A quantitative comparison of interval type-2 and type-1 fuzzy logic systems: First results

The question “When will an IT2 FLS outperform a T1 FLS?” has been asked by many, and is acknowledged by many experts to be arguably the most important unanswered question in the T2 field. As a research problem, this question turns into: Establish when and by how much a type-2 fuzzy logic system (T2 FLS) will outperform a type-1 (T1) FLS. This paper provides first results on solving this problem. Its approach is novel because it does not focus immediately on a specific application, but instead focuses on the common component to all performance analyses, thereby providing results that can be used by others in their application-based performance comparisons. The Wu-Mendel minimax uncertainty bounds, which in the past have been used to approximate the type-reduced set, and to also act as a starting point for designs of IT2 FLSs, play the key role in this paper. Although comparing an IT2 FLS to a T1 FLS seems like a daunting task, because of the complicated nature of the equations that describe them, this paper shows that when an IT2 FLS is expanded about a T1 FLS-itself a new concept-, surprisingly, very simple first results are obtained.