Centroid of a type-2 fuzzy set

By Nilesh N. Karnik, Jerry M. Mendel. Information Sciences, 2001

1,245 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e55255c25737f27f307a87eff35c8f864847474e

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Citations in the corpus

Interval Type-2 Fuzzy Logic Systems Made Simple (2006, background): “In general, there are no closed-form formulas for and ; however , Karnik and Mendel [7] have developed two very simple and easy to implement iterative algorithms for computing these end-points exactly, and they can be run in parallel.”
An efficient centroid type-reduction strategy for general type-2 fuzzy logic system (2008, methodology): “To date, type-reduction methods have been developed by Karnik and Mendel [ 3 ] and are”
Enhanced Karnik--Mendel Algorithms (2009, methodology): “[12] D. Wu and J. M. Mendel, “Aggregation using the linguistic weighted average and interval type-2 fuzzy sets,” IEEE Trans.”
Computing derivatives in interval type-2 fuzzy logic systems (2004, methodology): “These two four-step iterative-procedures (steps 1) and 2) are initialization steps) have been proven by Karnik and Mendel [2] to converge to the exact solutions in no more than iterations.”
Interval type-2 fuzzy logic systems (2000, methodology): “In this paper, for illustrative purposes, we focus on center-of-sets type-reduction, which can be expressed as (47) where interval set determined by two end points and ; ; and centroid of the type-2 interval consequent set (the centroid of a type-2 fuzzy set is described in [11], [16], and [12]); .”
Advances in type-2 fuzzy sets and systems (2007, methodology): “When Karnik and Mendel [29] introduced TR they required adherence to the following:”
A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets (2009, methodology): “Switch points L and R, as well as cl(Ã) and cr(Ã), are computed by using the iterative KM Algorithms [7], [16], [28].”
Computing with words and its relationships with fuzzistics (2007, methodology): “The Karnik–Mendel (KM) algorithms [8,15] are used to do this, and these algorithms are monotonically and super-exponentially convergent [21].”
Uncertainty measures for interval type-2 fuzzy sets (2007, methodology): “8 A e where S is the union operation, and It has been shown [28,46,51] that c l ð ~ A Þ and c r ð ~ A Þ can be expressed as Switch points x L and x R , as well as c l ð e A Þ and c r ð e A Þ , are computed by using the iterative KM Algorithms [46,28] given in the Appendix.”
Optimization of Interval Type-2 Fuzzy Logic Controllers for a Perturbed Autonomous Wheeled Mobile Robot Using Genetic Algorithms (2009, background): “It is known that type-2 fuzzy sets enable modeling and minimizing the effects of uncertainties in rule-based FLS [22].”
Encoding Words Into Interval Type-2 Fuzzy Sets Using an Interval Approach (2008, methodology): “Mendel and Wu [20] have shown that the centroid of an IT2 FS is a measure of the uncertainty of such an FS, and that, although the centroid cannot be computed in closed form [6], centroid bounds4 can be expressed explicitly in terms of the geometry (parameters) of an FOU.”