Risk analysis of fuzzy control systems with (n+1)-inputs and 1-output FLC

This paper proposes a fundamental method to analyze the uncertain fuzzy control systems by the methodology of functional analysis based on the fuzzy mapping concept. First of all, a completely continuous operator is defined, and some fuzzy mapping simultaneous equations are introduced by using the defined operator. In the next place, the existence conditions of the likely solutions of the fuzzy mapping simultaneous equations are discussed for the given membership grades. Last of all, it is shown that the simultaneous equations correspond to the input–output relation of the uncertain control systems with the (n+1)-inputs and 1-output fuzzy logic controllers, and this mathematical discussion is applied to the risk analysis of the systems.