Moscow technical university of communications and informatics (department of telecommunications security, professor)
Russian Federation
Russian Federation
Russian Federation
When data are incomplete, standard fuzzy data mining methods face an unacceptable trade-off: deleting objects with missing values loses up to a third of the sample and introduces systematic bias under the MAR mechanism, while mean imputation destroys the covariance structure and produces rules with artificially inflated support. This paper proposes a different solution – a presence function φ: U × A → [0, 1] that embeds the handling of missing values directly into the fuzzy support formula. An object with a missing attribute is neither discarded nor «repaired»: it participates in the analysis with a reduced weight φ₀, and the rest is handled by the t-norm. A number of theoretical properties are proved: anti-monotonicity of support for an arbitrary t-norm, robustness to attribute noise via the Lipschitz constant, invariance to monotone scale transformations, and the limiting cases φ₀ → 0 and φ₀ → 1/kₐ. Under 30 % MCAR missingness with φ₀ = 0,3, the share of recovered patterns is 21–38 percentage points higher than with listwise deletion. Three strategies for constructing fuzzy partitions are proposed: uniform, quantile-based and optimization-based. The dependence of the quality of extracted patterns on the parameter φ₀ under different missingness mechanisms is studied in detail. An experimental comparison on synthetic data confirmed that φ₀ = 0,3 under MCAR missingness provides a 21–38 percentage point higher share of recovered patterns than listwise deletion at a 30 % missingness level.
presence function, incomplete data, fuzzy data mining, fuzzy information system, MCAR/MAR/MNAR missingness mechanisms, fuzzy partitions, anti-monotonicity of fuzzy support, t-norm, imputation, listwise deletion
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