Fuzzy Reasoning as a Control Problem

Abstract

Different from the dominant view of treating fuzzy reasoning as generalization of classical logical inference, in this paper fuzzy reasoning is treated as a control problem. A new fuzzy reasoning method is proposed that employs an explicit feedback mechanism to improve the robustness of fuzzy reasoning. The fuzzy rule base given a priori serves as a controlled object, and the fuzzy reasoning method serves as the corresponding controller. The fuzzy rule base and the fuzzy reasoning method constitute a control system that may be open loop or closed loop, depending on the underlying reasoning goals/constraints. The fuzzy rule base, the fuzzy reasoning method, and the corresponding reasoning goals/constraints define the three distinct ingredients of fuzzy reasoning. While various existing fuzzy reasoning methods are essentially a static mapping from the universe of single fuzzy premises to the universe of single fuzzy consequences, the new fuzzy reasoning method maps sequences of fuzzy premises to sequences of fuzzy consequences and is a function of the underlying reasoning goals/constraints. The Monte Carlo simulation shows that the new fuzzy reasoning method is much more robust than the optimal fuzzy reasoning method proposed in our previous work. The explicit feedback mechanism embedded in the fuzzy reasoning method does significantly improve the robustness of fuzzy reasoning, which is concerned with the effects of perturbations associated with given fuzzy rule bases and/or fuzzy premises on fuzzy consequences. The work presented in this paper sets a new starting point for various principles of feedback control and optimization to be applied in fuzzy reasoning or logical inference and to explore new forms of reasoning including robust reasoning and adaptive reasoning. It can be also expected that the new fuzzy reasoning method presented in this paper can be used for modeling and control of complex systems and for decision-making under complex environments.