ICOD: Inclusion Degree-Based Conditional Outlier Detection in Mixed Attribute Data

Abstract Purpose This study aims to detect conditional outliers, which become anomalous only within a specified context, in mixed attribute data. It addresses contextual relevance, uncertainty and fuzziness that are often overlooked by conventional methods. Design/Methodology/Approach ICOD integrates fuzzy inclusion theory with fuzzy rough sets. An inclusion based membership function measures how closely each object’s fuzzy information granule conforms to a conditional subset. To avoid examining all attribute combinations, ICOD builds an attribute sequence and a nested attribute subset sequence for each object. Their membership degrees are combined with granule size weights to form a conditional outlier factor. The evaluation includes comparative experiments, parameter sensitivity analysis, ablation analysis, and Friedman and Nemenyi tests. Findings Experiments on 11 public datasets, comprising 22 contextual subsets, show that ICOD outperforms eight comparison methods on most subsets. It obtains the best results on 18 of the 22 subsets and statistically significant improvements over seven of the eight methods. Research Limitations Pairwise fuzzy relations require O (| AT || OB | 2 ) time and space, which may limit scalability on large datasets. Conditional subsets are constructed using domain informed filters, so robustness to alternative and data driven context construction strategies requires further study. Practical Implications ICOD enables domain experts to define relevant subgroups and identify deviations within them. Its unified treatment of heterogeneous attributes may support context dependent applications such as medical screening, transaction monitoring and fault detection while reducing information loss caused by preprocessing. Originality/Value ICOD characterizes anomalies through graded contextual conformity rather than global statistical deviation. Its value lies in combining fuzzy inclusion based membership, dynamically constructed object specific attribute and attribute subset sequences, and granule size weighting within a unified conditional outlier score that accounts for uncertainty.