Interval Type-2 Fuzzy Logic Systems Made Simple

TLDR

General type‑2 fuzzy set mathematics is computationally complex, so most practitioners use interval T2 fuzzy sets, but learning general T2 FS still imposes a heavy educational burden that hinders widespread adoption of interval T2 fuzzy logic systems. This tutorial shows that interval T2 fuzzy logic systems can be built using only type‑1 fuzzy set mathematics, eliminating the need to learn general type‑2 fuzzy set theory. The authors derive the necessary interval T2 fuzzy logic system components directly from type‑1 fuzzy set theory, bypassing the general type‑2 framework. As a result, interval T2 fuzzy logic systems can now be developed straightforwardly without the prior complex type‑2 mathematics.

Abstract

To date, because of the computational complexity of using a general type-2 fuzzy set (T2 FS) in a T2 fuzzy logic system (FLS), most people only use an interval T2 FS, the result being an interval T2 FLS (IT2 FLS). Unfortunately, there is a heavy educational burden even to using an IT2 FLS. This burden has to do with first having to learn general T2 FS mathematics, and then specializing it to an IT2 FSs. In retrospect, we believe that requiring a person to use T2 FS mathematics represents a barrier to the use of an IT2 FLS. In this paper, we demonstrate that it is unnecessary to take the route from general T2 FS to IT2 FS, and that all of the results that are needed to implement an IT2 FLS can be obtained using T1 FS mathematics. As such, this paper is a novel tutorial that makes an IT2 FLS much more accessible to all readers of this journal. We can now develop an IT2 FLS in a much more straightforward way