A NEURAL FUZZY SYSTEM WITH LINGUISTIC TEACHING SIGNALS

A neural fuzzy system learning with linguistic teaching signals is proposed in this paper. This system is able to process and learn numerical information as well as linguistic information. It can be used either as an adaptive fuzzy expert system or as an adaptive fuzzy controller. At first, we propose a five-layered neural network for the connectionist realization of a fuzzy inference system. The connectionist structure can house fuzzy logic rules and membership functions for fuzzy inference. We use alpha-level sets of fuzzy numbers to represent linguistic information, The inputs, outputs, and weights of the proposed network can be fuzzy numbers of any shape. Furthermore, they can be hybrid of fuzzy numbers and numerical numbers through the use of fuzzy singletons. Based on interval arithmetics, two kinds of learning schemes are developed for the proposed system: fuzzy supervised learning and fuzzy reinforcement learning. They extend the normal supervised and reinforcement learning techniques to the learning problems where only linguistic teaching signals are available. The fuzzy supervised learning scheme can train the proposed system with desired fuzzy input-output pairs which are fuzzy numbers instead of the normal numerical values, With fuzzy supervised learning, the proposed system can be used for rule base concentration to reduce the number of rules in a fuzzy rule base. In the fuzzy reinforcement learning problem that we consider, the reinforcement signal from the environment is linguistic information (fuzzy critic signal) such as ''good,'' very good,'' or ''bad,'' instead of the normal numerical critic values such as ''0'' (success) or ''-1'' (failure). With the fuzzy critic signal from the environment, the proposed system can learn proper fuzzy control rules and membership functions. We discuss two kinds of fuzzy reinforcement learning problems: single-step prediction problems and multistep prediction problems. Simulation results are presented to illustrate the performance and applicability of the proposed system.