Fuzzy integral for rule aggregation in fuzzy inference systems

Tomlin, Leary; Anderson, Derek T.; Wagner, Christian; Havens, Timothy C.; Keller, James M.

Abstract

The fuzzy inference system (FIS) has been tuned and re-vamped many times over and applied to numerous domains. New and improved techniques have been presented for fuzzification, implication, rule composition and defuzzification, leaving one key component relatively underrepresented, rule aggregation. Current FIS aggregation operators are relatively simple and have remained more-or-less unchanged over the years. For many problems, these simple aggregation operators produce intuitive, useful and meaningful results. However, there exists a wide class of problems for which quality aggregation requires non- additivity and exploitation of interactions between rules. Herein, we show how the fuzzy integral, a parametric non-linear aggregation operator, can be used to fill this gap. Specifically, recent advancements in extensions of the fuzzy integral to \unrestricted" fuzzy sets, i.e., subnormal and non- convex, makes this now possible. We explore the role of two extensions, the gFI and the NDFI, discuss when and where to apply these aggregations, and present efficient algorithms to approximate their solutions.

Citation

Tomlin, L., Anderson, D. T., Wagner, C., Havens, T. C., & Keller, J. M. (in press). Fuzzy integral for rule aggregation in fuzzy inference systems. Communications in Computer and Information Science, 610, https://doi.org/10.1007/978-3-319-40596-4_8

• Journal Article Type: Article
• Acceptance Date: Jun 20, 2016
• Online Publication Date: Jun 11, 2016
• Deposit Date: Aug 4, 2017
• Publicly Available Date: Aug 4, 2017
• Journal: Communications in Computer and Information Science
• Print ISSN: 1865-0929
• Electronic ISSN: 1865-0929
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 610
• Book Title: Information Processing and Management of Uncertainty in Knowledge-Based Systems
• DOI: https://doi.org/10.1007/978-3-319-40596-4_8
• Keywords: Fuzzy inference system, Choquet integral, Fuzzy integral, gFI, NDFI, Fuzzy measure
• Public URL: https://nottingham-repository.worktribe.com/output/794254
• Publisher URL: https://link.springer.com/chapter/10.1007%2F978-3-319-40596-4_8
• Additional Information: Tomlin L., Anderson D.T., Wagner C., Havens T.C., Keller J.M. (2016) Fuzzy Integral for Rule Aggregation in Fuzzy Inference Systems. In: Carvalho J., Lesot MJ., Kaymak U., Vieira S., Bouchon-Meunier B., Yager R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham.; ; The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-40596-4_8.; ; Proceedings of the 16th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2016, 20-24 June 2016, Eindhoven, The Netherlands.