The fuzzy integral for missing data

Numerous applications in engineering are plagued by incomplete data. The subject explored in this article is how to extend the fuzzy integral (FI), a parametric nonlinear aggregation function, to missing data. We show there is no universally correct solution. Depending on context, different types of...

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Bibliographic Details
Published inIEEE International Fuzzy Systems conference proceedings pp. 1 - 8
Main Authors Islam, Muhammad Aminul, Anderson, Derek T., Petry, Fred, Smith, Denson, Elmore, Paul
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2017
Subjects
Boundary conditions
Choquet integral
Computational modeling
Data models
Frequency modulation
fuzzy integral
Mathematical model
missing data
Training
Uncertainty
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Summary:Numerous applications in engineering are plagued by incomplete data. The subject explored in this article is how to extend the fuzzy integral (FI), a parametric nonlinear aggregation function, to missing data. We show there is no universally correct solution. Depending on context, different types of uncertainty are present and assumptions are applicable. Two major approaches exist, use just observed data or model/impute missing data. Three extensions are put forth with respect to just use observed data and a two step process, modeling/imputation and FI extension, is proposed for using missing data. In addition, an algorithm is proposed for learning the FI relative to missing data. The impact of using and not using modeled/imputed data relative to different aggregation operators-selections of underlying fuzzy measure (capacity)-are also discussed. Last, a case study and data-driven learning experiment are provided to demonstrate the behavior and range of the proposed concepts.
ISSN:1558-4739
DOI:10.1109/FUZZ-IEEE.2017.8015475