Fuzzy Approximate Optimal Solution of the Fuzzy Transportation Problems (FTP) Under Interval Form Using Monte Carlo Approach

Abstract

This article presents two phases of procedure to solve the transportation problem under data interval. In the first phase, the problem is transformed into a trapezoidal fuzzy transportation problem by using a trisectional fuzzification. The second phase is to employ the Monte Carlo method based on the alpha-cuts to find the fuzzy optimal solution of the fuzzy transportation problem (FTP). A numerical example is provided to illustrate the capability of the proposed approach and compare it with the existing method. The proposed approach is able to obtain the fuzzy optimal solution of FTP. The computations of the fuzzy optimal solution FTP are conducted by using the Monte Carlo approach by employ random numbers generated by rand(), sort() and reshape() function in the Matlab software. The results indicated that the aforementioned approach can be had a big potential to be further optimized by taking large random numbers.