fuzzy completion time for alternative stochastic networks

in this paper a network comprising alternative branching nodes with probabilistic outcomes is considered. in other words, network nodes are probabilistic with exclusive-or receiver and exclusive-or emitter. first, an analytical approach is proposed to simplify the structure of network. then, it is assumed that the duration of activities is positive trapezoidal fuzzy number (tfn). this paper combines the randomness and fuzziness and shows that the fuzzy completion time of alternative stochastic network is a fuzzy-valued random variable. then, the probability function of network fuzzy completion time and its expected value is defined. finally, the applications and computations are illustrated in a numerical example.