Representing membership functions as elements in function space

This paper generalizes the geometric representation of membership functions comprising a finite number of characteristic points. An extended class of membership functions, satisfying certain monotonicity conditions, can now be expressed as elements in the space of square integrable functions. Specifically, bell-shaped membership functions, which were not possible before, can now be accommodated with this generalized representation. An example interpolation problem, treated using both the finite-dimensional approach and the generalized approach, is included for illustration