A modified fuzzy approach for the fully fuzzy multi-objective and multi-level integer quadratic programming problems based on a decomposition technique

What is it about?

In this paper, a new modified fuzzy approach was modeled to deal with the fully fuzzy multi-objective and multi-level integer quadratic programming (FFMMQP) problems. In the proposed approach, each fuzzy problem was converted to three crisp multi-objective quadratic problems based on the decomposition technique. Then the concept of a tol- erance membership functions and multi-objective optimization in the decomposition form was used to generate the Pareto optimal fuzzy solution for the given FFMMQP problems. To check the validity of the method, one numerical example was provided. Obtained results clarify that the proposed technique creates a powerful tool which demanded for solving the fully fuzzy multi-level problems. The work will be able to help solve real life and industrial prob- lems which are usually complicated, uncertain and continuously subject to changes, by considering the fuzziness in the formulation of the model. For future research, one possible direction is to apply the pro- posed approach to deal with the real world decision making situation such as a multi-level logistics plan- ning problem under fully fuzzy environments.

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Photo by Anastasia Zhenina on Unsplash

Photo by Anastasia Zhenina on Unsplash

Why is it important?

This paper focuses on extending and applying a fuzzy approach for utilization with the fully fuzzy multi-objective and multi-level integer quadratic programming (FFMMQP) problems. First, the decomposition technique is used to convert the fuzzy problem for each level into three crisp multi-objective integer quadratic (MQP) problems namely, Middle-MQP, Upper-MQP and Lower-MQP problem. Each crisp problem has its own variables. Furthermore, the functions of each problem have several quadratic functions. Then by considering the individual solution of each objective function, the middle, upper and lower membership functions are constructed. Second, the concept of the tolerance membership function and multi-objective optimization in the decomposition form is used to establish decomposed Tchebycheff problems to achieve the Pareto optimal fuzzy solution for the FFMMQP problems

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