Target Layer Activation Function of a Neural Netwrok with Ordinal Target (3 events)


I have a neural network with an input layer, two hidden layer and one target layer. The target is binary (1,0). The activation function is the logistic one. The second hidden layer has thrre outputs H21, H22, H32. These outpus are combined in a combination function n31 that is the input to the target layer that is output from it with an activation function p=exp(n31)/(1+exp(n31)). This is the probability of event (1) and 1-p is the probability of non-event (0).

What if the target is ordinal with three events (e.g. 0,1,2)? What target layer activation function should we use and what is its formula?

Thanks in advance,