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

Abstract

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. An example is provided to prove the theoretical results.