Fuzzy aggregation

It is well established that the combination of a set of classifiers designed for a given pattern recognition task may achieve higher classification rates than any single classifier.

Several combination schemes have been proposed in the literature. The linear combination rule is certainly one of the most widely used techniques due to its simplicity and intuitive interpretability. Further, its effectiveness has been proved both experimentally and, for some types of classifiers, analytically. Despite these qualities, the linear combination rule is not able to completely capture the predisposition of a specific classifier to recognize particular categories of input patterns. Indeed, the linear combination rule associates, for each class or for all classes, a unique weight with each classifier for the overall classifier output space. In fact, in different regions of this space, the reliability of the classifiers could be different.

To take this different reliability into account, we propose the use of a modified first-order Takagi-Sugeno (TS) fuzzy model with convex linear functions as rule consequents. The antecedent of each TS rule identifies a fuzzy region of the classifier output space, while the consequent performs as many linear combinations of the classifier outputs as there are classes.

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