The parametric definition of membership functions in XFL3

This paper presents a study of the different kinds of membership function (MF) definitions, regarding free MFs and families of MFs, and describes the capabilities of XFL3 (the formal specification language defined by Xfuzzy 3) to manage them. This includes not only the possibility of using them in a system design, but also the capability for extending the available functions with new user-defined membership functions and families. An application example has been included in order to discuss on the suitable parametric definition of the functions.