Fuzzy systems and wavelets: relationship study

摘要

This paper considers the complementarity and equivalence relationships between fuzzy systems and wavelets. Under the framework of function approximation, basic elements of fuzzy systems and wavelets theory will firstly be reviewed. With the specific choices of fuzzy membership function and scaling function, it is shown that fuzzy system is actually complement to wavelets in function space. Equivalence relation-ship is further explored by the introduction of multiscale fuzzy systems. These relationships imply that advances in one field, such as structure or parameter learning algorithms or accuracy and convergence analysis, etc., can be carried over directly to the other.