Fuzzy harmonic mean technique for solving fully fuzzy multilevel multiobjective linear programming problems - Fathy, E.; Hassanien, A.E. (Alexandria engineering journal, 2022)
•A fully fuzzy multilevel multiobjective linear programming problem is developed.•A new methodology based on the fuzzy harmonic mean technique is introduced.•It is applied to the multilevel multiobjective production planning model for a supply chain under a fully fuzzy environment. This paper illustrates how the fuzzy harmonic mean technique can efficiently solve fully fuzzy multilevel multiobjective linear programming (FFMMLP) problems. First, at each level, the FFMMLP problem can be converted into three crisp multiobjective linear programming (CMLP) problems using the crisp linear technique. Then, the fuzzy harmonic mean technique is utilized to aggregate each crisp problem's multiobjective into a single objective. Second, the ensuing final, single-objective problem is constructed using the harmonic mean for each level. Finally, it is solved to obtain a fuzzy compromise solution for the FFMMLP problem in general. Two examples are given to obtain the application of the proposed method. One example is applying the proposed approach to a multilevel multiobjective production planning model for a supply chain under a fully fuzzy environment.