INVITED TALKS - ABSTRACTS

Theory and Applications of Fuzzy Signatures

In Computational Intelligence, in most situations we face problems with the input data being complex and complicated. Some parts of the data are missing or not known yet. In such scenarios, human beings still could come to a decision based on the available data but it is an increasingly difficult problem to construct an effective complex decision model. The concept of fuzzy signatures was introduced to help model these kinds of problems.Fuzzy signatures are sparse hierarchical multi-aggregative fuzzy descriptors, which are aggregated to an atomic value or compared with another fuzzy signature to get a final degree of match. Fuzzy signatures use the hierarchical structure present within a data set to decompose its underlying global relation into several hierarchically organized local relations that can be modeled easily with sets of input sub-spaces. This means that one or several components of the structure are determined at a higher level by a sub-tree of other components with a meaningful aggregation that is specific to that sub-tree. When problems occur with some missing components, the resulting structures of the problem may slightly differ. That means we are still able to find an approximated decomposition to its global relation with the available branches. That is, these available data can be compared and aggregated to a final degree of match.

Neural networks constructed with Fuzzy Flip-Flops

This talk concerns the role that fuzzy norms play in the study of behavior of fuzzy J-K and D flip-flops (F3). We define various types of F3s based on well known operators, presenting their characteristic equations, illustrating their behavior by their respective graphs belonging to various typical values of parameters. Connecting the inputs of the fuzzy J-K flip-flop in a particular way, namely, by applying an additional inverter in the connection of the input J to K (K=1-J), a fuzzy D flip-flop is obtained. When input K is connected to the complemented output (K=1-Q), or in the case of K=1-J, the J-Q(t+1)characteristics of the F3s derived from the Yager, Dombi, Hamacher, Frank, Dubois-Prade and Fodor t-norms present more or less sigmoidal behavior. Two different interpretations of fuzzy D flip-flops is also presented. We pointed out the strong influence of the idempotence axiom in D F3’s behavior. Also we have shown that a few F3 types are suitable for realizing neurons in multilayer perceptrons. A method for constructing Multilayer Perceptron Neural Networks (MLP NN) with the aid of fuzzy systems, particularly by deploying fuzzy flip-flops as neurons is proposed. The aim of this presentation is to present a comparison of the performance of several type neural networks based on fuzzy J-K and also fuzzy D flip-flops (the latter derived from the former type). The behavior of algebraic, Yager, Dombi and Hamacher type fuzzy flip-flop neural networks are presented. The best fitting t-norm and corresponding fuzzy flip-flop type will be presented in terms of function approximation capability.

On white noise representability and model-recostruction of stochastic systems (with applications)

The paper presents different important representations for system identification of dynamical models. The presentation compares the various (canonical) parametrization possibilities of a rational (analytic or coanalytic, casual or anticausal) spectral factor using system invariants. It also shows how to transform the forward (backward) state-space representations into forward (backward) ARMA and MFD forms. The problem of controllability, observability, constructability and their reachability, and their relationships to the internal and external model types are also discussed in detail. We show that they can be used for the analysis of acausal spectral factors, when there is no specification on the pole structure of the corresponding transfer function. An immediate consequence of this fact is that different spectral factors may share the same state-space. The zero structure of the spectral factors is also mentioned proving that it depends only on the state-space. The lecture shows 16 different canonical representations for the practical identification of dynamic systems. Finally, the paper presents interesting applications too, in the modeling and identification of vehicle systems dynamics.