IDEAS home Printed from https://ideas.repec.org/a/spr/opsear/v58y2021i4d10.1007_s12597-021-00522-8.html
   My bibliography  Save this article

Solving the general fully neutrosophic multi-level multiobjective linear programming problems

Author

Listed:
  • Kailash Lachhwani

    (National Institute of Technical Teacher’s Training and Research)

Abstract

This paper addresses the general fully neutrosophic multi-level multiobjective programming problems i.e. ML-MOLPPs in which not only coefficients of each objective at each level but also all coefficients and parameters in the constraints are fully neutrosophic numbers in the form of trapezoidal neutrosophic numbers (NNs). From the point of view of complexity of the problem, it is proposed to apply ranking function of NNs to convert problem into equivalent ML-MOLPPs with crisp values of neutrosophic coefficients and parameters. Then suitable membership function for each objective and decision variable are formulated using lowest and highest value of each objective and decision variables of converted ML-MOLPP. Formulation of membership functions for decision variables (using corresponding values to maximum and minimum of objectives) will avoid decision deadlock in hierarchical structure. Accordingly, simple fuzzy goal programming strategy is applied to build FGP solution models. With the help of linear programming techniques on these solution models, compromise optimal solution of original fully neutrosophic ML-MOLPP is obtained. The proposed approach is a unique and simple method to provide compromise optimal solution to decision makers of general fully neutrosophic ML-MOLPP. The proposed approach is illustrated with numerical example to show its uniqueness and simplicity as solution technique. A case study is also discussed to demonstrate its applicability on real problems.

Suggested Citation

  • Kailash Lachhwani, 2021. "Solving the general fully neutrosophic multi-level multiobjective linear programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1192-1216, December.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:4:d:10.1007_s12597-021-00522-8
    DOI: 10.1007/s12597-021-00522-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12597-021-00522-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s12597-021-00522-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. S. Osman & O. E. Emam & M. A. El Sayed, 2017. "Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 816-840, December.
    2. Wang, Danping & Du, Gang & Jiao, Roger J. & Wu, Ray & Yu, Jianping & Yang, Dong, 2016. "A Stackelberg game theoretic model for optimizing product family architecting with supply chain consideration," International Journal of Production Economics, Elsevier, vol. 172(C), pages 1-18.
    3. José-Fernando Camacho-Vallejo & Álvaro Eduardo Cordero-Franco & Rosa G. González-Ramírez, 2014. "Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-14, February.
    4. Fontaine, Pirmin & Minner, Stefan, 2014. "Benders Decomposition for Discrete–Continuous Linear Bilevel Problems with application to traffic network design," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 163-172.
    5. K. Ganesan & P. Veeramani, 2006. "Fuzzy linear programs with trapezoidal fuzzy numbers," Annals of Operations Research, Springer, vol. 143(1), pages 305-315, March.
    6. Lachhwani, Kailash, 2015. "Modified FGP approach for multi-level multi objective linear fractional programming problems," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1038-1049.
    7. Kis, Tamás & Kovács, András, 2013. "Exact solution approaches for bilevel lot-sizing," European Journal of Operational Research, Elsevier, vol. 226(2), pages 237-245.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lv, J. & Li, Y.P. & Huang, G.H. & Ding, Y.K. & Li, X. & Li, Y., 2022. "Planning energy economy and eco-environment nexus system under uncertainty: A copula-based stochastic multi-level programming method," Applied Energy, Elsevier, vol. 312(C).
    2. Kailash Lachhwani, 2024. "An improved solution for fully neutrosophic multi-level linear programming problem based on Laplace transform," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 867-896, June.
    3. Mustapha Kaci & Sonia Radjef, 2023. "An adaptive method to solve multilevel multiobjective linear programming problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(3), pages 29-44.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. M. A. El Sayed & Ibrahim A. Baky & Pitam Singh, 2020. "A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1374-1403, December.
    2. Serrano, Breno & Minner, Stefan & Schiffer, Maximilian & Vidal, Thibaut, 2024. "Bilevel optimization for feature selection in the data-driven newsvendor problem," European Journal of Operational Research, Elsevier, vol. 315(2), pages 703-714.
    3. Liang, Jinpeng & Wu, Jianjun & Gao, Ziyou & Sun, Huijun & Yang, Xin & Lo, Hong K., 2019. "Bus transit network design with uncertainties on the basis of a metro network: A two-step model framework," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 115-138.
    4. Mashadi & Yuliana Safitri & Sukono & Igif Gimin Prihanto & Muhamad Deni Johansyah & Moch Panji Agung Saputra, 2024. "The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations," Mathematics, MDPI, vol. 12(7), pages 1-14, March.
    5. Hawaf AbdAlhakim & O. E. Emam & A. A. Abd El-Mageed, 2019. "Architecting a fully fuzzy information model for multi-level quadratically constrained quadratic programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 56(2), pages 367-389, June.
    6. Soroush Safarzadeh, 2023. "A game theoretic approach for pricing and advertising of an integrated product family in a duopoly," Journal of Combinatorial Optimization, Springer, vol. 45(5), pages 1-26, July.
    7. Kailash Lachhwani, 2024. "An improved solution for fully neutrosophic multi-level linear programming problem based on Laplace transform," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 867-896, June.
    8. Hossein Abdollahnejad Barough, 2011. "A linear programming priority method for a fuzzy transportation problem with non-linear constraints," Fuzzy Information and Engineering, Springer, vol. 3(2), pages 193-208, June.
    9. Manuel Arana-Jiménez & Carmen Sánchez-Gil, 2020. "On generating the set of nondominated solutions of a linear programming problem with parameterized fuzzy numbers," Journal of Global Optimization, Springer, vol. 77(1), pages 27-52, May.
    10. Xiaobin Yang & Haitao Lin & Gang Xiao & Huanbin Xue & Xiaopeng Yang, 2019. "Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    11. M. S. Osman & O. E. Emam & M. A. El Sayed, 2017. "Stochastic Fuzzy Multi-level Multi-objective Fractional Programming Problem: A FGP Approach," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 816-840, December.
    12. Tan, Zhijia & Yang, Hai & Tan, Wei & Li, Zhichun, 2016. "Pareto-improving transportation network design and ownership regimes," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 292-309.
    13. Sujeet Kumar Singh & Shiv Prasad Yadav, 2018. "Intuitionistic fuzzy multi-objective linear programming problem with various membership functions," Annals of Operations Research, Springer, vol. 269(1), pages 693-707, October.
    14. Eltoukhy, Abdelrahman E.E. & Wang, Z.X. & Chan, Felix T.S. & Fu, X., 2019. "Data analytics in managing aircraft routing and maintenance staffing with price competition by a Stackelberg-Nash game model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 143-168.
    15. Mohebifard, Rasool & Hajbabaie, Ali, 2019. "Optimal network-level traffic signal control: A benders decomposition-based solution algorithm," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 252-274.
    16. Qin, Yichen & Ng, Kam K.H., 2023. "Analysing the impact of collaborations between airlines and maintenance service company under MRO outsourcing mode: Perspective from airline's operations," Journal of Air Transport Management, Elsevier, vol. 109(C).
    17. Sujit De & Shib Sana, 2015. "Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach," Annals of Operations Research, Springer, vol. 233(1), pages 57-76, October.
    18. Haque, Khademul & Mishra, Sabyasachee & Golias, Mihalis M., 2021. "Multi-period transportation network investment decision making and policy implications using econometric framework," Research in Transportation Economics, Elsevier, vol. 89(C).
    19. Reza Ghanbari & Khatere Ghorbani-Moghadam & Nezam Mahdavi-Amiri, 2021. "A time variant multi-objective particle swarm optimization algorithm for solving fuzzy number linear programming problems using modified Kerre’s method," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 403-424, June.
    20. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:opsear:v:58:y:2021:i:4:d:10.1007_s12597-021-00522-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.