A Parametric Approach for Solving Interval–Valued fractional Continuous Static Games


  • Mervat Elshafei




Continuous Static Games, Nonlinear Programming Problem, Fractional Programming problem, Interval-Valued optimization


The aim of this paper is to show that a parametric approach can be used to solve fractional continuous static games with interval-valued in the objective function and in the constraints. In this game, cooperation among all the players is possible, and each player helps the others up to the point of disadvantage to himself, so we use the Pareto-minimal solution concept to solve this type of game. The Dinkelbach method is used to transform fractional continuous static games into non- fractional continuous static games. Moreover, an algorithm with the corresponding flowchart to explain the suggested approach is introduced. Finally, a numerical example to illustrate the algorithm’s steps is given.


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Author Biography

Mervat Elshafei

Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt.


Thomas L. Vincent, and Walter J.Grantham, Optimality in Parametric Systems. John Wiley and Sons, New York, Chichester. Brisbane, Toronto (1981).

P. Frihouf, M. Krstic and T.Basar, Nash Equilibrium Seeking in Non-cooperative Games, IEEE Transaction on Automatic Control, 57(5) (2012) 1192-1207.

A.V. Heusiger and C. Kanzow, Relaxation Methods for generalized Nash Equilibrium Problems with Inexact Line Search, Journal of Optimization Theory and Applications, 143 (1) (2009) 159-183.

M.Borza, A.S.Rambely, and M. Saraj Solving Linear Fractional Programming Problems with Interval Coefficients in the Objective Function, Applied Mathematical Sciences, (69) (2012) 3443-3452.

M. Jayalakshmi, A New Approach for Solving Quadratic Fractional programming Problems. International Journal of Applied Research, 1 (10) (2015) 788-792.

M. Jayalakshmi, On Solving Linear Factorized Quadratic Fractional Programming Problems, International Journal of Applied Research, 1(9) (2015) 1037-1040.

S. Singh, and N. Haldar, A New Method to Solve Bi-level Quadratic Linear Fractional Programming Problems, International Game Theory Review, 17 (2) (2015) 1540017-1540043.

T. Antczak, A Modified Objective Function Method for Solving Nonlinear Multi-Objective Fractional Programming Problems, Journal of Mathematical Analysis and Application, 322 (2006) 971 – 989.

T. Ibaraki, H.I.J. Iwase, T. Hasegawa, and H. Mine, Algorithms for Quadratic Fractional Programming Problems, Journal of the Operations Research, 19 (2) (1976) 174 -181.

W. Dinkelbach, On Nonlinear Fractional Programming, Management Science, 13 (1967) 492-498.

H. Chung Wu, On Interval–Valued Nonlinear Programming Problems, Journal of Mathematical Analysis and Applications, 338 (2008) 299-316.

S. Effati, and M. Pakdaman Solving the Interval-valued Linear Fractional Programming Problem, American Journal of Computational Mathematics, 2(2012) 51- 55.




How to Cite

Elshafei, M. (2019). A Parametric Approach for Solving Interval–Valued fractional Continuous Static Games. JOURNAL OF ADVANCES IN MATHEMATICS, 17, 155–164. https://doi.org/10.24297/jam.v17i0.8419