Fuzzy Integral for Rule Aggregation in Fuzzy Inference Systems
The fuzzy inference system (FIS) has been tuned and revamped 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.
KeywordsFuzzy inference system Choquet integral Fuzzy integral gFI NDFI Fuzzy measure
This work has been partially supported by the U.S. Army Research Office, the U.S. Army and RDECOM CERDEC NVESD via W911NF-16-1-0017, W911NF-14-1-0114, W911NF-14-1-0673, W909MY-13-C-0013 and 57940-EV. This work was also partially funded by RCUK’s EP/M02315X/1.
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