Solving fully linear programming problem based on Z-numbers

Document Type : Original Manuscript

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Faculty of engineering and natural science, Istinye university, Istanbul, Turkey.

3 I.A.U., Science and Research Branch

4 Department of Mathematics, Islamic Azad University, Iran

5 Imam Khomeini Int. University

6 Faculty of engineering and natural sciences, Istinye University, Istanbul, Turkey

7 College of Engineering and Technology, American University of the Middle East, Kuwait

Abstract

Generally exploring the exact solution of linear programming problems in which all variables and parameters are  Z-numbers, is either not possible or difficult. Therefore, a few numerical methods to find the numerical solutions do act an  important role in these problems. In this paper, we concentrate on introducing a new numerical method to solve such  problems based on the ranking function. After proving the necessary theories, for more illustrations and the correctness  of the topic, some theoretical and practical examples are also provided. Finally, the results obtained from the proposed  method have been compared with some existing methods.

Keywords

References

[1] R. A. Alive, O. H. Huseynov, R. R. Alizadeh, The arithmetic of Z-numbers. Theory and applications, World Scientific, Singapore, 2015.
[2] T. Allahviranloo, S. Abbasbandy, R. A. Saneifard, Method for ranking of fuzzy numbers using new weighted distance, Mathematical and Computational Applications, 16(2) (2011), 359-369.
[3] A. Abbaszadeh Sori, A. Ebrahimnejad, H. Motameni, The fuzzy inference approach to solve multi-objective con[1]strained shortest path problem, Journal of Intelligent and Fuzzy Systems, 38 (2020), 4711-4720.
[4] A. Ebrahimnejad, An effective computational attempt for solving fully fuzzy linear programming using MOLP problem, Journal of Industrial and Production Engineering, (2019), 59-69.
[5] A. Ebrahimnejad, Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem, Operational Research, (2020), 121-152.
[6] S. Ezadi, T. Allahviranloo, New multi-layer method for Z-number ranking using Hyperbolic Tangent function and convex combination, Intelligent Automation Soft Computing, (2017), 1-7.
[7] S. Ezadi, T. Allahviranloo, Two new methods for ranking of Z-numbers based on sigmoid function and sign method, International Journal of Intelligent Systems, (2018), 1-12.
[8] P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets and Systems, 130(3) (2002), 321-330.
[9] F. Hasankhani, T. Allahviranloo, A new method for solving linear programming problems using Z-numbers ranking, Mathematical Sciences, (2021), 35-46.
[10] B. Kang, D. Wei, Y. Li, Y. Deng, A method of converting Z-number to classical fuzzy number, Journal of Information and Computational Science, 3 (2012), 703-709.
[11] A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Applied Mathe[1]matical Modeling, 35(2) (2011), 817-823.
[12] H. Tanaka, T. Okuda, K. Asai, On fuzzy mathematical programming, The Journal of Cybernetics, 3 (1974), 37-46.
[13] J. L. Verdegay, A dual approach to solve the fuzzy linear programming problem, Fuzzy Sets and Systems, 14 (1984), 131-141.
[14] R. R. Yager, On Z-Valuations using Zadehs Z-numbers, International Journal of Intelligent Systems, 27 (2012), 259-278.
[15] L. A. Zadeh, Generalized theory of uncertainty (GTU)–principal concepts and ideas, Computational Statistics and Data Analysis, 51 (2006), 15-46.
[16] L. A. Zadeh, A note on Z-numbers, Information Sciences, 181 (2011), 2923-2932.
[17] H. J. Zimmermann, Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1 (1978), 45-55.