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Type reduction operators for interval type–2 defuzzification

Runkler, Thomas A.; Chen, Chao; John, Robert


Thomas A. Runkler

Robert John


Fuzzy sets are an important approach to model uncertainty. Defuzzification maps fuzzy sets to non–fuzzy (crisp) values. Type–2 fuzzy sets model uncertainty in the degree of membership in a fuzzy set. Type–2 defuzzification maps type–2 fuzzy sets to non–fuzzy values. Type reduction maps type–2 fuzzy sets to type–1 fuzzy sets, in order to make type–2 defuzzification easier and to implement more efficient type–2 defuzzification algorithms. This paper is a first step towards a theoretical foundation of the emerging field of type reduction. Five mathematical properties of type reduction are defined, and two existing type reduction methods (Nie–Tan and uncertainty weight) are examined with respect to our five properties. Furthermore, two new type reduction methods are proposed: consistent linear type reduction and consistent quadratic type reduction. All our five properties are satisfied by consistent quadratic type reduction.


Runkler, T. A., Chen, C., & John, R. (2018). Type reduction operators for interval type–2 defuzzification. Information Sciences, 467, 464-476.

Journal Article Type Article
Acceptance Date Aug 8, 2018
Online Publication Date Aug 10, 2018
Publication Date Oct 31, 2018
Deposit Date Aug 17, 2018
Publicly Available Date Aug 11, 2019
Journal Information Sciences
Print ISSN 0020-0255
Electronic ISSN 1872-6291
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 467
Pages 464-476
Keywords Defuzzification; Type 2 fuzzy sets
Public URL
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