This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork -based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an input-output mapping based on both human knowledge (in the form of fuzzy if-then rules) and stipulated input-output data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components on-linely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with ill-define...

This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational power, etc., can be applied to both models directly. It is of interest to observe that twomodels stemming from different origins turn out to be functional equivalent.

Fundamental and advanced developments in neuro-fuzzy synergisms for modeling and control are reviewed. The essential part of neuro-fuzzy synergisms comes from a common framework called adaptive networks, which unifies both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (Adaptive-Network-based Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neuro-fuzzy approaches are also addressed.

In this article advantages of various neural transfer functions are discussed.

The problem of generation desirable fuzzy rules is very important in the development of fuzzy systems. The purpose of this paper is to present a generation method of fuzzy control rules by learning from examples using genetic algorithms. We propose a real coded genetic algorithm for learning fuzzy rules, and an iterative process for obtaining a set of rules which covers the examples set with a covering value previously defined. Keywords: Fuzzy rules, learning, genetic algorithms. 1. Introduction Fuzzy rules based systems have been shown to be an important tool for modeling complex systems, where due to the complexity or the imprecision, classical tools are unsuccessful. In [19, 5] it was proved that fuzzy systems are universal approximators in the sense that for any continuous systems is possible to find a set of fuzzy rules able of approximating it with arbitrary accuracy. The problem is how to find the rules. There are different modes to derive them: - Based on Expert Experience ...

The problem of controlling processes that operate within a wide range of operating conditions is addressed. The operation of the process is decomposed into a set of operating regimes, and simple local state-space model structures are developed for each regime. These are combined into a global model structure using an interpolation method. Unknown local model parameters are identified using empirical data. The control problem is solved using a model predictive controller based on this model representation. As an example, a simulated batch fermentation reactor is studied. The model-based controller's performance is compared to the performance with an exact process model, and a linear model. It is experienced that a non-linear model with good prediction capabilities can be constructed using elementary and qualitative process knowledge combined with a sufficiently large amount of process data.

: We consider the problem of data-driven rule based modeling, where one tries to obtain fuzzy if-then rules that describe the relations between the relevant systems variables. Different modeling approaches have been proposed, however, most of them emphasize the function approximation capabilities of fuzzy systems, and little attention is paid to the inspectability of the rule base [1]. The inspectability is strongly related to the number of rules used by the model and to the partitioning of the input space (premise of the rule base). Fuzzy clustering methods have proven useful for obtaining this partitioning from data and to identify the rule base. Unlike the common approach of unsupervised clustering of the premise space, for systems identification it is useful to "supervise" the clustering by considering the product space of the in- and outputs. The cluster algorithm then seeks to establish groups within the data that are homogenous with regard to both the structure in the input as i...

This paper presents an innovative approach to the structure determination problem in fuzzy modeling. By using the well-known CART (classification and regression tree) algorithm as a quick preprocess, the proposed method can roughly estimate the structure (numbers of membership functions and number of fuzzy rules, etc.) of a fuzzy inference system; then the parameter identification is carried out by the hybrid learning scheme developed in our previous work [3, 2, 5]. Morevoer, the identified fuzzy inference system has the property that the total of firing strengths is always equal to one; this speeds up learning processes and reduces round-off errors. 1 Introduction Fuzzy modeling [11, 10] is a new branch of system identification which concerns with the construction of a fuzzy inference system (or fuzzy model) that can predict and hopefully explain the behavior of an unknown system described by a set of sample data. Two primary tasks of fuzzy modeling are structure determination...

We present a method for the learning of fuzzy logic membership functions and rules to approximate a numerical function from a set of examples of the function's independent variables and the resulting function value. This method uses a three-step approach to building a complete function approximation system: first, learning the membership functions and creating a cell-based rule representation; second, simplifying the cell-based rules using an informationtheoretic approach for induction of rules from discrete-valued data; and finally, constructing a computational (neural) network to compute the function value given its independent variables. This function approximation system is demonstrated with a simple control example: learning the truck and trailer backer-upper control system. I. Introduction The problem of approximating a function from a set of examples can be solved in a multitude of ways, including mathematicalmethods using an explicit model for the function to be learned and mo...

To design a fuzzy rule-based classi cation system (fuzzy classi er) with good generalization abilityina high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high (or even in nite) dimensional feature space. This paper investigates the connection between fuzzy classi ers and kernel machines, establishes a link between fuzzy rules and kernels, and proposes a learning algorithm for fuzzy classi ers. We rst show that a fuzzy classi er implicitly de- nes a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function. Fuzzy inference on the IF-part of a fuzzy rule can be viewed as evaluating the kernel function. The kernel function is then proven to be a Mercer kernel if the reference functions meet certain spectral requirement. The corresponding fuzzy classi er is named positive de - nite fuzzy classi er (PDFC). A PDFC can be built from the given training samples based on a support vector learning approach with the IF-part fuzzy rules given by the support vectors. Since the learning process minimizes an upper bound on the expected risk (expected prediction error) instead of the empirical risk (training error), the resulting PDFC usually has good generalization. Moreover, because of the sparsity properties of the SVMs, the number of fuzzy rules is irrelevant to the dimension of input space. In this sense, weavoid the \curse of dimensionality." Finally, PDFCs with dierent reference functions are constructed using the su...