Ordered weighted aggregation of fuzzy similarity relations and its application to detecting water treatment plant malfunction

Ordered weighted aggregation procedures have been introduced in many applications with promising results. In this paper, an innovative approach for ordered weighted aggregation of fuzzy relations is proposed. It allows the integration of component relations generated from different perspectives of a certain observation to form an overall fuzzy relation, deriving a useful similarity measure for observed data points. Two types of aggregation are investigated: (a) min/max operators are employed for the aggregation of component relations defined by the minimum T-norm; and (b) sum/product operators are employed for the aggregation of component relations defined by the Łukasiewicz T-norm. The resultant ordered weighted aggregations prove to preserve the desirable reflexivity and symmetry properties, with T-transitivity also conditionally preserved if appropriate weighting vectors are adopted. The conditions upon which the proposed aggregated relations preserve T-transitivity are studied. The characteristics of applying an aggregated relation in combination with clustering procedures is also experimentally examined, where fuzzy similarity relations regarding individual features are aggregated to support hierarchical clustering. An application to the detection of water treatment plant malfunction demonstrates that better results can be obtained with the transitive fuzzy relations acting as the required similarity measures, as compared to the use of non-transitive ones. By introducing transitivity to the aggregation the interpretability of the detection system is also enriched.