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\(T\)-generable indistinguishability operators and their use for feature selection and classification. (English) Zbl 1423.68497
Summary: \(T\)-generable indistinguishability operators are operators \(E\) that can be expressed in the form \(E = T(E_{\mu_1}, E_{\mu_2},\dots, E_{\mu_m})\), where \(T\) is a t-norm and \(E_\mu\) is the fuzzy relation generated by the fuzzy subset \(\mu\). In this paper, we analyse their relation with powers with respect to the t-norm \(T\) and with quasi-arithmetic means. For non-strict continuous Archimedean t-norms they are completely characterised as generable by crisp equivalence relations. These fuzzy relations are used to define a method, called JADE, useful for feature selection and classification tasks. JADE is based on minimising the distance between two indistinguishability measures: the one given by weighting the attribute-values describing the domain objects and the other one given by the correct classification taken as an equivalence relation. The preliminary experiments we carried out with JADE are promising concerning the accuracy in solving classification tasks. We also report some issues of the method that could be improved in the future.

68T37 Reasoning under uncertainty in the context of artificial intelligence
68T05 Learning and adaptive systems in artificial intelligence
68T10 Pattern recognition, speech recognition
UCI-ml; C4.5
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