Fuzzy harmonic mean technique for solving fully fuzzy multi-objective transportation problem

In this research article, an algorithm is developed using a fuzzy harmonic mean technique to solve a fully fuzzy multi-objective transportation problem (FFMOTP). First, the FFMOTP will be formalized mathematically, and then by using fuzzy arithmetic, it will be decomposed into three-level (lower, middle, & upper) multi-objective linear programming problems. After then, by using the fuzzy harmonic mean as a tool, the three-level multi-objective linear programming problems are converted into three-level single objective linear programming problems. Further, these single objective linear programming problems for all the three levels are solved to give the Combine fuzzy optimal solution. In the end, two numerical examples are solved to elaborate our proposed algorithm completely and compare the result obtained by our proposed algorithm with the results obtained using the other methods.