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On KM Algorithms for Solving Type-2 Fuzzy Set Problems

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1 Author(s)
Mendel, J.M. ; Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, USA

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.

Published in:

Fuzzy Systems, IEEE Transactions on  (Volume:21 ,  Issue: 3 )