Dr. Timothy Havens (CS, ICC-DataS), the William and Gloria Jackson Professor of Computer Systems, is co-author of an article published in the September 2021 issue of IEEE Transactions on Fuzzy Systems. The article is titled, “A Generalized Fuzzy Extension Principle and Its Application to Information Fusion.”
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.
Citation: M. A. Islam, D. T. Anderson, T. C. Havens and J. E. Ball, “A Generalized Fuzzy Extension Principle and Its Application to Information Fusion,” in IEEE Transactions on Fuzzy Systems, vol. 29, no. 9, pp. 2726-2738, Sept. 2021, doi: 10.1109/TFUZZ.2020.3006574.
The IEEE Transactions on Fuzzy Systems publishes high quality technical papers in the theory, design, and application of fuzzy systems. The journal’s impact factor is 12.029.