Continuous function identification with fuzzy cellular automata

Thus far, cellular automata have been used primarily to model the systems consisting of a number of elements which interact with one another only locally; in addition these interactions can be naturally modeled with a discrete type of computation. In this thesis, we will investigate the possibility of a cellular automata application to a problem involving continuous computations, in particular, a problem of continuous function identification from a set of examples. A fuzzy model of cellular automata is introduced and used throughout the study. Two main issues in the context of this application are addressed: representation of real values on a cellular automata structure and a technique which provides cellular automata with a capacity for learning. An algorithm for encoding real values into cellular automata state configurations and a gradient descent type learning algorithm for fuzzy cellular automata are proposed in this thesis. A fuzzy cellular automaton learning system was implemented in a software and its performance studied by means of the experiments. The effects of several system's parameters on its performance were examined. Fuzzy cellular automata demonstrated the capabilities of carrying out complex continuous computations and performing supervised gradient based learning.