Analytical structure of fuzzy controllers using arbitrary input fuzzy sets and Zadeh fuzzy AND operator

We have developed a general technique for deriving analytical input-output relation for the fuzzy controllers that use Zadeh AND operator and arbitrary input fuzzy sets. This technique is applicable to any type of fuzzy controllers (e.g., Mamdani type or Takagi-Sugeno type). The analytical structures that we have derived provide an unprecedented opportunity to insightfully and rigorously understand how fuzzy control works and examine the advantages and shortcomings of different design choices available for various components of the fuzzy controllers.