Abstract   This paper considers the complementarily and equivalence relationships between convex fuzzy systems with symmetry restrictions 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 convex fuzzy system with symmetry restrictions is actually complement to wavelets in function space. Equivalence relationship is further explored by the introduction of multi-scale 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.
['Yi Yu', 'Shaohua Tan']
Complementarity and equivalence relationships between convex fuzzy systems with symmetry restrictions and wavelets