Abstract
This paper proposes an algorithm to solve multi-level multi-objective quadratic programming problem with fuzzy parameters in the objective functions, This algorithm uses the tolerance membership function concepts and multi-objective optimization at each level to develop a fuzzy Max-Min decision model for generating satisfactory solution after applying linear ranking method on trapezoidal fuzzy numbers in the objective functions, An illustrative example is included to explain the results.
Highlights
Fuzzy approach uses the concept of tolerance membership to develop a fuzzy max-min decisionModel for generating Pareto optimal solution [1 and 3]
[4] Under the rules of simplex technique and the operations on trapezoidal fuzzy numbersEmamet al. ,suggested a new solution method to solve bi-level linear fractional integer programming problem with trapezoidal fuzzy numbers in the objective functions of the two levels .In [5]Dashetal. aimed to present a method in which a fuzzy multi objective nonlinear programming problem is reduced to crisp using ranking function and the crisp problem is solved by fuzzy programming technique
An algorithm is presented to solve (MLMOQPP) with fuzzy parameters in the objective functions, the algorithm is illustrated in the following series steps: Step 1: ComputeR A for all the coefficients ofthe (MLMOQPP) with fuzzy number in the objective functions (1) - (3), where A is a trapezoidal fuzzy number
Summary
Fuzzy approach uses the concept of tolerance membership to develop a fuzzy max-min decisionModel for generating Pareto optimal (satisfactory) solution [1 and 3]. In [3] Osman et al presented the concepts of tolerance membership function and multi-objective optimization at each level to develop a fuzzy max-min decision model for generating (satisfactory) solution for three level multi-objective programming problem. Aimed to present a method in which a fuzzy multi objective nonlinear programming problem is reduced to crisp using ranking function and the crisp problem is solved by fuzzy programming technique. In [6]Nasseri defined a quadratic programming problem with trapezoidal and/or triangularfuzzy numbers in the cost coefficients,constraint coefficients, and right-hand sides used linear ranking method to solve the problem
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