Lipschitz Continuity of Approximate Reasoning
Takashi Mitsuishi, Takanori Terashima, Toshimichi Homma, Yasunari Shidama · 2008
Lipschitz continuity of some approximate reasoning methods on the premise variables are described to guarantee the existence of the unique solution of the state equation of a fuzzy control. To obtain this result, some conditions must be given to the set of membership functions. Then we introduce some sets of membership functions used in Mamdani method, product-sum-gravity method and Larsen method and proved Lipschitz continuity of them.