On answering the question Where do I start in order to solve a new problem involving interval type-2 fuzzy sets?

This paper, which is tutorial in nature, demonstrates how the Embedded Sets Representation Theorem (RT) for a general type-2 fuzzy set (T2 FS), when specialized to an interval (I)T-2 FS, can be used as the starting point to solve many diverse problems that involve IT2 FSs. The problems considered are: set theoretic operations, centroid, uncertainty measures, similarity, inference engine computations for Mamdani IT2 fuzzy logic systems, linguistic weighted average, person membership function approach to type-2 fuzzistics, and Interval Approach to type-2 fuzzistics. Each solution obtained from the RT is a structural solution but is not a practical computational solution, however, the latter are always found from the former. It is this author's recommendation that one should use the RT as a starting point whenever solving a new problem involving IT2 FSs because it has had such great success in solving so many such problems in the past, and it answers the question Where do I start in order to solve a new problem involving IT2 FSs? (C) 2009 Elsevier Inc. All rights reserved.