Why triangular membership functions?

In this note we look at a certain theoretically sound motivation behind the common use of triangular (and trapezoidal) membership functions. The studies are completed within a conceptual framework of fuzzy modelling whose structure comprises of input and output interfaces linked with a single transformation module aimed at processing linguistic information. It is shown that under some additional mild assumptions these triangular fuzzy sets comply with a request for a uniformly excited codebook in the case of the input interfaces and a satisfaction of a zero-error reconstruction criterion being formulated for the output interface.