László Gál

Improvements to the bacterial memetic algorithm used for fuzzy rule base extraction

In this paper we discuss new methods to improve the bacterial memetic algorithm (BMA) used for fuzzy rule base extraction. The first two methods are knot order violation handling methods which improves the performance of the BMA rather in the case of more complex fuzzy rule base. The third method is a new modification of the BMA in which the order of the operators is modified. This method improves the performance of the BMA rather in the case of less complex fuzzy rule base.

Function approximation capability of a novel fuzzy flip-flop based neural network

The function approximation capability of various connectionist systems has been one of the most interesting problems. A method for constructing Multilayer Perceptron Neural Networks (MLP NN) with the aid of fuzzy operations based flip-flops able to approximate single and multiple variable functions is proposed. This paper introduces the concept of fuzzy flip-flop based neural network, particularly by deploying three types of fuzzy flip-flops as neurons. A comparative study of feedbacked fuzzy J-K and two kinds of fuzzy D flip-flops used as neurons, based on fuzzy algebraic, Yager, Dombi, Hamacher and Frank operations is given. Simulation results are presented for several test functions.

Function approximation performance of Fuzzy Neural Networks based on frequently used fuzzy operations and a pair of new trigonometric norms

A new triangular t-norm and t-conorm are presented. The new fuzzy operations combined with the standard negation are applied in a practical problem, namely, they are proposed as suitable triangular norms for defining a fuzzy flip-flop based neuron. Other fuzzy J-K and D flip-flop based neurons are constructed by using algebraic, Łukasiewicz, Yager, Dombi and Hamacher connectives. The function approximation performance of a Fuzzy Neural Networks (FNN) built up from various fuzzy neurons are evaluated using six increasingly more complicated problems: various sine waves, battery cell charging characteristics, two dimensional trigonometric functions and a six dimensional benchmark problem. It is shown that the new norms lead to FNNs with better approximation properties in some cases than all the previous ones.

Modified bacterial memetic algorithm used for fuzzy rule base extraction

In this paper we discuss an improved version of the Bacterial Memetic Algorithm (BMA) used for fuzzy rule base extraction. In previous works we have found several ways to improve the original BMA. Some of them perform well rather in the case of more complex fuzzy rule base, and some of them perform well rather in the case of less complex fuzzy rule base. We have combined the improvements into a new version of the BMA that performs well in each case investigated.

Multilayer Pereeptron implemented by fuzzy flip-flops

The paper introduces a novel method for constructing multilayer perceptron (MLP) neural networks (NN) with the aid of fuzzy systems, particularly by deploying fuzzy J-K flip-flops as neurons. The next state Q(t+1) of the J-K fuzzy flip-flops (F3) in terms of input J can be characterized by a more or less S-shaped function, for each F3 derived from the Yager, Dombi, and Fodor norms and co-norms. In this approach, J represents the neuron input. The other input K is wired to the complemental output (K 1-Q), thus an elementary fuzzy sequential unit with a single input and a single output is received The algebraic F3 having linear J-Q(t+1) characteristics is added to the above three. The paper proposes the investigation of the possibility of constructing multilayer perceptrons from such real fuzzy hardware units. Each of the four candidates for F3-based neurons is examined for its training capability by evaluating and comparing the approximation capabilities for two different transcendental functions. Simulation results are presented.

Fuzzy rule base extraction by the improved Bacterial Memetic Algorithm

In this paper we introduce new methods for handling knot order violation occurred in the bacterial memetic algorithm (BMA) used for fuzzy rule base extraction. These methods perform slightly better than the method used before and are easier to integrate with the bacterial memetic algorithm.

Learning the optimal parameter of the Hamacher t-norm applied for fuzzy-rule-based model extraction

Mamdani-type inference systems with trapezoidal-shaped fuzzy membership functions play a crucial role in a wide variety of engineering systems, including real-time control, transportation and logistics, network management, etc. The automatic identification or construction of such fuzzy systems input output data is one of the key problems in modeling. In the past years, the authors have investigated several different fuzzy t-norms, among others, algebraic and trigonometric ones, and the Hamacher product by substituting the standard “min” t-norm operation, in order to achieve better model fitting. In the present paper, the focus is on examining the general parametric Hamacher t-norm, where the free parameter quite essentially influences the quality of modeling and the learning capability of the model identification system. Based on a wide scope of simulation experiments, a quasi-optimal interval for the value of the Hamacher operator is proposed.

Three Step Bacterial Memetic Algorithm

In order to study the function approximation performance of Fuzzy Neural Networks built up from fuzzy J-K flip-flop neurons a new learning algorithm, the Three Step Bacterial Memetic Algorithm is proposed. Hybrid evolutionary methods that combine genetic type algorithms with “classic” local search have been applied to perform efficient global search. This novel version of the Bacterial Memetic Algorithm with Modified Operator Execution Order (BMAM) is a recently developed technique of hybrid type. This particular merger of evolutionary and gradient based algorithms combining both global and local search consists of bacterial mutation and, as a second step, the Levenberg-Marquardt (LM) method applied for each clone. This LM step saves in this way some potential solutions that could be lost otherwise after each mutation step. As a third step the LM algorithm is recalled for a few iterations for each individual of the population towards reaching the local optimum. In our novel algorithm various kinds of fast algorithm with less complexity, like Quasi-Newton algorithm, Conjugate Gradient algorithm, and two Backpropagation training algorithms: Gradient Descent and Gradient Descent with Adaptive Learning Rate and Momentum are nested in the bacterial mutation.

Fuzzy Rule Base Model Identification by Bacterial Memetic Algorithms

Fuzzy systems have been successfully used in the area of controllers for a long time. The Mamdani method is one of the most popular inference systems for practical applications. The main problem of Mamdani-type inference system and other fuzzy logic based controllers is how to gain the fuzzy rules the inference system based on. Several approaches have been proposed for automatic rule base identification. The bacterial type evolutionary algorithms have been successfully applied for solving this task. These algorithms are based on the Pseudo-Bacterial Genetic Algorithm and are supplied with operations and methods (e.g. the Levenberg-Marquardt method) to complete their task more efficiently. The goal is to create more accurate fuzzy rule bases from input-output data sets as quickly as possible. In this work, we summarize the bacterial type evolutionary algorithms used for fuzzy rule base identification.

Fuzzy Flip-Flop based Neural Networks as a novel implementation possibility of multilayer perceptrons

Fuzzy Flip-Flop based Neural Networks (FNN) constructed from fuzzy D flip-flops are studied as a novel technique to implement multilayer perceptrons. The starting point of this approach is the concept of fuzzy flip-flop (F3), as the extension of the binary counterpart. Fuzzy D flip-flop based neurons are viewed, as sigmoid function generators. Their characteristic equations contain simple fuzzy operations, thus enabling easy implementability. FNNs have an interconnected fuzzy neuron structure composed from a large number of neurons acting in parallel which are capable of learning, and are suitable for function approximation. In this paper we propose the FPGA implementation of Łukasiewicz operations, furthermore of fuzzy D flip-flop neurons based on Łukasiewicz norms.