Type-2 Fuzzy Sets and Systems: Some Questions and Answers (edited)

There are now thousands of articles that have been written about type-2 fuzzy sets and systems. Why did such fuzzy sets come into being? Are they meant to replace type-1 fuzzy sets? How more complicated are they than type-1 fuzzy sets? So many questions! For someone who is new to a type-2 fuzzy set, as is true for the majority of attendees at WCCI-2014, you may find its literature confounding because there are more ways to represent a type-2 fuzzy set than there are for a type-1 fuzzy set. This is due to the three-dimensional nature of the membership function of a type-2 fuzzy set as opposed to the two-dimensional nature of a type-1 fuzzy set. Having more representations to learn about may pose a barrier for newbies. My goal in the rest of this talk is to break down this barrier. Although I could have chosen to talk about many aspects of type-2 fuzzy sets and systems including their applications (there already are two special issues of the Computational Intelligence Magazine that do this very well), I have chosen for the rest of my talk to focus on answering three barrier-busting questions: 1. What are the different ways to mathematically represent a T2 FS? 2. Why are different representations needed 3. Which ones are useful for design? I emphasize design because, being an engineer, I want to be able to use a type-2 fuzzy set to do something better than if I had not used it.