New Framework for Fuzzy Logic Reasoning: A Robust Control Theoretic Approach

Fuzzy reasoning gathered significant attention for its extensive utility since it was introduced. This work puts emphasis on its theoretical aspects and presents a framework for fuzzy logic reasoning considering time-varying uncertainty based on robust control theory. The proposed framework is built upon one basic setting, the Fundamental Axiom of Reasoning, which provides a criterion to demonstrate the validness of a chain reasoning by analytically quantifying its truth value based on multiple fuzzy implication models. The fuzzy reasoning system is casted to a dynamic system where the reasoning process is proactively controlled without violating the basic setting. The time-varying uncertainty in system variables or parameters is addressed by involving the delicately designed robust control. Furthermore, the diverse ways in which time-varying uncertainty impacts the system are also discussed, from modeling stage to control stage. Finally, an automated speed control problem with time-varying uncertainty is considered to demonstrate how to apply the proposed framework.