Fuzzy polynomials for solving the fuzzy multi-choice optimal programming problem

Document Type : Original Article

Authors

Faculty of Mathematics, Statistics and Computer Science, University of Sistan and Baluchistan, Zahedan, Iran

10.22034/jfsa.2023.188514

Abstract

One of the methods of solving multi-objective programming problems is the use of ideal programming problems,
in which the decision maker considers an ideal level for each objective function. In real-life problems,
several ideal levels may be available for an objective function, or these ideal levels are of fuzzy type,
in which case fuzzy multi-choice ideal programming problems arise. In this article, the introduction and solution
of fuzzy multi-choice ideal programming problems are discussed, so that first the problem becomes a fuzzy multi-choice
programming problem in which there are several choices for the right side of the constraints, then using fuzzy binary
polynomials and polynomials Fuzzy linear least squares is a classic linear programming problem, which is solved using
Lingo software.
The described algorithm is used to solve a practical example in the field of fuzzy multi-choice ideal programming
problems, and the previous results are compared and analyzed with the results obtained from this method.











 









 

 


 

Keywords

References

[1] Acharya, S., & Biswal, M. P. (2015). Application of multi-choice fuzzy linear programming problem to a garment manufacture company. Journal of Information and Optimization Sciences, 36(6), 569-593.
[2] Aggrawal, S., Sharma, U. (2013). Fully fuzzy multi-choice multi-objective linear programming solution via devition degree. International journal of pure and applied bioscience, 19(1), 49.
[3] Al Qahtani, H., El-Hefnawy, A. El-Ashram, M. M. & Fayomi A. (2019). A goal programming approach to multichoice multiobjective stochastic transoirtation problems with exterma value distribution. Advances in Operator Theory, 1-6.
[4] Bankian-Tabrizi, B., Shahanaghi, K., & Jabalameli, M. S. (2012). Fuzzy multi-choice goal programming. Applied Mathematical Modelling, 36(4), 1415-1420.
[5] Biswal, M. P., & Acharya, S. (2009). Multi-choice multi-objective linear programming problem. Journal of Interdisciplinary Mathematics, 12(5), 606-637.
[6] Biswal, M. P., & Acharya, S. (2009). Transformation of a multi-choice linear programming problem. Applied Mathematics and computation, 210(1), 182-188.
[7] Chang, C. T. (2007). Multi-choice goal programming. Omega, 35(4), 389-396.
[8] Chang, C. T. (2008). Revised multi-choice goal programming. Applied mathematical modelling,
32(12), 2587-2595.
[9] Charnes, A., & Cooper, W. W. (1957). Management models and industrial applications of linear programming. Management science, 4(1), 38-91.
[10] Hannan, E. L. (1985). An assessment of some criticisms of goal programming. Computers & Operations Research, 12(6), 525-541.
[11] Hannan, E. L. (1981). On fuzzy goal programming. Decision sciences, 12(3), 522-531.
[12] Keshteli, G. R.& Nasseri, S. H. (2020) A milti-parametric approach to solve flexible fuzzy multi-choice goal programming. Punjab University Journal of Mathematics, 51(12), 93-108.
[13] Lee, S. M. (1972). Goal programming for decision analysis. Publishers, Philadelphia.
[14] Narasimhan, R. (1980). Goal programming in a fuzzy environment. Decision sciences, 11(2), 325-336.
[15] Patro, K. K., Acharya, M. M., Biswal, M. P., & Acharya, S. (2015). Computation of a multi-choice
goal programming problem. Applied Mathematics and Computation, 271, 489-501.
[16] Tamiz, M., Jones, D., & Romero, C. (1998). Goal programming for decision making: An overview of the current state-of-the-art. European Journal of operational research, 111(3), 569-581.
[17] Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy sets and systems, 1(1), 45-55.

Files

History

  • Receive Date: 26 January 2024
  • Accept Date: 26 January 2024

Share

How to cite

Statistics