# Omar M. Saad, Mervat M. Elshafei and Marwa M. Sleem, Interactive Approach for Multi-level Quadratic Fractional Programming Problems, Volume 2017, Number 4, Pages 1-13, 2017.

**Abstract:** This paper, present an Interactive decision making method for multi-level quadratic fractional programming \textbf{(MLQFP)} problems. The upper-level objective function is quadratic fractional problem in which both the numeratorand denominator of the objective function can be factorized into linear function, the second-level objective function is quadratic fractional programming \textbf{(QPP)} problem in which the objective function can be factorized into linear functions and the denominator of the objective function in linear type and the third-level objective function is linear fractional with linear constraint. \textbf{(MLQFP)} problem is transformed into an equivalent bi-level quadratic fractional programming \textbf{(QFP)} problem by forcing the duality gap of the lower-level problem to zero. Then by using interactive approach for solving \textbf{(BLFQP)} problem, the first level decision maker \textbf{(FLDM)} give the preferred as satisfactory solution that are acceptable in rank order to second level decision maker. \textbf{(SLDM)} take the satisfactory solution one by one to seek the solutions, who will search for the preferred solution of \textbf{(FLDM)} until the preferred solution is reached. Finally, an illustrative numerical example is provided.

**Key words :** Multi-level programming; Quadratic Programming; Fractional Programming; Linear Programming.

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Omar M. Saad, Mervat M. Elshafei and Marwa M. Sleem, Interactive Approach for Multi-level Quadratic Fractional Programming Problems, Â International Journal of Advances in Mathematics, Volume 2017, Number 4, Pages 1-13, 2017.