Type reduction operators for interval type–2 defuzzification

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

Abstract

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.

Citation

Runkler, T. A., Chen, C., & John, R. (2018). Type reduction operators for interval type–2 defuzzification. Information Sciences, 467, 464-476. https://doi.org/10.1016/j.ins.2018.08.023

• 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
• DOI: https://doi.org/10.1016/j.ins.2018.08.023
• Keywords: Defuzzification; Type 2 fuzzy sets
• Public URL: https://nottingham-repository.worktribe.com/output/1036717
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0020025518306285?via%3Dihub
• Contract Date: Aug 17, 2018