Fuzzy Integral-based Rule Aggregation in Fuzzy Logic


Anderson, Derek T.

Committee Member

Younan, Nicolas H.

Committee Member

Ball, John E.

Date of Degree


Original embargo terms

MSU Only Indefinitely

Document Type

Graduate Thesis - Open Access


The fuzzy inference system 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 rule aggregation relatively underrepresented. 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 nonditivity and exploitation of interactions between rules. Herein, the fuzzy integral, a parametric non-linear aggregation operator, is 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. The roles of two extensions, gFI and the NDFI, are explored and demonstrate when and where to apply these aggregations, and present efficient algorithms to approximate their solutions.



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