Interval type-2 fuzzy linear programming problem with vagueness in the resources vector

Document Type : Research Paper

Authors

Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

Abstract

One of the special cases of type-2 fuzzy sets are the interval type-2 fuzzy sets, which are less complicated and easier to understand than T2FSs. In this study, we explore the interval type-2 fuzzy linear programming problem with the resources vector that have imprecision of the vagueness type. These types of vagueness are expressed via membership functions. First, we review the three available methods, including the Figueroa and Sarani methods. Then, using the three ideas of Verdegay, Werners, and Guu and Wu for solving fuzzy linear programming problems with vagueness in the resources vector, we propose three new methods for solving interval type-2 fuzzy linear programming problems with vagueness in the resources vector. Finally, we demonstrate the effectiveness of our proposed methods by solving an example and comparing the results obtained with each other and with those of previous methods.

Keywords

Main Subjects

References

1] Abdolmaleki, SF., & Bugallo, PMB. (2021). Evaluation of renewable energy system for sustainable development. Renewable Energy and Environmental Sustainability, 6, 44. https://doi.org/10.1051/rees/2021045
[2] Akram, M., Ullah, I.,& Allahviranloo, T. (2022). A new method to solve linear programming problems in the environment of picture fuzzy sets. Iranian Journal of Fuzzy Systems, 19(6), 29-49. https://doi.org/10.22111/ijfs.2022.7208
[3] Akram, M., Ullah, I., & Allahviranloo, T. (2022). A new method for the solution of fully fuzzy linear programming models. Computational and Applied Mathematics, 41(1), 55. https://doi.org/10.1007/s40314-021-01756-4
[4] Akram, M., Ullah, I., & Allahviranloo, T. (2023). An interactive method for the solution of fully Z-number linear programming models. Granular Computing, 8(6), 1205-1227. https://doi.org/10.1007/s41066-023-00402-0
[5] Allahdadi, M., & Batamiz, A. (2021). Generation of some methods for solving interval multi-objective linear programming models. OPSERCH, 58(4), 1077-1115. https://doi.org/10.1007/s12597-021-00512-w
[6] Ashayerinasab, HA., Mishmast Nehi, H., & Allahdadi, M. (2018). Solving the interval linear programming problem: A new algorithm for a general case. Expert Systems with Applications, 93, 39-49. https://doi.org/10.1016/j.eswa.2017.10.020
[7] Bellman, RE., & Zadeh, LA. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B-141. https://doi.org/10.1287/mnsc.17.4.B141
[8] Bojan-Dragos, CA., Precup, RE., Preitl, S., Roman, RC., Hedrea, EL., & Szedlak-Stinean, AI. (2021). GWO-based optimal tuning of type-1 and type-2 fuzzy controllers for electromagnetic actuated clutch systems. IFAC-PapersOnLine, 54(4), 189-
194. https://doi.org/10.1016/j.ifacol.2021.10.032
[9] Castillo, O., Castro, JR., & Melin, P. (2023). Forecasting the COVID-19 with interval type-3 fuzzy logic and the fractal dimension. International Journal of Fuzzy Systems, 25(1), 182-197. https://doi.org/10.1007/s40815-022-01351-7
[10] Figueroa-Garcia, JC., & Hernandez, G. (2012). Computing optimal solutions of a linear programming problem with interval type-2 fuzzy constraints. In Hybrid Artificial Intelligent Systems: 7th International Conference, HAIS 2012, Salamanca, Spain, March 28-30th, Proceedings, Part I 7 (pp. 567-576). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-28942-2_ 51
[11] Figueroa-Garcia, JC. (2008). Linear programming with interval type-2 fuzzy right hand side parameters. In NAFIPS 2008-2008 Annual Meeting of the North American Fuzzy Information Processing Society, (pp. 1-6). IEEE. https://doi.org/10.1109/NAFIPS.2008.4531280
[12] Figueroa-Garcia, JC. (2009). Solving fuzzy linear programming problems with interval type-2 RHS. In 2009 IEEE International Conference on Systems, Man and Cybernetics (pp. 262-267). IEEE. https://doi.org/10.1109/ICSMC.2009.5345943
[13] Figueroa-Garcia, JC., & Hernandez, G. (2014). A method for solving linear programming models with interval type-2 fuzzy constraints. Pesquisa Operacional, 34, 73-89. https://doi.org/10.1590/S0101-74382014005000002
[14] Golpayegani, Z., & Mishmast Nehi, H. (2013). Interval type-2 fuzzy linear programming: general uncertainty model. In 44th Annual Iranian Mathematics Conference, Mashhad, Iran (pp. 85-88). https://sid.ir/paper/840171/fa [In Persian]
[15] Guu, SM., & Wu, YK. (1999). Two-phase approach for solving the fuzzy linear programming problems. Fuzzy Sets and Systems, 107(2), 191-195. https://doi.org/10.1016/S0165-0114(97)00304-7
[16] Klir, G. J., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall Inc. Upper Saddle River, NJ, USA.
[17] Li, H., Dai, X., Zhou, L., & Wu, Q. (2023). Encoding words into interval type-2 fuzzy sets: The retained region approach. Information Sciences, 629, 760-777. https://doi.org/10.1016/j.ins.2023.02.022
[18] Mendel, JM., John, RI., & Liu, F. (2006). Interval type-2 fuzzy logic systems made simple. IEEE Transactions on Fuzzy Systems, 14(6), 808-821. https://doi.org/10.1109/TFUZZ.2006.879986
[19] Mendel, JM., Liu, F., & Zhai, D. (2009). α-plane representation for type-2 fuzzy sets: Theory and applications. IEEE Transactions on Fuzzy Systems, 17(5), 1189-1207. https://doi.org/10.1109/TFUZZ.2009.2024411
[20] Pan, X., & Wang, Y. (2021). Evaluation of renewable energy sources in China using an interval type-2 fuzzy large-scale group risk evaluation method. Applied Soft Computing, 108, 107458. https://doi.org/10.1016/j.asoc.2021.107458
[21] Pozna, C., Precup, RE., Horváth, E., & Petriu, EM. (2022). Hybrid particle filter–particle swarm optimization algorithm and application to fuzzy controlled servo systems. IEEE Transactions on Fuzzy Systems, 30(10), 4286-4297. https://doi.org/10.1109/TFUZZ.2022.3146986
[22] Qin, J., Liu, X., & Pedrycz, W. (2017). An extended TODIM multi-criteria group decision making method for green supplier selection in interval type-2 fuzzy environment. European Journal of Operational Research, 258(2), 626-638. https://doi.org/10.1016/j.ejor.2016.09.059
[23] Sarani, A., & Mishmast Nehi, H. (2014). Interval type-2 fuzzy linear programming problem. 7th International Conference on Iranian Operations Research, Semnan, Iran, May. [In Persian]
[24] Shaocheng, T. (1994). Interval number and fuzzy number linear programmings. Fuzzy Sets and Systems, 66(3), 301-306. https://doi.org/10.1016/0165-0114(94)90097-3
[25] Singh, D., Shukla, A., Hui, KL., & Sain, M. (2022). Hybrid Precoder Using Stiefel Manifold Optimization for Mm-Wave Massive MIMO System. Applied Sciences, 12(23), 12282. https://doi.org/10.3390/app122312282
[26] Tanaka, H., Ichihashi, H., &Asai, K. (1986). A value of information in FLP problems via sensitivity analysis. Fuzzy Sets and Systems, 18(2), 119-129. https://doi.org/10.1016/0165-0114(86)90015-1
[27] Verdegay, JL. (1982). Fuzzy mathematical programming. Fuzzy Information and Decision Processes, 231, 237.
[28] Wang, X., & Huang, G. (2014). Violation analysis on two-step method for interval linear programming. Information Sciences, 281, 85-96. https://doi.org/10.1016/j.ins.2014.05.019
[29] Werners, B. (1987). Interactive multiple objective programming subject to flexible constraints. European Journal of Operational Research, 31(3), 342-349. https://doi.org/10.1016/0377-2217(87)90043-9
[30] Wu, Q., Zhou, L., Chen, Y., & Chen, H. (2019). An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods. Information Sciences, 502, 394-417. https://doi.org/10.1016/j.ins.2019.06.049
[31] Wu, Q., Liu, X., Qin, J., & Zhou, L. (2021). Multi-criteria group decision-making for portfolio allocation with consensus reaching process under interval type-2 fuzzy environment. Information Sciences, 570, 668-688. https://doi.org/10.1016/j.ins.2021.04.096
[32] Li, X., Ye, B., & Liu, X. (2022). The solution for type-2 fuzzy linear programming model based on the nearest interval approximation. Journal of Intelligent and Fuzzy Systems, 42(3), 2275-2285. https://doi.org/10.3233/JIFS-211568
[33] Zadeh, LA. (1965). Fuzzy sets. Information and Control, 8(3) 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
[34] Zadeh, LA. (1975). The concept of a linguistic variable and its application to approximate reasoning-I. Information Sciences, 8(3), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5
[35] Zadeh, LA. (1975). The concept of a linguistic variable and its application to approximate reasoning-II. Information Sciences, 8(3), 301-357. https://doi.org/10.1016/0020-0255(75)90046-8
[36] Zadeh, LA. (1975). The concept of a linguistic variable and its application to approximate reasoning-III. Information Sciences, 9(1), 43-80. https://doi.org/10.1016/0020-0255(75)90017-1
[37] Zimmermann, HJ. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55. https://doi.org/10.1016/0165-0114(78)90031-3
[38] Zhou, F., Huang, GH., Chen, GX., & Guo, HC. (2009). Enhanced-interval linear programming. European Journal of Operational Research, 199(2), 323-333. https://doi.org/10.1016/j.ejor.2008.12.019
Journal of Mahani Mathematical Research

Articles in Press, Accepted Manuscript
Available Online from 10 February 2024

Files

History

  • Receive Date: 24 September 2023
  • Revise Date: 20 January 2024
  • Accept Date: 09 February 2024

Share

How to cite

Statistics