Using measures of similarity and inclusion for multiple classifier fusion by decision templates

Decision templates (DT) are a technique for classifier fusion for continuous-valued individual classifier outputs. The individual outputs considered here sum up to the same value (e.g., statistical classifiers, yielding some estimates of the posterior probabilities for the classes). First, the DT fusion algorithm is explained. Second, we show that two similarity measures (S1 and S2) and two inclusion indices (I1 and I2) between fuzzy sets (see Dubois and Prade, 1980) produce the same DT classifier. The equivalence is proven by showing that for every object submitted for classification, all 4 measures induce the same ordering on the set of class labels (through DT fusion), thereby assigning the object to the same class.