The simplest way to obtain a linear controller characteristic is to use singletons as consequent terms with entirely overlapping input terms. Singletons are normalized rectangular membership functions with an infinitely small width. Using singleton membership functions for consequent terms makes the Center of Area (CoA) defuzzification method identical to the Center of Maximum (CoM) method. The following image shows the controller for the CoA method using singleton membership functions.
The controller characteristic remains relatively unchanged when you leave the input terms entirely overlapped to vary the overlapping degree of the membership functions for the consequent terms, especially if all the consequent terms are equal in width. Then only the typical values of the consequent terms are significant.
Therefore, in most closed-loop control applications, you can use singleton membership functions to model the output terms sufficiently rather than using triangular or other membership function types.