THEORETICAL-ANALYSIS OF CRISP-TYPE FUZZY-LOGIC CONTROLLERS USING VARIOUS T-NORM SUM-GRAVITY INFERENCE METHODS

The input-output parametric relationship of a class of crisp-type fuzz y logic controllers (FLC's) using various t-norm sum-gravity inference methods is studied. Four most important t-norms are used to calculate the matching level of each control rule and the explicit mathematical forms of reasoning surfaces obtained by using these four t-norms are addressed. Reasoning surfaces of these crisp-type FLC's are proved to be composed of a two-dimensional (2-D) multilevel relay no matter whic h t-norm is used and a local position-dependent nonlinear compensator with output pattern influenced by the t-norms is selected. By analyzin g the intrinsic operation of the four t-norms, the authors find that b oth standard intersection and algebraic product are suitable operators to perform the inference of the FLC, However, bounded difference and drastic intersection are disqualified because they cannot satisfy some important criteria. A measure of relative degree-of-nonlinearity is d efined to examine the output figures of these crisp-type FLC's, The ul timate behavior of these crisp-type FLC's as the number of linguistic terms approaches infinity is also explored, The local stability criter ia for the proportional-integral (PI)-type fuzzy control systems and t he natural global stability characteristic for the proportional-deriva tive (PD)-type fuzzy control systems are also examined.