How do I create a back propagation neural network that has different kinds of output?

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I'm sorry, I've just learned about the neural network and I have not yet understood in its implementation. Suppose I want to make a back propagation neural network that accepts multiple real numbers as input and produces two types of output, which is a real number, and the other is a choice that is between A, B, and C or only the choice between 0 and 1. What activation function should I use or how do I structure and compute it?

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The activation function depends on the values of the input and output signals. Here http://www.mathworks.com/help/nnet/ug/multilayer-neural-network-architecture.html are some example of transfer functions. As I understood, all your input and output values are positive numbers, so pureline or logsig functions are maybe the most suitable for your problem. When you form your input and output matrix be careful with sorting input and output values (first row in input matrix correspond to the first row in output matrix). Hope this help you.