On KM Algorithms for Solving Type-2 Fuzzy Set Problems

Computing the centroid and performing type-reduction for type-2 fuzzy sets and systems are operations that must be taken into consideration. Karnik-Mendel (KM) algorithms are the standard ways to do these operations; however, because these algorithms are iterative, much research has been conducted d...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2013-06, Vol.21 (3), p.426-446
Main Author: Mendel, J. M.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Approximation algorithms
Centroid
Convergence
Frequency selective surfaces
Fuzzy sets
general type-2 fuzzy sets (GT2 FSs)
interval type-2 fuzzy sets (IT2 FSs)
Karnik-Mendel (KM) algorithms
Optimization
Shape
tutorial
type-reduction (TR)
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Summary:Computing the centroid and performing type-reduction for type-2 fuzzy sets and systems are operations that must be taken into consideration. Karnik-Mendel (KM) algorithms are the standard ways to do these operations; however, because these algorithms are iterative, much research has been conducted during the past decade about centroid and type-reduction computations. This tutorial paper focuses on the research that has been conducted to 1) improve the KM algorithms; 2) understand the KM algorithms, leading to further improved algorithms; 3) eliminate the need for KM algorithms; 4) use the KM algorithms to solve other (nonfuzzy logic system) problems; and 5) use (or not use) KM algorithms for general type-2 fuzzy sets and fuzzy logic systems.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2012.2227488