Subject Areas : Statistics

omekolsoom khazaee kohpar ¹ , S. H. Nasseri ²

1 - mazandaran university
2 - Department of Mathematics, University of Mazandaran, Babolsar, Iran.

Received: 2017-10-31 Accepted : 2018-01-31 Published : 2024-01-18

Keywords: برنامه ریزی کسری خطی, برنامه ریزی فازی, برنامه ریزی چند هدفه,

References:


[1] خزائی کوه پر ا.، (1396)، بهبود روش های حل مسائل برنامه ريزی کسری خطی چندهدفه با پارامترهای مشکک، پايان نامه دکتری، دانشگاه مازندران، بابلسر.

[2] ناصری س ه.، عطاری ح.، (1394)، برنامه ريزی خطی فازی، انتشارات دانشگاه مازندران، بابلسر.

[3] ناصری س ه.، غلامی ا.، ابراهيم نژاد ع.، فلاح جلودار م.، (1395)، يک رويکرد جديد مبتنی بر آلفا برش‌ها برای حل مدل تحليل پوششی داده‌ها با ورودی‌ها و خروجی‌های تصادفی فازی، پژوهش های نوين در رياضی، دوره 2، شماره 5، صص 61 تا 70.

[4] Isbell J.R., Marlow W.H. (1956). Attrition games. Naval Research Logistics Quarterly, 3, 1-99.

[5] Charnes A., Cooper W.W. (1962). Programming with linear fractional functions. Naval Research Logistics Quarterly, 9, 181-186.

[6] Gilmore P.C., Gomory R.E. (1963). Linear programming approach to the cutting stock problem: Part 2. Operations Research, 11, 863-867.

[7] Martos B. (1964). Hyperbolic programming. Naval Research Logistics Quarterly, 11, 135-155.

[8] Swarup K. (1965). Linear fractional functional programming. Operations Research, 13, 1029-1036.

[9] Dantzig G.B. (1962). Linear Programming and Extension. Princeton University Press, Princeton, New Jersey.

[10] Chadha S.S. (2002). Fractional programming with absolute-value function. European Journal of Operations Research, 141, 233-238.

[11] Chan C.-T. (2005). Fractional programming with absolute-value functions: a fuzzy goal programming approach. Applied Mathematics and Computation, 167, 508-515.

[12] Tantawy S.F. (2008). A new procedure for solving linear fractional programming problems. Mathematical and Computer Modelling, 48, 969-973.

[13] Tantawy S.F. (2007). Using feasible directions to solve linear fractional programming problems. Australian Journal of Basic and Applied Sciences, 1, 109-114.

[14] Mojtaba B., Azmin S., Mansour S. (2012). Solving linear fractional programming problems with interval coefficients in the objective function: A new approach. Applied Mathematical Sciences, 6, 3442-3452.

[15] Bellman R.E., Zadeh L.A. (1970). Decision making in a fuzzy environment. Management Science, 17, 141-164.

[16] Tanaka H., Okuda T., Asai K. (1973). On fuzzy mathematical programming. Journal of Cybernetics and Systems, 3, 37-46.

[17] Baky, I.A. (2010). Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach. Applied Mathematical Modeling, 34, 2377-2387.

[18] Dutta D., Rao J.R., Tiwari R.N. (1993). Effect of tolerance in fuzzy linear fractional programming. Fuzzy Sets and Systems, 55, 133-142.

[19] Li D.F., Chen S. (1996). A fuzzy programming approach to fuzzy linear fractional programming with fuzzy coefficients. Journal of Fuzzy Mathematics, 4, 829-834.

[20] Nasseri S.H., Khazaee Kohpar O. (2015). Pareto-optimal solutions in multi-objective linear programming with fuzzy numbers. Annals of Fuzzy Mathematics and Informatics, 9, 823-833.

[21] Pal B.B., Moitra B.N., Maulik U. (2003). A goal programming procedure for fuzzy multiobjective linear fractional programming problem. Fuzzy Sets and Systems, 139, 395-405.

[22] Chinnadurai V., Muthukumar S. (2016). Solving the linear fractional programming problem in a fuzzy environment: Numerical approach. Applied Mathematical Modelling, 40, 6148-6164.

[23] Nasseri S.H., Khazaee Kohpar O. (2017). An improved approach for solving interval number and fuzzy number LP problems with its application in fuzzy multi-objective linear fractional programming. submitted.

[24] Klir G.J., Clair V.S., Yuan B. (1997). Fuzzy set theory: foundation and application. Printice-Hall Inc.

[25] Ma M., Friedman M., Kandel A. (1999). A new fuzzy arithmetic. Fuzzy Sets and Systems, 108, 83-90.

[26] Goetschel R., Voxman W. (1986). Elementary fuzzy calculus. Fuzzy Sets and Systems, 18, 31-43.

[27] Craven B.D. (1988). Fractional Programming. Heldermann Verlag, Berlin.
[28] Chakraborty M., Gupta S. (2002). Fuzzy mathematical programming for multi objective linear fractional programming problem. Fuzzy Sets and Systems, 125, 335-342.

[29] Schaible S. (1976). Fractional programming 1:duality. Management Science, 22, 658-667.

[30] Schaible S. (1978). Analyse and Anwendungen Von Quotienten Programmen. Verlag Anton Hain, Meisenheim am Glan.

[31] Ganesan K., Veeramani P. (2006). Fuzzy linear programs with trapezoidal fuzzy numbers. Annals of Operations Research, 143, 305-315.

[32] Cao B-Y. (2010). Optimal Models and Methods with Fuzzy Quantities. Springer- Verlag Berline Heidelberg.

[33] Lodwick W.A., Kacprzyk J. (2010). Fuzzy Optimization: Recent advances and applications. Springer- Verlag Berline Heidelberg.

[34] Zimmermann J. (1976). Description and optimization of fuzzy systems. International Journal of General Systems, 2, 209-215.