Since FLS’s can be represented as layered feedforward networks, the same concept of BP can be applied, to train all design parameters of the FLS. It is a powerful training technique that can be applied to networks with feedforward structure, to turn them into adaptive systems. The backpropagation (BP) algorithm is one of the main reasons that artificial neural networks have gained so much in popularity. The generated fuzzy rules are collected into a common rulebase and combined using fuzzy set theory techniques to construct a final FLS. The one-pass (OP) method, is a table-lookup method that allows us to generate fuzzy rules from given input–output pairs, by performing a simple OP operation on the given numerical and/or linguistic data. One of the most widely used methods for constructing FLS’s, mainly because of its simplicity, is table-lookup. Some of these design methods are data intensive, some are aimed at computational simplicity, some are recursive (thus giving the FLS an adaptive nature), some are offline, and some are application specific. There exists a variety of design methods, such as –,, –,, , –,, ,, ,, ,, to name a few, that can be used to construct FLS’s with different properties and characteristics. As we will show in Section II, a FLS can be expressed as a linear combination of nonlinear functions. Methods to generate the desired surface using a linear combination of basis functions (typically, nonlinear transformations of the input). The authors are with the Signal and Image Processing Institute, Department of Electrical Engineering-Systems, University of Southern California, Los Angeles, CA 90089 USA.
This work was supported by the National Science Foundation under Grant MIP9 419 386. Manuscript received Augrevised February 18, 1997. Within the framework of approximation, and interpolation theory, it is common among many approximation/interpolation In addition, the system produced by the learning algorithm should be able to generalize to certain regions of the multidimensional space where no training data was given, i.e., it should be able to interpolate the given input–output data. Given a set of input–output pairs, the task of learning is essentially equivalent to determining a system that provides an optimal fit to the input–output pairs, with respect to a cost function. Designing a FLS can be viewed as approximating a function, or fitting a complex surface in a (probably) high dimensional space. Unlike conventional stochastic models used to model such processes, FLS’s do not make any assumptions regarding the structure of the process, nor do they invoke any kind of probabilistic distribution model, i.e., they belong to the general family of model-free, data driven, nonparametric methods. Even if the process to be modeled is nonstationary, the system can be updated to reflect the changing statistics of the process. This is one of the most commonly used learning paradigms, called supervised learning. The system can “learn” the nonlinear mapping by being presented a sequence of input signal and desired response pairs, which are used in conjunction with an optimization algorithm to determine the values of the system parameters. The nonlinearity property is particularly important when the underlying physical mechanism to be modeled is inherently nonlinear.
UZZY LOGIC SYSTEMS (FLS’s) are nonlinear systems capable of inferring complex nonlinear relationships between input and output variables. Index Terms- Backpropagation method, chaotic time series, design, forecasting, fuzzy logic systems, one-pass method, RLS method. We compare and illustrate systems designed with each one of the methods, using an example on the predictive modeling of a nonlinear dynamic (chaotic) system.
In order to effectively construct such models, we discuss several design methods with different properties and features. Mouzouris (Invited Paper)Ībstract- We present a formulation of a fuzzy logic system (FLS) that can be used to construct nonparametric models of nonlinear processes, given only input–output data. 11, NOVEMBER 1997ĭesigning Fuzzy Logic Systems Jerry M. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-II: ANALOG AND DIGITAL SIGNAL PROCESSING, VOL.
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