Fuzzy continuous input-output controllers are universal approximators

The aim of this paper is twofold: (i) To analyse why the fuzzy input-output controllers proposed by Buckley and Hayashi [Fuzzy Sets and Systems 58 (1993) 273] are hardly continuous and, based on this analysis, a special necessary and sufficient condition for the controllers being continuous is obtained. (ii) To amend Buckley-Hayashi's controllers so that to make them unconditionally continuous.