Deriving the input-output mathematical relationship for a class of interval type-2 mamdani fuzzy controllers

Abstract

Most fuzzy controllers, type-1 (T1) or type-2 (T2), have been used and treated as black boxes in that their explicit mathematical input-output mappings (i.e., analytical structures) are unknown. Revealing and analyzing the analytical structure is important as it will lay a solid foundation for better understanding, more insightful analysis, and more effective design of fuzzy control systems. We previously developed a general technique to derive the analytical structures of the type-1 fuzzy controllers that employed Zadeh AND operator. We now extend our study to a class of typical interval type-2 fuzzy controller that adopt Zadeh AND operator and the popular Karnik-Mendel iterative center-of-sets type reducer. A novel analytical structure deriving technique is developed. And the resulting input-output mathematical relationship for the controller is received.