Continuity of approximate reasoning using L-R fuzzy number as input

The authors present a mathematical framework for studying a fuzzy feedback control system, which is constructed by IF-THEN type fuzzy rules through a kind of product-sum-gravity method. Moreover, the L-R fuzzy number is used instead of a definite value as a premise variable in IF-THEN fuzzy rule. Then, we show that the system has an optimal feedback control by essential use of compactness of sets of fuzzy membership functions.