Stage-dependent fuzzy-valued loss function in two-stage binary classifier

In this paper, a model to deal with two-stage Bayesian classifier, under the assumption of complete probabilistic information, is introduced. The loss function in our problem is stage-dependent fuzzy-valued. This fuzzy loss function means that the loss depends on the stage at which misclassification is made. The model is firstly based on the notion of fuzzy random variable and secondly on the subjective ranking of fuzzy number defined by Campos and Gonzalez. The comparison with crisp stage-dependent loss function is given. Finally, an example illustrating this case of Bayesian analysis is considered.