COMPRESSION AND EXPANSION OF FUZZY RULE BASES BY USING CRISP-FUZZY NEURAL NETWORKS

A fuzzy neural network with knowledge discovery (FNNKD) is designed to perform adaptive compensatory fuzzy reasoning based on more useful an d more heuristic primary fuzzy sets. In order to overcome the weakness of the conventional crisp neural network and the fuzzy operation-orie nted neural network, we have developed a general fuzzy reasoning-orien ted fuzzy neural network called a crisp-fuzzy neural network (CFNN) th at is capable of extracting high-level knowledge such as fuzzy IF-THEN rules from either crisp data or fuzzy data. A CFNN can effectively co mpress a 5 X 5 fuzzy IF-THEN rule base of a cart-pole balancing system to a 3 X 3 one, then to a 2 X 2 one, and finally to a 1 X 1 one, and can expand on invalid sparse 3 x 3 fuzzy IF-THEN rule base of a cart-p ole balancing system to a valid 5 X 5 one. In addition, a CFNN can con trol a more complex cart-pole balancing system with random fuzzy noise inputs and outputs (i.e., nonconventional using crisp inputs and outp uts without any noise). The simulations have indicated that a CFNN is an efficient neurofuzzy system with abilities to discover new fuzzy kn owledge from either numerical data or fuzzy data, compress and expand fuzzy knowledge, and do fuzzy reasoning.