eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2019-11-25 7 6 191 195 10.12691/ajams-7-6-1 AJAMS2019761 article Nasser A. El-Sherbeny nasserelsherbeny@yahoo.com 1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt The Minimum Cost Flow Problem (MCFP) is a well-known combinatorial optimization and a logical distribution problem. The MCFP is an NP-hard problem with many applications in logistic networks and computer networks. The Fuzzy Minimum Cost Flow Problem with Fuzzy Time-Windows (FMCFPFTW) is an extension of the MCFP. The goal of the problem is to find the minimum amount of the fuzzy flow from the source to the sink that satisfies all constraints of the fuzzy shortest dynamic f-augmenting path with the fuzzy dynamic residual network. We consider a generalized fuzzy version of the MCFP of the fuzzy network. We propose the mathematical model of the FMCFPFTW. Finally, a new algorithm of the FMCFPFTW is presented. http://pubs.sciepub.com/ajams/7/6/1/ajams-7-6-1.pdf combinatorial optimization minimum cost flow time-windows fuzzy time-windows