László T. Kóczy

Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases

Abstract Rule based fuzzy approximate reasoning uses various techniques of modified modus ponens . The observation is in most cases not identical with any of the antecedents in the rules. However, a conclusion still can be computed by using some combination of all consequents where an overlapping of observation and antecedent is present. If the rule base is sparse, i.e., it contains insufficient information on the total state space, it might occur that an observation has absolutely no overlapping with any of the antecedents and so not even a single rule is fired, i.e., no conclusion can be computed on the basis of modus ponens . In such a case, interpolative reasoning in the strict sense can be applied: some kind of (weighted) average of the flanking rules is calculated. This technique can be extended to a form of extrapolation, when the observation is not flanked from both sides. Linear interpolation and extrapolation is presented, and then the idea is extended to arbitrary approximation.

Algebraic fuzzy flip-flop circuits

Abstract Algebraic fuzzy flip-flop circuits in discrete and continuous mode are presented. The algebraic fuzzy flip-flop is one example of the general fuzzy flip-flop concept which has been defined as an extension of the binary J - K flip-flop. Two types of the algebraic fuzzy flip-flop, which are reset type and set type, are defined using complementation, algebraic product, and algebraic sum operations for fuzzy negation, t-norm, and s-norm, respectively. A unified equation of the reset type and set type of an algebraic fuzzy flip-flop is derived for the purpose of realization of hardware circuits. Based on the equation, two types of hardware circuits, in discrete mode and continuous mode, are constructed. Moreover the characteristics of various fuzzy flip-flops presented previously are investigated such as min-max fuzzy flip-flop in both discrete and continuous mode, and the algebraic fuzzy flip-flop presented in this paper.

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.

Fuzzy flip-flop

A great deal of research had been directed towards the realization of a ‘fuzzy computer’. A few types of fuzzy processors which can perform various fuzzy operations, e.g. fuzzy negation, min, max and fuzzy inference, have been proposed and realized by Yamakawa [1, 2] and Togai [3]. These fuzzy inference chips have opened new opportunities for artificial intelligence. However, all of them were based on single-step fuzzy inference. In oder to realize multi-stage fuzzy inference, fuzzy memory modules are indispensable. In the case of an ‘ordinary’ computer, a binary flip-flop circuit, which can memorize single bits of information has been widely used as a fundamental element of memory modules.

Comparison of Various Evolutionary and Memetic Algorithms

Optimization methods known from the literature include gradient based techniques and evolutionary algorithms. The main idea of the former methods is to calculate the gradient of the objective function at the actual point and then to step towards better values according to this function value. Evolutionary algorithms imitate a simplified abstract model of evolution observed in the nature. Memetic algorithms traditionally combine evolutionary and other, e.g. gradient techniques to exploit the advantages of both methods. Our current research aims to discover the properties, especially the efficiency (i.e. the speed of convergence) of particular evolutionary and memetic algorithms. For this purpose the techniques are compared by applying them on several numerical optimization benchmark functions and on machine learning problems.

Signatures: Definitions, operators and applications to fuzzy modelling

This paper presents a new framework for the symbolic representation of data which is referred to as signatures. The definitions of signatures and of signature trees are first given. Original operators on signatures are next presented, i.e., contraction, extension, pruning, addition, multiplication, and grafting. Attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed. An example is included to accompany the theoretical results.

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.

Comparative analysis of interpolative and non-interpolative fuzzy rule based machine learning systems applying various numerical optimization methods

In this paper interpolative and non-interpolative fuzzy rule based machine learning systems are investigated by using simulation results. The investigation focuses mainly on two objectives: to compare the efficiency of the inference techniques combined with different numerical optimization methods for solving machine learning problems and to discover the difference between the properties of systems applying interpolative and non-interpolative inference techniques.

A concept reduction approach for fuzzy cognitive map models in decision making and management

Abstract Policy making, strategic planning and management in general are complex decision making tasks, where the formulation of a quantitative mathematical model may be difficult or impossible due to lack of numerical data and dependence on imprecise verbal expressions. For such systems, knowledge representation graphs and cognitive maps are most familiar and often used for modelling complexity and aiding decision making. Fuzzy Cognitive Maps (FCM), as graph-based cognitive models, have been successfully used for knowledge representation and reasoning. In modelling complex systems usually a large number of concepts need to be considered. However, it is often difficult in real applications to find the appropriate number of concepts. Using only a few concepts is not enough to represent the modelled system with the required precision, and increasing the number of concepts increases the complexity of the model quadratically; it is burdensome to work with for the experts. The contribution of this paper is two-fold: (i) to propose a new concept reduction approach for FCM and (ii) to apply it on developing less complex FCM for management and decision making. The behaviour of reduced models is analysed through a number of scenarios with respect to the original complex system. The main idea of the reduction is a clustering based on fuzzy tolerance relations. The new approach is focused on reducing complexity in the modelling process, which provides a more transparent and easy to use model for policy makers. The applicability of the proposed method is demonstrated via literature examples and a solid waste management case study that initiated this research. The results clearly show the advantageous characteristics of the proposed concept reduction method for FCM and its aid in policy making.

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.