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چکیده
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In this paper, we aim to introduce a class of multi-commodity network flow problems. Here, we deal with a multi-commodity flow problem with a fractional objective function that is investigated in a fuzzy random hybrid environment. This paper aims to provide a model that manages unknown coefficients in fractional multi-commodity networks. In this problem, the coefficients of the objective function in the numerator of the fraction and the arc capacity are assumed to be fuzzy random variables and the coefficients of the objective function in the denominator of the fraction are assumed to be fuzzy variables. Since this problem is investigated simultaneously in both random and fuzzy environments, we use a probability-possibility approach to convert the problem to a deterministic form. Next, we get the problem out of the fractional mode using the variable transformation method and finally, examine the efficiency of the proposed method by providing some numerical examples.
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