Algorithms of multilevel synthesis of fuzzy functions

This paper presents a new method of multilevel synthesis of fuzzy functions obtained from the behavioural description of a fuzzy system being implemented. New methodology relies on representing the fuzzy functions by logic expressions in the form of polynomials, which can be transformed according to the rules of polynomial algebra. The transformations are based on the extraction of common subexpressions, which is supported by a new algorithm of fuzzy division. As a result of the synthesis, the minimised multilevel structure of the fuzzy cells is obtained.