Nonmonotonicity and discretization error in fuzzy rule-based control using COA and MOM defuzzification

Mamdani-style controllers are often implemented using evenly-spaced triangular membership functions in which memberships in adjacent linguistic terms sum to one. However, it is often desirable to modulate the response curve of a controller by making it flatter or steeper in the vicinity of zero. We investigate three methods of modifying the consequent linguistic terms to achieve this, in the context of two methods of defuzzification. Discretization error is taken into consideration by comparing four levels of consequent granularity with the exact solutions. Nonmonotonicity behavior in the shapes of the control surface is observed and described in the context.