fully fuzzy multilevel multiobjective linear programming problems

What is it about?

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

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Why is it important?

This work can be applied to real-life applications such that supply chain management, network interdiction, traffic and transportation network design, safety and accident management, policy making, energy management, taxation problems, capacitated lot-sizing problems, and so on. For example, it may be applied on solving the airport slot-scheduling problem, since the growth rate of the demand for transport services is expected to exceed the growth rate of airport infrastructure development and the airport’s capacity [37]. Another real life application is sustainable water system planning and Arid agri- cultural regions [38]. Since, all over the world, the water scar-city crisis threatens food production and sustainable development, especially for arid agricultural areas. Therefore, it is necessary to develop plans and strategies to manage agricultural water in a sustainable manner and improve the efficiency of water management, as there are many complications in agricultural water management in arid areas that affect decision-making levels Multiple targets, water users and uncertainty.

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