Paper Info
Title
Super-Exponential Convergence of the Karnik-Mendel Algorithms Used for Type-reduction in Interval Type-2 Fuzzy Logic Systems
Abstract
Computing the centroid of an interval T2 FS is an important operation in a type-2 fuzzy logic system (where it is called type-reduction), but it is also a potentially time-consuming operation. The Karnik-Mendel (KM) iterative algorithms are widely used for doing this. In this paper we prove that these algorithms converge monotonically and super-exponentially fast. Both properties are highly desirable for iterative algorithms and explain why in practice the KM algorithms have been observed to converge very fast, thereby making them very practical to use.
Year
DOI
Venue
2006
10.1109/FUZZY.2006.1681870
Vancouver, BC
Keywords
Field
DocType
convergence of numerical methods,fuzzy logic,fuzzy set theory,fuzzy systems,iterative methods,type theory,Karnik-Mendel iterative algorithm,fuzzy set theory,interval type-2 fuzzy logic systems,super-exponential convergence,type-reduction
Computer science,Type theory,Fuzzy set,Artificial intelligence,Fuzzy control system,Fuzzy logic system,Monotonic function,Mathematical optimization,Iterative method,Fuzzy logic,Algorithm,Machine learning,Centroid
Conference
ISSN
ISBN
Citations 
1098-7584
0-7803-9488-7
5
PageRank 
References 
Authors
0.43
12
2
Name
Order
Citations
PageRank
Mendel, J.M.1109261042.42
Feilong Liu242915.52