an:07118086
Zbl 1423.68497
Armengol, Eva; Boixader, Dionís; García-Cerdaña, Àngel; Recasens, Jordi
\(T\)-generable indistinguishability operators and their use for feature selection and classification
EN
Fuzzy Sets Syst. 360, 33-48 (2019).
0165-0114
2019
j
68T37 68T05 68T10
\(T\)-generable indistinguishability operator; similarity relation; quasi-arithmetic mean; feature selection; classification
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 \textsf{JADE}, useful for feature selection and classification tasks. \textsf{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 \textsf{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.