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AIMS Mathematics

2023, Volume 8, Issue 4: 7714-7730. doi: 10.3934/math.2023387
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Research article

A fuzzy based solution to multiple objective LPP

  • Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
  • Received: 02 October 2022 Revised: 22 December 2022 Accepted: 26 December 2022 Published: 18 January 2023

  • This study presents a Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) method to solve the Linear Programming Problem (LPP). Initially Multiple Objective Linear Programming Problem (MOLPP) is solved using Chandra Sen's approach along with various types of mean approaches. Furthermore, FMOLPP is solved using Chandra Sen's approach and various categories of fuzzy mean techniques. The simplex form is used to solve the LPP, where the three-tuple symmetric triangular fuzzy number with the constraints of the fuzzy objective function is considered. We have presented a comparative study of optimum values of MOLPP with optimum values of FMOLPP, to show the significance of our proposed method.

    Citation: M Junaid Basha, S Nandhini. A fuzzy based solution to multiple objective LPP[J]. AIMS Mathematics, 2023, 8(4): 7714-7730. doi: 10.3934/math.2023387

    Related Papers:

  • This study presents a Fuzzy Multiple Objective Linear Programming Problem (FMOLPP) method to solve the Linear Programming Problem (LPP). Initially Multiple Objective Linear Programming Problem (MOLPP) is solved using Chandra Sen's approach along with various types of mean approaches. Furthermore, FMOLPP is solved using Chandra Sen's approach and various categories of fuzzy mean techniques. The simplex form is used to solve the LPP, where the three-tuple symmetric triangular fuzzy number with the constraints of the fuzzy objective function is considered. We have presented a comparative study of optimum values of MOLPP with optimum values of FMOLPP, to show the significance of our proposed method.


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    [1] X. P. Yang, B. Y. Cao, Bing-Yuan, H. T. Lin, Multi-objective fully fuzzy linear programming problems with triangular fuzzy numbers, 2014 11th International Conference on Fuzzy Systems and Knowledge Discovery, 2014,171–177.
    [2] S. P. Wan, J. Y. Dong, Possibility linear programming with trapezoidal fuzzy numbers, Appl. Math. Model., 38 (2014), 1660–1672. https://doi.org/10.1016/j.apm.2013.09.006 doi: 10.1016/j.apm.2013.09.006
    [3] S. P. Wan, D. F. Li, Fuzzy mathematical programming approach to heterogeneous multi attribute decision-making with interval-valued intuitionistic fuzzy truth degrees, Inf. Sci., 325 (2015), 484–503. https://doi.org/10.1016/j.ins.2015.07.014 doi: 10.1016/j.ins.2015.07.014
    [4] S. Wan, J. Dong, Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees, Inform. Fusion, 26 (2015), 49–65. https://doi.org/10.1016/j.inffus.2015.01.006 doi: 10.1016/j.inffus.2015.01.006
    [5] S. P. Wan, F. Wang, L. L. Lin, J. J. Dong, An intuitionistic fuzzy linear programming method for logistics outsourcing provider selection, Knowl.-Based Syst., 82 (2015), 80–94. https://doi.org/10.1016/j.knosys.2015.02.027 doi: 10.1016/j.knosys.2015.02.027
    [6] G. L. Xu, S. P. Wan, J. Y. Dong, A hesitant fuzzy programming method for hybrid MADM with incomplete attribute weight information, Informatica, 27 (2016), 863–892.
    [7] U. Sharma, S. Aggarwal, Solving fully fuzzy multi-objective linear programming problem using nearest interval approximation of fuzzy number and interval programming, Int. J. Fuzzy Syst., 20 (2018), 488–499. https://doi.org/10.1007/s40815-017-0336-8 doi: 10.1007/s40815-017-0336-8
    [8] S. P. Wan, Y. L. Qin, J. Y. Dong, A hesitant fuzzy mathematical programming method for hybrid multi-criteria group decision making with hesitant fuzzy truth degrees, Knowl.-Based Syst., 138 (2017), 232–248. https://doi.org/10.1016/j.knosys.2017.10.002 doi: 10.1016/j.knosys.2017.10.002
    [9] 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. Making, 16 (2017), 269–295. https://doi.org/10.1007/s10700-016-9250-z doi: 10.1007/s10700-016-9250-z
    [10] S. P. Wan, Z. Jin, J. Y. Dong, Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with pythagorean fuzzy truth degrees, Knowl. Inf. Syst., 55 (2018), 437–466. https://doi.org/10.1007/s10115-017-1085-6 doi: 10.1007/s10115-017-1085-6
    [11] J. Y. Dong, S. P. Wan, A new trapezoidal fuzzy linear programming method considering the acceptance degree of fuzzy constraints violated, Knowl.-Based Syst., 148 (2018), 100–114. https://doi.org/10.1016/j.knosys.2018.02.030 doi: 10.1016/j.knosys.2018.02.030
    [12] C. Sen, Duality in solving multi-objective optimization (MOO) problems, AJOR, 9 (2019), 109–113. https://doi.org/10.4236/ajor.2019.93006 doi: 10.4236/ajor.2019.93006
    [13] J. H. Dong, S. P. Wan, A new method for solving fuzzy multi-objective linear programming problems, IJFS, 16 (2019), 145–159.
    [14] C. Sen, Improved averaging techniques for solving multi-objective optimization (MOO) problems, SN Appl. Sci., 2 (2020), 286.
    [15] S. P. Wan, G. L. Xu, J. Y. Dong, An atanassov intuitionistic fuzzy programming method for group decision making with interval-valued atanassov intuitionistic fuzzy preference relations, Appl. Soft Comput., 95 (2020), 106556. https://doi.org/10.1016/j.asoc.2020.106556 doi: 10.1016/j.asoc.2020.106556
    [16] S. P. Wan, Z. H. Chen, J. Y. Dong, Bi-objective trapezoidal fuzzy mixed integer linear program-based distribution center location decision for large-scale emergencies, Appl. Soft Comput., 110 (2021), 107757. https://doi.org/10.1016/j.asoc.2021.107757 doi: 10.1016/j.asoc.2021.107757
    [17] K. Gilda, S. Satarkar, Defuzzification: Maxima methods with improved efficiency and their performance evaluation, 2022 IEEE Delhi Section Conference, 2022, 1–6. https://doi.org/10.1109/DELCON54057.2022.9753474 doi: 10.1109/DELCON54057.2022.9753474
    [18] E. Fathy, A. E. Hassanien, Fuzzy harmonic mean technique for solving fully fuzzy multilevel multiobjective linear programming problem, Alex. Eng. J., 61 (2022), 8189–8205. https://www.sciencedirect.com/science/article/pii/S1110016822000230
    [19] Y. Xu, W. Q. Gao, Q. R. Zeng, G. J. Wang, J. Ren, Y. X. Zhang, A feasible fuzzy-extended attributes-based access control technique, Secur. Commun. Netw., 2018 (2018), 6476315. https://doi.org/10.1155/2018/6476315 doi: 10.1155/2018/6476315
    [20] S. Faizi, W. Salabun, S. Ullah, T. Rashid, J. Wieckowski, A new method to support decision-making in an uncertain environment based on normalized interval-valued triangular fuzzy numbers and comet technique, Symmetry, 12 (2020), 516. https://doi.org/10.3390/sym12040516 doi: 10.3390/sym12040516
    [21] Z. I. Sohag, M. Asadujjaman, A proposed new average method for solving multi-objective linear programming problem using various kinds of mean techniques, Math. Lett., 4 (2018), 25–33. https://doi.org/10.11648/j.ml.20180402.11 doi: 10.11648/j.ml.20180402.11
    [22] S. H. Nasseri, A. Ebrahimnejad, A fuzzy dual simplex method for fuzzy number linear programming problem, AFSS, 5 (2010), 81–95.
    [23] J. J. Saade, B. H. Diab, Defuzzification methods and new techniques for fuzzy controllers, IJECE, 3 (2004), 161–174.
    [24] A. Chandramohan, M. V. C. Rao, M. S. Arumugam, Two new and useful defuzzification methods based on root mean square value, Soft Comput., 10 (2006), 1047–1059. https://doi.org/10.1007/s00500-005-0042-6 doi: 10.1007/s00500-005-0042-6
    [25] Q. M. Liu, F. G. Shi, Stratified simplex method for solving fuzzy multi-objective linear programming problem, J. Intell. Fuzzy Syst., 29 (2015), 2357–2364.
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