Journal
INFORMATION SCIENCES
Volume 179, Issue 19, Pages 3418-3431Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2009.05.008
Keywords
Interval type-2 fuzzy sets; Representation Theorem; Embedded sets; Centroid; Uncertainty measures; Similarity; Fuzzy logic system; Linguistic weighted average; Fuzzistics
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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.
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