An AND-OR Fuzzy Neural Network

Abstract

Fuzzy neural network combines the theories of fuzzy logical and neural network, including learning, association, identification, self-adaptation and fuzzy information process. The logic neurons have received much concern all the time as the important components of neural networks. From the models designing to the algorithms studying, there are many achievements. Glorennec[1]proposed a general artificial neuron to realize Lukasiewicz logical operate. Yager[2] employed a group of OWA fuzzy Aggregation operators to form OWA neuron. Pedrycz and Rocha [3] proposed aggregation neurons and referential neurons by integrating fuzzy logic and neural network and discuss the relation about the ultimate network structure and practical problem; Pedrycz i.e. [4],[5],[6] constructed a knowledgebased network by AND, OR neurons to solve classified problem and pattern recognition. Bailey i.e. [7] extended the single hidden layer to two hidden layers for improve complex modeling problems. Pedrycz and Reformat designed fuzzy neural network constructed by AND, OR neurons to modeling the house price in Boston [8]. We consider this multi-input-single-output (MISO) fuzzy logic-driven control system based on Pedrycz. Pedrycz[8] transformed T norm and S norm into product and probability operators, formed a continuous and smooth function to be optimized by GA and BP. But there is no exactly symbolic expression for every node, because of the uncertain structure. In this paper, the AND-OR FNN is firstly named as AND-OR fuzzy neural network, The indegree and out-degree for neuron and the connectivity for layer are defined in order to educe the symbolic expression of every layer directly employing Zadeh operators, formed a continuous and rough function. The equivalence is proved between the architecture of AND-OR FNN and the fuzzy weighted Mamdani inference in order to utilize the AND-OR FNN to auto-extract fuzzy rules. The piecewise optimization of AND-OR FNN consists two phases, first the blueprint of network is reduced by GA and PA; the second phase, the parameters are refined by ACS (Ant Colony System). Finally this approach is applied to design AND-OR FNN ship controller. Simulating results show the performance is much better than ordinary fuzzy controller.