Received December 22, 2021. Published online September 15, 2022.
Abstract: The aim of this paper is solving an intuitionistic fuzzy multi-objective linear programming problem containing intuitionistic fuzzy parameters, intuitionistic fuzzy maximization/minimization, and intuitionistic fuzzy constraints. To do this, a linear ranking function is used to convert the intuitionistic fuzzy parameters to crisp ones first. Then, linear membership and non-membership functions are used to manipulate intuitionistic fuzzy maximization/minimization and intuitionistic fuzzy constraints. Then, a multi-objective optimization problem is formulated containing maximization of membership functions and minimization of non-membership functions. To solve this problem, the minimax and weighted sum methods are used. Then, the described procedure is summarized as an algorithm to solve the problem, and a numerical example is solved by the proposed method. Finally, to investigate the capability and performance of the model, a supplier selection problem, which is one of the important applications in supply chain management, is solved by the proposed algorithm.
References: [1] A. A. H. Ahmadini, F. Ahmad: Solving intuitionistic fuzzy multiobjective linear programming problem under neutrosophic environment. AIMS Math. 6 (2021), 4556-4580. DOI 10.3934/math.2021269 | MR 4220424
[2] A. Amid, S. H. Ghodsypour, C. O'Brien: A weighted max-min model for fuzzy multi-objective supplier selection in a supply chain. Int. J. Prod. Econ. 131 (2011), 139-145. DOI 10.1016/j.ijpe.2010.04.044
[3] P. P. Angelov: Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst. 86 (1997), 299-306. DOI 10.1016/S0165-0114(96)00009-7 | MR 1454190 | Zbl 0915.90258
[4] K. T. Atanassov: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 (1986), 87-96. DOI 10.1016/S0165-0114(86)80034-3 | MR 0852871 | Zbl 0631.03040
[5] S. K. Bharati, S. R. Singh: Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment. Soft Comput. 23 (2019), 77-84. DOI 10.1007/s00500-018-3100-6 | Zbl 1415.90115
[6] K.-H. Chang: A novel supplier selection method that integrates the intuitionistic fuzzy weighted averaging method and a soft set with imprecise data. Ann. Oper. Res. 272 (2019), 139-157. DOI 10.1007/s10479-017-2718-6 | MR 3895140 | Zbl 1434.90018
[7] M. Ehrgott: Multicriteria Optimization. Springer, Berlin (2005). DOI 10.1007/3-540-27659-9 | MR 2143243 | Zbl 1132.90001
[8] H. Garg: A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems. Appl. Soft Comput. 38 (2016), 988-999. DOI 10.1016/j.asoc.2015.10.040
[9] A. Kabiraj, P. K. Nayak, S. Raha: Solving intuitionistic fuzzy linear programming problem. Int. J. Intelligence Sci. 9 (2019), 44-58. DOI 10.4236/ijis.2019.91003
[10] D.-F. Li: A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems. Comput. Math. Appl. 60 (2010), 1557-1570. DOI 10.1016/j.camwa.2010.06.039 | MR 2679124 | Zbl 1202.91054
[11] D.-F. Li: Linear programming method for MADM with interval-valued intuitionistic fuzzy sets. Expert Syst. Appl. 37 (2010), 5939-5945. DOI 10.1016/j.eswa.2010.02.011
[12] R. Malhotra, S. K. Bharati: Intuitionistic fuzzy two stage multiobjective transportation problems. Adv. Theor. Appl. Math. 11 (2016), 305-316.
[13] S. Mohan, A. P. Kannusamy, S. K. Sidhu: Solution of intuitionistic fuzzy linear programming problem by dual simplex algorithm and sensitivity analysis. Comput. Intell. 37 (2021), 852-872. DOI 10.1111/coin.12435 | MR 4270699
[14] G. Qu, W. Qu, Z. Zhang, J. Wang: Choquet integral correlation coefficient of intuitionistic fuzzy sets and its applications. J. Intell. Fuzzy Syst. 33 (2017), 543-553. DOI 10.3233/JIFS-162131 | Zbl 1376.68134
[15] M. Sakawa: Fuzzy Sets and Interactive Multiobjective Optimization. Springer, New York (1993). DOI 10.1007/978-1-4899-1633-4 | MR 1216139 | Zbl 0842.90070
[16] S. K. Singh, S. P. Yadav: Modeling and optimization of multi objective non-linear programming problem in intuitionistic fuzzy environment. Appl. Math. Modelling 39 (2015), 4617-4629. DOI 10.1016/j.apm.2015.03.064 | MR 3354856 | Zbl 1443.90067
[17] S. K. Singh, S. P. Yadav: A new approach for solving intuitionistic fuzzy transportation problem of type-2. Ann. Oper. Res. 243 (2016), 349-363. DOI 10.1007/s10479-014-1724-1 | MR 3529807 | Zbl 1348.90658
[18] H. S. Tooranloo, A. Iranpour: Supplier selection and evaluation using interval-valued intuitionistic fuzzy AHP method. Int. J. Procurement Management 10 (2017), 539-554. DOI 10.1504/IJPM.2017.086399
[19] S. Wan, J. Dong: A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making. J. Comput. Syst. Sci. 80 (2014), 237-256. DOI 10.1016/j.jcss.2013.07.007 | MR 3105919 | Zbl 1311.68156
[20] S. Wan, J. Dong: A novel extension of best-worst method with intuitionistic fuzzy reference comparisons. IEEE Trans. Fuzzy Syst. 30 (2022), 1698-1711. DOI 10.1109/TFUZZ.2021.3064695
[21] S.-P. Wan, D.-F. Li: Atanassov's intuitionistic fuzzy programming method for heterogeneous multiattribute group decision making with Atanassov's intuitionistic fuzzy truth degrees. IEEE Trans. Fuzzy Syst. 22 (2013), 300-312. DOI 10.1109/TFUZZ.2013.2253107
[22] S.-P. Wan, D.-F. Li: Fuzzy mathematical programming approach to heterogeneous multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees. Inf. Sci. 325 (2015), 484-503. DOI 10.1016/j.ins.2015.07.014 | MR 3392316 | Zbl 1390.91119
[23] S.-P. Wan, F. Wang, J.-Y. Dong: A novel group decision making method with intuitionistic fuzzy preference relations for RFID technology selection. Appl. Soft Comput. 38 (2016), 405-422. DOI 10.1016/j.asoc.2015.09.039
[24] S.-P. Wan, F. Wang, L.-L. Lin, J.-Y. Dong: An intuitionistic fuzzy linear programming method for logistics outsourcing provider selection. Knowledge-Based Syst. 82 (2015), 80-94. DOI 10.1016/j.knosys.2015.02.027
[25] S.-P. Wan, F. Wang, G.-L. Xu, J.-Y. Dong, J. Tang: An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations. Fuzzy Optim. Decis. Mak. 16 (2017), 269-295. DOI 10.1007/s10700-016-9250-z | MR 3682924 | Zbl 1428.90090
[26] A.-P. Wei, D.-F. Li, P.-P. Lin, B.-Q. Jiang: An information-based score function of interval-valued intuitionistic fuzzy sets and its application in multiattribute decision making. Soft Comput. 25 (2021), 1913-1923. DOI 10.1007/s00500-020-05265-0 | Zbl 7560958
[27] J. Ye: Expected value method for intuitionistic trapezoidal fuzzy multicriteria decision-making problems. Expert Syst. Appl. 38 (2011), 11730-11734. DOI 10.1016/j.eswa.2011.03.059
Affiliations: Hassan Hassanpour, Department of Mathematics, University of Birjand, 9717434765, Birjand, Iran, e-mail: hhassanpour@birjand.ac.ir; Elham Hosseinzadeh (corresponding author), Department of Mathematics, Kosar University of Bojnord, Arkan Road, after Imam Hassan Hospital, 9415615458, Bojnord, Iran, e-mail: e.hosseinzadeh@kub.ac.ir; Mahsa Moodi, Department of Mathematics, University of Birjand, 9717434765, Birjand, Iran, e-mail: moodi464348@birjand.ac.ir
