Towards a paradigm for fuzzy logic control

Some scalar definitions in fuzzy logic control (FLC) are extended to the n-dimensional case, including vector fuzzy number and membership vector. A rigorous mathematical expression is given for the function g(x) (e.g. the `reasoning surface´) manufactured by a fuzzy associative memory (FAM). For the existence and uniqueness of solutions in any closed-loop system with a fuzzy logic controller, it is shown that the FAM function g(x) must be Lipschitz. This places restrictions on the allowed rules in the FLC. An algorithm is proposed for FLC design. It is shown that, under appropriate assumptions, the FLC manufactures an easily computed Lipschitz FAM function g(x) passing through a certain set of sample points associated with the membership functions