A New Method for Solving the Fully Z-Numbers Linear Programming Problems

Subject Areas : International Journal of Mathematical Modelling & Computations

Mahboobeh Joghataeea ¹ , Farhad Hosseinzadeh ^{2 *} , Ali Ebrahimnejadd ³ , Tofigh Allahviranloo ⁴

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research Branch,Islamic Azad University, Tehran,Iran
3 - Department of Mathematics, Islamic Azad University, Qaemshahr, Iran
4 - Faculty of engineering and natural sciences, Bahcesehir University, Istanbul, Turkey

Received: 2023-02-11 Accepted : 2023-03-25 Published : 2023-03-01

Keywords: Fuzzy Z-number, Z-Linear Programming, Ranking method, Non-negative fuzzy Numbers,

Abstract :

Decisions are based on information. To be useful, information must be reliable. The concept of a Z-number relates to the issue of reliability of the information. the fully Z-number linear programming problems (FZLPP) in which all the parameters, as well as the variables, are represented by fully Z-numbers is a good topic for readers. and in this study, we proposed a practical method to solve fully Z-numbers linear programming by using the fuzzy ranking method for constraints and converting objective function to a multi-objective function, and finding their optimal solution with Z-number.

References:

[1] Alive, R.A., Alizadeh, A.V., Huseynov, O.H.: The arithmetic of Z-numbers, Inform. Sciences 290, (2015), 134–155.
[2] Tanaka, H., Okuda, T., Asai, K.: On fuzzy mathematical programming. The Journal of Cybernetics 3, (1974), 37–46.
[3] Zimmermann, H.J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, (1978), 45–55.
[4] Abbaszadeh Sori, A., A. Ebrahimnejad, H. Motameni. The fuzzy inference approach to solve multi-objective constrained shortest path problem, Journal of Intelligent & Fuzzy Systems, 38, (2020), 4711–4720.
[5] Delgado, M., Verdegay, J.L., Vila, M.A.: A general model for fuzzy linear programming. Fuzzy Sets Syst. 29, (1989), 21–29.
[6] Ebrahimnejad, A.: New method for solving Fuzzy transportation problems with LR fat fuzzy numbers. Inf. Sci. 357, (2016), 108–124.
[7] Ebrahimnejad, A., An efective computational attempt for solving fully fuzzy linear programming using MOLP problem, Journal of Industrial and Production Engineering, (2019), 59–69.
[8] Mahdavi-Amiri, N., Nasseri, S.H.: Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables. Fuzzy Sets Syst. 158, (2007), 1961–1978.
[9] Maleki, H.R., Tata, M., Mashinchi, M.: Linear programming with fuzzy variables. Fuzzy Sets Syst. 109, (2000), 21–33.
[10] Verdegay, J.L.: A dual approach to solve the fuzzy linear programming problem. Fuzzy Sets Syst. 14, (1984), 131–141.
[11] Yager, R.R.: On Z-Valuations Using Zadeh’s Z-Numbers. Int. J. Intell. Syst. 27, (2012), 259–278.
[12] Alive, O.H. Huseynov, R.R. Alive, A.V. Alizadeh., The arithmetic of Z-numbers. Theory and Applications, World Scientifc, Singapore, (2015).
[13] Alive, R.A., O.H. Huseynov, and R. Serdaroglu., Ranking of Z-numbers, and its Application in Decision Making. Int. J.
[14] Kang, B., Wei, D., Li, Y., Deng, Y.: A method of converting Z-numberto classical fuzzy number. Journal of Information and Computational Science 3, (2012), 703–709.
[15] Kang, B., Wei, D., Li, Y., Deng, Y.: Decision Making Using Z-numbers under Uncertain Environment. Journal of Computational Information Systems 7, (2012), 2807–2814.
[16] Ezadi, S., T. Allahviranloo., New multi-layer method for Z-numberranking using Hyperbolic Tangent function and convex combination, Intelligent Automation Soft Computing., (2017), 1–7.
[17] Hasankhani, F, Allahviranloo, T., A new method for solving linear programming problems using Z-numbers ranking, Mathematical Sciences, (2021), 35-46.
[18] Edalatpanah, S.A.; Shahabi, S. A new two-phase method for the fuzzy primal simplex algorithm. Int. Rev, Pure Appl. Math. (2012), 8, 157–164.
[19] Rodríguez, R.M.; Martínez, L.; Herrera, F.; Torra, V. A Review of Hesitant Fuzzy Sets: Quantitative and Qualitative Extensions. In Fuzzy Logic in Its 50th Year; Springer International Publishing: Cham, Switzerland, (2016), 109–128.
[20] Zadeh L. A. Calculus of fuzzy restrictions, eds. Zadeh, L. A., Fu, K.S., Tanaka, K. and Shimura, M.” Fuzzy sets and Their Applications to Cognitive and Decision Processes,” (Academic Press, New York), (1975), 1–39.
[21] Zadeh, L. A. Generalized theory of uncertainty (GTU) – principal concepts and ideas, Comput. Stat. Data An., 51, (2006), 15-46.
[22] Zadeh, L. A. Probability measures of fuzzy events, J. Math. Anal. Appl.23(2), (1968), 421–427.
[23] Ezadi, S., T. Allahviranloo., Numerical solution of linear regression based on Z-numbers by improved neural network, IntellIgent Automation and Soft ComputIng, (2017), 1-11.
[24] Ebrahimnejad, A.: Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem. Operational Research, (2020),121-152.
[25] Kumar, A., Kaur J., Singh P:"A new method for solving fully fuzzy linear programming problems"; Applied Mathematical Modeling, Vol. 35, (2011).