Fuzzy Expert Networks
H.C. Fu, Jean Jyh-Jiun Shann · 1993
The proposed fuzzy expert network is an event-driven, acyclic neural network designed for fine knowledge learning of a fuzzy expert system. The coarse knowledge, i.e. fuzzy rules, of a fuzzy expert system can be constructed in the structure of the network. The fuzzy expert network contains five types of nodes: Input, Membership-Function, AND, OR, and Defuzzification Nodes. Each input node of the fuzzy expert network represents an input variable of the fuzzy expert system, and is used as a buffer to broadcast the input to its membership-function nodes. Each membershipfunction node represents one of the membership functions associated with a particular variable. We define a modified Quadratic Sigmoid function [1] to approximate a trapezoidal normalized membership function. Each AND node represents the IF-part of some fuzzy rules. We define a parametric operation, called Fuzzy-MIN, which combines the upper bound (the min operator) and the lower bound (the drastic product) [2] of fuzzy intersections for the AND nodes. Each OR node represents the THEN-part of some fuzzy rules. Therefore, the operation performed in an OR node is to integrate the rules of the same consequence. We define another parametric operation, called Fuzzy-MAX, which combines the lower bound (the max operator) and the upper bound (the drastic sum) [2] of fuzzy unions for the OR nodes. Each defuzzification node represents either an intermediate variable or an output variable, and performs the defuzzification of all the related membership functions. The backpropagation-like learning used in the network is focused on the learning of fine knowledge including the certainty factors of fuzzy rules, and the parameters of the fuzzy-MIN and fuzzy-MAX operations. The learning rules for the adjustment of certainty factors, the parameters of the operations of AND nodes, and the parameters of the operations of OR nodes are based on the gradient descent search. The evaluation of the gradients for adjustment of the learnable items of the network were derived. A general purpose simulator of the proposed fuzzy expert network has been implemented in a Sun SPARC station. An exemplar fuzzy expert system was converted to a fuzzy expert network for observing the behavior of the network. After the fine knowledge learning, the fuzzy expert network contains precise knowledge such that the output can be produced in a more accurate manner than that of the original fuzzy system. In the near future, we plan to further study on the learnability of the parameters of membership functions.