2,588 research outputs found
Time series prediction by perturbed fuzzy model
This paper presents a fuzzy system
approach to the prediction of nonlinear
time series and dynamical systems based
on a fuzzy model that includes its
derivative information. The underlying
mechanism governing the time series,
expressed as a set of IFâTHEN rules, is
discovered by a modified structure of fuzzy
system in order to capture the temporal
series and its temporal derivative information.
The task of predicting the future is
carried out by a fuzzy predictor on the
basis of the extracted rules and by the
Taylor ODE solver method. We have
applied the approach to the benchmark
Mackey-Glass chaotic time series.This work was supported by the Portuguese Fundação para a CiĂȘncia e a Tecnologia (FCT) under grant POSI/SRI/41975/2001
A novel computational approach to approximate fuzzy interpolation polynomials
This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form yp=anxnp+âŻ+a1xp+a0 where aj is crisp number (for j=0,âŠ,n), which interpolates the fuzzy data (xj,yj)(forj=0,âŠ,n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient
Systems Structure and Control
The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc
Learning fuzzy systems: an ojective function-approach
One of the most important aspects of fuzzy systems is that they are
easily understandable and interpretable. This property, however, does not
come for free but poses some essential constraints on the parameters of a
fuzzy system (like the linguistic terms), which are sometimes overlooked when
learning fuzzy system automatically from data. In this paper, an objective
function-based approach to learn fuzzy systems is developed, taking these
constraints explicitly into account. Starting from fuzzy c-means clustering,
several modifications of the basic algorithm are proposed, affecting the shape
of the membership functions, the partition of individual variables and the
coupling of input space partitioning and local function approximation
HÀgusad teist liiki integraalvÔrrandid
KÀesolevas doktoritöös on uuritud hÀgusaid teist liiki integraalvÔrrandeid. Need vÔrrandid sisaldavad hÀgusaid funktsioone, s.t. funktsioone, mille vÀÀrtused on hÀgusad arvud.
Me tĂ”estasime tulemuse sileda tuumaga hĂ€gusate Volterra integraalvĂ”rrandite lahendite sileduse kohta. Kui integraalvĂ”rrandi tuum muudab mĂ€rki, siis integraalvĂ”rrandi lahend pole ĂŒldiselt sile. Nende vĂ”rrandite lahendamiseks me vaatlesime kollokatsioonimeetodit tĂŒkiti lineaarsete ja tĂŒkiti konstantsete funktsioonide ruumis. Kasutades lahendi sileduse tulemusi tĂ”estasime meetodite koonduvuskiiruse.
Me vaatlesime ka nĂ”rgalt singulaarse tuumaga hĂ€gusaid Volterra integraalvĂ”rrandeid. Uurisime lahendi olemasolu, ĂŒhesust, siledust ja hĂ€gusust. Ălesande ligikaudseks lahendamiseks kasutasime kollokatsioonimeetodit tĂŒkiti polĂŒnoomide ruumis. TĂ”estasime meetodite koonduvuskiiruse ning uurisime lĂ€hislahendi hĂ€gusust. Nii analĂŒĂŒs kui ka numbrilised eksperimendid nĂ€itavad, et gradueeritud vĂ”rke kasutades saame parema koonduvuskiiruse kui ĂŒhtlase vĂ”rgu korral.
Teist liiki hĂ€gusate Fredholmi integraalvĂ”rrandite lahendamiseks pakkusime uue lahendusmeetodi, mis pĂ”hineb kĂ”igi vĂ”rrandis esinevate funktsioonide lĂ€hendamisel TĆĄebÔƥovi polĂŒnoomidega. Uurisime nii tĂ€pse kui ka ligikaudse lahendi olemasolu ja ĂŒhesust. TĂ”estasime meetodi koonduvuse ja lĂ€hislahendi hĂ€gususe.In this thesis we investigated fuzzy integral equations of the second kind. These equations contain fuzzy functions, i.e. functions whose values are fuzzy numbers.
We proved a regularity result for solution of fuzzy Volterra integral equations with smooth kernels. If the kernel changes sign, then the solution is not smooth in general. We proposed collocation method with triangular and rectangular basis functions for solving these equations. Using the regularity result we estimated the order of convergence of these methods.
We also investigated fuzzy Volterra integral equations with weakly singular kernels. The existence, regularity and the fuzziness of the exact solution is studied. Collocation methods on discontinuous piecewise polynomial spaces are proposed. A convergence analysis is given. The fuzziness of the approximate solution is investigated. Both the analysis and numerical methods show that graded mesh is better than uniform mesh for these problems.
We proposed a new numerical method for solving fuzzy Fredholm integral equations of the second kind. This method is based on approximation of all functions involved by Chebyshev polynomials. We analyzed the existence and uniqueness of both exact and approximate fuzzy solutions. We proved the convergence and fuzziness of the approximate solution.https://www.ester.ee/record=b539569
Best Approximation Results for Fuzzy-Number-Valued Continuous Functions
In this paper, we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued continuous function and a real-valued one. Then, we prove the existence of the best approximation of a fuzzy-number-valued continuous function to the space of real-valued continuous functions by using the well-known Michael selection theorem
The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions
A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model
Low rank surrogates for polymorphic fields with application to fuzzy-stochastic partial differential equations
We consider a general form of fuzzy-stochastic PDEs depending on the interaction of probabilistic
and non-probabilistic ("possibilistic") influences. Such a combined modelling of aleatoric
and epistemic uncertainties for instance can be applied beneficially in an engineering context for
real-world applications, where probabilistic modelling and expert knowledge has to be accounted
for. We examine existence and well-definedness of polymorphic PDEs in appropriate function
spaces. The fuzzy-stochastic dependence is described in a high-dimensional parameter space,
thus easily leading to an exponential complexity in practical computations.
To aleviate this severe obstacle in practise, a compressed low-rank approximation of the problem
formulation and the solution is derived. This is based on the Hierarchical Tucker format which
is constructed with solution samples by a non-intrusive tensor reconstruction algorithm. The performance
of the proposed model order reduction approach is demonstrated with two examples.
One of these is the ubiquitous groundwater flow model with Karhunen-Loeve coefficient field
which is generalized by a fuzzy correlation length
Fuzzy System Identification Based Upon a Novel Approach to Nonlinear Optimization
Fuzzy systems are often used to model the behavior of nonlinear dynamical systems in process control industries because the model is linguistic in nature, uses a natural-language rule set, and because they can be included in control laws that meet the design goals. However, because the rigorous study of fuzzy logic is relatively recent, there is a shortage of well-defined and understood mechanisms for the design of a fuzzy system. One of the greatest challenges in fuzzy modeling is to determine a suitable structure, parameters, and rules that minimize an appropriately chosen error between the fuzzy system, a mathematical model, and the target system. Numerous methods for establishing a suitable fuzzy system have been proposed, however, none are able to demonstrate the existence of a structure, parameters, or rule base that will minimize the error between the fuzzy and the target system.
The piecewise linear approximator (PLA) is a mathematical construct that can be used to approximate an input-output data set with a series of connected line segments. The number of segments in the PLA is generally selected by the designer to meet a given error criteria. Increasing the number of segments will generally improve the approximation. If the location of the breakpoints between segments is known, it is a straightforward process to select the PLA parameters to minimize the error. However, if the location of the breakpoints is not known, a mechanism is required to determine their locations. While algorithms exist that will determine the location of the breakpoints, they do not minimize the error between data and the model. This work will develop theory that shows that an optimal solution to this nonlinear optimization problem exists and demonstrates how it can be applied to fuzzy modeling.
This work also demonstrates that a fuzzy system restricted to a particular class of input membership functions, output membership functions, conjunction operator, and defuzzification technique is equivalent to a piecewise linear approximator (PLA). Furthermore, this work develops a new nonlinear optimization technique that minimizes the error between a PLA and an arbitrary one-dimensional set of input-output data and solves the optimal breakpoint problem. This nonlinear optimization technique minimizes the approximation error of several classes of nonlinear functions leading up to the generalized PLA. While direct application of this technique is computationally intensive, several paths are available for investigation that may ease this limitation. An algorithm is developed based on this optimization theory that is significantly more computationally tractable. Several potential applications of this work are discussed including the ability to model the nonlinear portions of Hammerstein and Wiener systems
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