On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes

This paper is about some important changes in type-2 fuzzy set (T2 FS) definitions and notations that have occurred during the past 16 years. It summarizes the evolution of how the primary membership (Jx) has been used in both the mathematical descriptions of a T2 FS and its footprint of uncertainty (FOU); discusses notational problems associated with the secondary membership function; explains why and when one should distinguish between the FOU and the domain of uncertainty (DOU); explains why no errors have been introduced into T2 FS computations because of notation; and, it provides recommendations notational changes that can be used by all authors.