A Generalized Fuzzy Extension Principle and Its Application to Information Fusion
Document Type
Article
Publication Date
9-2021
Department
College of Computing
Abstract
Zadeh's extension principle (ZEP) is a fundamental concept in fuzzy set (FS) theory that enables crisp mathematical operation on FSs. A well-known shortcoming of ZEP is that the height of the output FS is determined by the lowest height of the input FSs. In this article, we introduce a generalized extension principle (GEP) that eliminates this weakness and provides flexibility and control over how membership values are mapped from input to output. Furthermore, we provide a computationally efficient point-based FS representation. In light of our new definition, we discuss two approaches to perform aggregation of FSs using the Choquet integral. The resultant integrals generalize prior work and lay a foundation for future extensions. Last, we demonstrate the extended integrals via a combination of synthetic and real-world examples.
Publication Title
IEEE Transactions on Fuzzy Systems
Recommended Citation
Islam, M.,
Anderson, D.,
Havens, T. C.,
&
Ball, J.
(2021).
A Generalized Fuzzy Extension Principle and Its Application to Information Fusion.
IEEE Transactions on Fuzzy Systems,
29(9), 2726-2738.
http://doi.org/10.1109/TFUZZ.2020.3006574
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/15358