A multiobjective approach for solving fully fuzzy linear fractional programming problems with trapezoidal fuzzy numbers

Document Type : Original Article

Authors

1 Department of Mathematics, Gonbad Kavous University,, Gonbad Kavous, Iran

2 Department of Mathematics, Faculty of Basic Sciences, University of Shahrood

Abstract

Fractional programming problems is one of the efficient and common tools in many problems of real worlds,
because optimizing the ratio of the purposes creates better vision than optimizing any of proposes, separately. But, as the values observed in the real world are inaccurate and ambiguous due to incomplete or inaccessible information, in this paper fuzzy numbers are used and a fuzzy linear fractional programming problem is created. In this paper, a new method for solving fully fuzzy linear fractional programming problems with trapezoidal fuzzy numbers and inequality constraints is proposed. In this method, the fuzzy problem is transformed to a multi-objective linear programming problem and then using lexicographical order the optimal solution is obtained. Finally, using some examples, the presented method is implemented practically and compared with other methods. Also, desirability of the new approach in terms of simplicity of operations and accuracy of the results is measured.
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Keywords

References

[1]ابراهیم نژاد، ع. ‎(1398)‎ بازبینی یک مدل ریاضی برای حل مساله‌ی برنامه‌ریزی خطی تماما فازی با اعداد ذوزنقه‌ای. پژوهش‌های نوین در ریاضی.
 
[2] Alharbi, M. G. and Khalifa, H. A. (2021). On solutions of fully fuzzy linear fractional programming problems using close interval approximation for normalized heptagonal fuzzy numbers. Applied Mathematics and Information Sciences, 15(4), 471-477.
 
[3] Arya, R., Singh, P., Kumari, S. and Obaidat, M. (2019). An approach for solving fully fuzzy multi-objective linear fractional optimization problems. Soft Computing, 24, 9105–9119.
 
[4] Ben-Tal, A., El-Ghaoui, L. and Nemirovski, A. (2009). Robust Optimization. Princeton Series in Applied Mathematics, Princeton University Press.
 
[5] Bhatia, T. K., Kumar, A., Sharma, M. K. and Appadoo, S. S. (2022). Mehar approach to solve fuzzy linear fractional minimal cost flow problems. Journal of Intelligent and Fuzzy Systems, In Press, DOI: 10.3233/JIFS-212909.
 
[6] Borza, M. and Rambely, A. S. (2021). A new method to solve multi-objective linear fractional problems, Fuzzy Information and Engineering, 13(3), 323-334.
 
[7] Chinnadurai, V. and Muthukumar, S. (2016). Solving the linear fractional programming problem in a fuzzy environment: Numerical approach. Applied Mathematical Modelling, 40(11-12), 6148-6164.
 
[8] Das, S. K., Edalatpanah, S. A. and Mandal, T. (2018). A proposed model for solving fuzzy linear fractional programming problem: Numerical Point of View. Journal of Computational Science, 25, 367-375.
 
[9] Das, S. K., Mandal, T. and Edalatpanah, S. A. (2017). A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-Operations research, 51(1), 285-297.
 
[10] Das, S. K. and Mandal, T. (2017). A new model for solving fuzzy linear fractional programming problem with ranking function. Journal of applied research on industrial engineering, 4(2), 89-96.
 
[11] Deb, M. (2018). A study of fully fuzzy linear fractional programming problems by signed distance ranking technique. In Optimization Techniques for Problem Solving in Uncertainty (pp. 73-115). IGI Global.
 
[12] Dutta, D., Tiwari, R.N. and Rao, J.R. (1992). Multiple objective linear fractional programming- A fuzzy set theoretic approach. Fuzzy Sets Syst, 52, 39-45.
 
[13] Ebrahimnejad, A., Ghomi, S. J. and Mirhosseini-Alizamini, S. M. (2017). A new approach for solving fully fuzzy linear fractional programming problems. In 2017 IEEE 4th International Conference on Knowledge-Based Engineering and Innovation (pp. 862-865). IEEE.
 
[14] Ebrahimnejad, A., Verdegay, J. L. (2018). Fuzzy Sets-Based Methods and Techniques for Modern Analytics. Studies in Fuzziness and Soft Computing, vol. 364. Springer, Cham.
 
[15] Ebrahimnejad, A. (2019). An effective computational attempt for solving fully fuzzy linear programming using MOLP problem. Journal of Industrial and Production Engineering, 36(2), 59-69.
 
[16] Ehrgott, M. (2005). Multicriteria Optimization Springer, Berlin.
 
[17] Farnam, M., and Darehmiraki, M. (2020). Hesitant Fuzzy Linear Fractional Programming Problem. In International Online Conference on Intelligent Decision Science (pp. 864-872). Springer, Cham.
 
[18] Kumar, A., Kaur, J., Singh, P. (2011). A new method for solving fully fuzzy linear programming problems. Applied Mathematical Modelling, 35, 817–823.
 
 [19] Kumar, A., Kaur, J. (2014). Fuzzy optimal solution of fully fuzzy linear programming problems using ranking function. Journal of Intelligent Fuzzy Systems, 16(1), 337-344.
 
[20] Kumar, A., Kaur, A. (2014). Optimal way of selecting cities and conveyances for supplying coal in uncertain environment, adhana, 39(1), 165-187.
 
[21] Kumar-Das, S. (2019). A new method for solving fuzzy linear fractional programming problem with new ranking function. International Journal of Research in Industrial Engineering, 8(4), 384-393.
 
[22] Li, D. F. and Chen, S. (1996). A fuzzy programming approach to fuzzy linear fractional programming with fuzzy coefficients. The Journal of Fuzzy Mathematics, 4, 829-834.
 
[23] Loganathan, T., and Ganesan, K. (2019). A solution approach to fully fuzzy linear fractional programming problems. In Journal of Physics: Conference Series (Vol. 1377, No. 1, p. 012040). IOP Publishing.
 
[24] Loganathan, T., and Ganesan, K. (2021). Solution of fully Fuzzy Linear Fractional Programming Problem-A Simple Approach. In IOP Conference Series: Materials Science and Engineering (Vol. 1130, No. 1, p. 012047). IOP Publishing.
 
[25] Mahmoodirad, A., Garg, H., and Niroomand, S. (2020). Solving fuzzy linear fractional set covering problem by a goal programming based solution approach. Journal of Industrial Management Optimization.
 
[26] Mehlawat, M. K. and Kumar, S. (2012). A solution procedure for a linear fractional programming problem with fuzzy numbers. In Proceedings of the International Conference on Soft Computing for Problem Solving (SocProS 2011) December 20-22, 2011 (pp. 1037-1049). Springer, India.
 
[27] Pop, B. and Stancu-Minasian, I.M. (2008). A method of solving fuzzy fuzzified linear fractional programming problems. J. Appl. Math. Comput, 27, 227-242.
 
[28] Pramy, F. A. (2018). An approach for solving fuzzy multi-objective linear fractional programming problems. International Journal of Mathematical, Engineering and Management Sciences, 3(3), 280-293.
 
[29] Safaei, N. (2014). A new method for solving fully fuzzy linear fractional programming with a triangular fuzzy numbers. Applied Mathematics and Computational Intelligence, 3(1), 273-281.
 
[30] Sakawa, M. and Yano, H. (1988). An interactive fuzzy satisficing method for multi objective linear fractional programming problems. Fuzzy Sets Syst, 28, 129- 144.
 
[31] Sakawa, M., Yano, H. and Takahashi, J. (1992). Pareto optimality for multi objective linear fractional programming problems with fuzzy parameters. Inf. Sci, 63, 33-53.
 
[32] Shapiro, A., Dentcheva, D. and Ruszczynski, A. (2021). Lectures on Stochastic Programming. Modeling and Theory. SIAM.
 
[33] Stancu-Minasian, I.M. and Pop, B. (2003). On a fuzzy set approach to solving multiple objective linear fractional programming problem. Fuzzy Sets Syst, 134, 397-405.
 
[34] Stanojevic, B. and Stancu-Minasian, I.M. (2009). On solving fuzzified linear fractional programs. Adv.Model.Optim, 11, 503-523.
 
[35] Stanojevic, B. and I.M. Stancu-Minasian, I.M. (2012). Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs. Yugoslav J. Oper. Res, 1, 41 -50.
 
[36] Toksari, M.D. (2008). Taylor series approach to fuzzy multi objective linear fractional programming. Inf. Sci, 178, 1189-1204.
 
[37] Veeramani, C. and Sumathi, M. (2014). Fuzzy mathematical programming approach for solving fuzzy linear fractional Programming Problems. RAIRO Operations research, 48(1), 109-122.
 
[38] Veeramani, C. and Sumathi, M. (2016). A new method for solving fuzzy linear fractional Programming Problems. Journal Of Intelligent Fuzzy Systems, 31(3), 1831-1843.
 
[39] Veeramani, C., Sharanya, S. and Ebrahimnejad, A. (2020). Optimization for multi-objective sum of linear and linear fractional programming problem. Fuzzy nonlinear programming approach. Mathematical Sciences, 1-15.
 
[40] Wang, Y. M., Yang, J. B., Xu, D. L. and Chin, K. S. (2006). On the centroids of fuzzy numbers. Fuzzy Sets Syst, 157(7), 919-926.
 
[41] Younsi-Abbaci, L., and Moulai, M. (2021). Solving the Multi-Objective Stochastic Interval-Valued Linear Fractional Integer Programming Problem. AsianEuropean Journal of Mathematics.
 
[42] Zadeh, L.A. (1965). Fuzzy Sets. Inf. Control, 8, 338-353.
Fuzzy Systems and its Applications
Volume 5, Issue 2 - Serial Number 11
January 2023
Pages 121-154

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History

  • Receive Date: 11 November 2021
  • Revise Date: 24 May 2022
  • Accept Date: 23 September 2022

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