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.

Genetic programming and bacterial algorithm for neural networks and fuzzy systems design

In the field of control systems it is common to use techniques based on model adaptation to carry out control for plants for which mathematical analysis may be intricate. Increasing interest in biologically inspired learning algorithms for control techniques such as Artificial Neural Networks and Fuzzy Systems is in progress. In this line, this paper gives a perspective on the quality of results given by two different biologically connected learning algorithms for the design of B-spline neural networks (BNN) and fuzzy systems (FS). One approach used is the Genetic Programming (GP) for BNN design and the other is the Bacterial Evolutionary Algorithm (BEA) applied for fuzzy rule extraction. Also, the facility to incorporate a multi-objective approach to the GP algorithm is outlined, enabling the designer to obtain models more adequate for their intended use.

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.

Bacterial algorithm applied for fuzzy rule extraction

This paper presents a method of using the so-colled "bacterial algorithm" (4,5) for extracting a fuzzy rule base from a training set. The bewly proposed bacterial evolutionary algorithm (BEA) is shown. In our application one bacterium corresponds to a fuzzy rule system.

Anytime information processing based on fuzzy and neural network models

In modern measurement and control systems, the available time and resources are often not only limited, but could change during the operation of the system. In these cases, the so-called anytime algorithms could be used advantageously. While diflerent soft computing methods are wide-spreadly used in system modeling, their usability in these cases are limited.

Completely supervised training algorithms for B-spline neural networks and neuro-fuzzy systems

Complete supervised training algorithms for B-spline neural networks and fuzzy rule-based systems are discussed. By interducing the relationship between B-spline neural networks and certain types of fuzzy models, training algorithms developed initially for neural networks can be adapted by fuzzy systems.

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.

Fuzzy rule extraction from input/output data

Several alternative approaches have been discussed: Levenberg-Marquardt - no satisfactory convergence speed + local minimum, Bacterial algorithm - problems with large dimensionality (speed), Clustering - no safe criterion for number of clusters + dimentionality problem.

Fuzzy model identification by evolutionary, gradient based and memtic algorithms

One of the crucial problems of fuzzy rule modeling is how to find an optimal or at least a quasi-optimal rule base fro a certain system. In most applications there is no human expert available, or, the result of a human expert's decision is too much subjective and is not reproducible, thus some automatic method to determine the fuzzy rule base must be deployed.

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.

Generate disaggregated soil allocation data using a Minimum Cross Entropy Model

Montado ecosystem in the Alentejo Region, south of Portugal, has enormous agro-ecological and economics heterogeneities. A definition of homogeneous sub-units among this heterogeneous ecosystem was made, but for them is disposal only partial statistical information about soil allocation agro-forestry activities. The paper proposal is to recover the unknown soil allocation at each homogeneous sub-unit, disaggregating a complete data set for the Montado ecosystem area using incomplete information at sub-units level. The methodological framework is based on a Generalized Maximum Entropy approach, which is developed in thee steps concerning the specification of a r order Markov process, the estimates of aggregate transition probabilities and the disaggregation data to recover the unknown soil allocation at each homogeneous sub-units. The results quality is evaluated using the predicted absolute deviation (PAD) and the "Disagegation Information Gain" (DIG) and shows very acceptable estimation errors.

Combined disaggregation of agricultural land uses, livestock numbers and crops' production: an entropy approach

This paper presents several combined agricultural data disaggregation models in order to recover the farms' land uses, the livestock numbers and main crops' productions. The proposed approach estimates incomplete information at disaggregated level through entropy, using an information prior, and generating information for a combined calculation use of data in the estimation of other variables. The models were applied to the region of Algarve, to some rural pilot areas (Salir-Ameixial-Cachopo and Alcoutim) for livestock data, since this data in some Algarve's inland areas is needed for a European forest fire prevention project, and to the agrarian zones in a more complex framework. The results are promising. They were validated, in cross reference to real data, having proven to be valid and reliable. The total error was small and a considerable level of information heterogeneity was recovered. The total error was about 27,9% for the counties' land uses and 21% for the agrarian zones, and for the livestock it was also acceptable. The level of heterogeneity recovered was always higher than 50%, revealing some improvements regarding previous studies.