VHDL Framework for Modeling Fuzzy Automata

Fuzzy set theory has been used to extend different domains of mathematics and also domains from applied sciences and from engineering, such that now there exists fuzzy logic, fuzzy arithmetic, fuzzy expert systems, fuzzy logic controllers (FLCs), fuzzy automata, fuzzy flip-flops, etc. In this work we concentrate on fuzzy automata (FA), which are fuzzy logic extensions of crisp automata (or finite state machines). Many researchers have noticed that, while crisp automata are widely used, being incorporated in almost any technical device, fuzzy automata have very few practical applications, being rather a theoretic concept. Among the factors that contributed to this situation we can enumerate: 1) the lack of controllability of FA (in certain conditions the degree of membership of the states of FA decrease towards zero and cannot be increased after that) and 2) there are too many types of fuzzy automata. We developed a VHDL framework that can be used for modeling fuzzy automata and for investigating their performance. In this paper we use several examples of FA from literature in order to illustrate how our VHDL framework can investigate the efficiency of different functions used for computing the degree of membership of the next state of a FA. We also show that some techniques proposed in literature for improving the performance of FA (more precisely, to avoid the degree of membership of FA states to decrease toward zero) are not effective on the fuzzy automata from these examples.