters and creates new clusters based on a statistical control distance-based criteria. ePFM also uses an utility measure to evaluate the quality of the current cluster structure. Computational experiments consider data of the main global equity market indexes of United States, London, Germany, Spain and Brazil from January 2000 to December 2012 for VaR estimation using ePFM, traditional VaR benchmarks such as Historical Simulation, GARCH, EWMA, and Extreme Value Theory and state of the art evolving approaches. The results show that ePFM is a potential candidate for VaR modeling, with better performance than alternative approaches.

Identificação fuzzy-multimodelos para sistemas não lineares

This paper presents a new multi-model technique of dentification in ANFIS for nonlinear systems. In this technique, the structure used is of the fuzzy Takagi-Sugeno of which the consequences are local linear models that represent the system of different points of operation and the precursors are membership functions whose adjustments are realized by the learning phase of the neuro-fuzzy ANFIS technique. The models that represent the system at different points of the operation can be found with linearization techniques like, for example, the Least Squares method that is robust against sounds and of simple application. The fuzzy system is responsible for informing the proportion of each model that should be utilized, using the membership functions. The membership functions can be adjusted by ANFIS with the use of neural network algorithms, like the back propagation error type, in such a way that the models found for each area are correctly interpolated and define an action of each model for possible entries into the system. In multi-models, the definition of action of models is known as metrics and, since this paper is based on ANFIS, it shall be denominated in ANFIS metrics. This way, ANFIS metrics is utilized to interpolate various models, composing a system to be identified. Differing from the traditional ANFIS, the created technique necessarily represents the system in various well defined regions by unaltered models whose pondered activation as per the membership functions. The selection of regions for the application of the Least Squares method is realized manually from the graphic analysis of the system behavior or from the physical characteristics of the plant. This selection serves as a base to initiate the linear model defining technique and generating the initial configuration of the membership functions. The experiments are conducted in a teaching tank, with multiple sections, designed and created to show the characteristics of the technique. The results from this tank illustrate the performance reached by the technique in task of identifying, utilizing configurations of ANFIS, comparing the developed technique with various models of simple metrics and comparing with the NNARX technique, also adapted to identification

Desenvolvimento de um ambiente para projeto de controladores fuzzy para dispositivos móveis

Fuzzy intelligent systems are present in a variety of equipment ranging from household appliances to Fuzzy intelligent systems are present in a variety of equipment ranging from household appliances to small devices such as digital cameras and cell phones being used primarily for dealing with the uncertainties in the modeling of real systems. However, commercial implementations of Fuzzy systems are not general purpose and do not have portability to different hardware platforms. Thinking about these issues this work presents the implementation of an open source development environment that consists of a desktop system capable of generate Graphically a general purpose Fuzzy controller and export these parameters for an embedded system with a Fuzzy controller written in Java Platform Micro Edition To (J2ME), whose modular design makes it portable to any mobile device that supports J2ME. Thus, the proposed development platform is capable of generating all the parameters of a Fuzzy controller and export it in XML file, and the code responsible for the control logic that is embedded in the mobile device is able to read this file and start the controller. All the parameters of a Fuzzy controller are configurable using the desktop system, since the membership functions and rule base, even the universe of discourse of the linguistic terms of output variables. This system generates Fuzzy controllers for the interpolation model of Takagi-Sugeno. As the validation process and testing of the proposed solution the Fuzzy controller was embedded on the mobile device Sun SPOT ® and used to control a plant-level Quanser®, and to compare the Fuzzy controller generated by the system with other types of controllers was implemented and embedded in sun spot a PID controller to control the same level plant of Quanser®