IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1540-d410912.html
   My bibliography  Save this article

Lexicographic Methods for Fuzzy Linear Programming

Author

Listed:
  • Boris Pérez-Cañedo

    (Department of Mathematics, University of Cienfuegos, Cienfuegos 55100, Cuba)

  • José Luis Verdegay

    (Department of Computer Science and Artificial Intelligence, University of Granada, 18071 Granada, Spain)

  • Eduardo René Concepción-Morales

    (Department of Informatics, University of Cienfuegos, Cienfuegos 55100, Cuba)

  • Alejandro Rosete

    (Facultad de Ingeniería Informática, Universidad Tecnológica de La Habana José Antonio Echeverría (Cujae), Marianao La Habana 19390, Cuba)

Abstract

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.

Suggested Citation

  • Boris Pérez-Cañedo & José Luis Verdegay & Eduardo René Concepción-Morales & Alejandro Rosete, 2020. "Lexicographic Methods for Fuzzy Linear Programming," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1540-:d:410912
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1540/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1540/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Amit Kumar & Anila Gupta, 2011. "Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions," Fuzzy Information and Engineering, Springer, vol. 3(1), pages 3-21, March.
    3. P. L. Yu, 1973. "A Class of Solutions for Group Decision Problems," Management Science, INFORMS, vol. 19(8), pages 936-946, April.
    4. Jagdeep Kaur & Amit Kumar, 2013. "A New Method to Find the Unique Fuzzy Optimal Value of Fuzzy Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 529-534, February.
    5. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    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. Figueroa–García, Juan Carlos & Hernández, Germán & Franco, Carlos, 2022. "A review on history, trends and perspectives of fuzzy linear programming," Operations Research Perspectives, Elsevier, vol. 9(C).
    2. Sandra González-Gallardo & Ana B. Ruiz & Mariano Luque, 2021. "Analysis of the Well-Being Levels of Students in Spain and Finland through Interval Multiobjective Linear Programming," Mathematics, MDPI, vol. 9(14), pages 1-27, July.

    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. Chen, Lisa Y. & Wang, Tien-Chin, 2009. "Optimizing partners' choice in IS/IT outsourcing projects: The strategic decision of fuzzy VIKOR," International Journal of Production Economics, Elsevier, vol. 120(1), pages 233-242, July.
    2. P. Senthil Kumar & R. Jahir Hussain, 2016. "A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 7(2), pages 39-61, April.
    3. Chi-Yo Huang & Jih-Jeng Huang & You-Ning Chang & Yen-Chu Lin, 2021. "A Fuzzy-MOP-Based Competence Set Expansion Method for Technology Roadmap Definitions," Mathematics, MDPI, vol. 9(2), pages 1-26, January.
    4. 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.
    5. Qun Niu & Han Wang & Ziyuan Sun & Zhile Yang, 2019. "An Improved Bare Bone Multi-Objective Particle Swarm Optimization Algorithm for Solar Thermal Power Plants," Energies, MDPI, vol. 12(23), pages 1-22, November.
    6. Lin, Sheng-Wei, 2016. "The critical success factors for a travel application service provider evaluation and selection by travel intermediaries," Tourism Management, Elsevier, vol. 56(C), pages 126-141.
    7. Shalabh Singh & Sonia Singh, 2022. "Shipment in a multi-choice environment: a case study of shipping carriers in US," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(4), pages 1195-1219, December.
    8. Balasundaram Baranidharan & Ieva Meidute-Kavaliauskiene & Ghanshaym S. Mahapatra & Renata Činčikaitė, 2022. "Assessing the Sustainability of the Prepandemic Impact on Fuzzy Traveling Sellers Problem with a New Fermatean Fuzzy Scoring Function," Sustainability, MDPI, vol. 14(24), pages 1-17, December.
    9. Vuciterna, Rina & Thomsen, Michael & Popp, Jennie & Musliu, Arben, 2017. "Efficiency and Competitiveness of Kosovo Raspberry Producers," 2017 Annual Meeting, February 4-7, 2017, Mobile, Alabama 252770, Southern Agricultural Economics Association.
    10. Berna Tektas Sivrikaya & Ferhan Cebi & Hasan Hüseyin Turan & Nihat Kasap & Dursun Delen, 2017. "A fuzzy long-term investment planning model for a GenCo in a hybrid electricity market considering climate change impacts," Information Systems Frontiers, Springer, vol. 19(5), pages 975-991, October.
    11. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    12. Milad Zamanifar & Seyed Mohammad Seyedhoseyni, 2017. "Recovery planning model for roadways network after natural hazards," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 87(2), pages 699-716, June.
    13. Weiqiang Shen & Chuanlin Zhang & Xiaona Zhang & Jinglun Shi, 2019. "A fully distributed deployment algorithm for underwater strong k-barrier coverage using mobile sensors," International Journal of Distributed Sensor Networks, , vol. 15(4), pages 15501477198, April.
    14. Kim, Jong Soon & Whang, Kyu-Seung, 1998. "A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function," European Journal of Operational Research, Elsevier, vol. 107(3), pages 614-624, June.
    15. Berna Tektaş & Hasan Hüseyin Turan & Nihat Kasap & Ferhan Çebi & Dursun Delen, 2022. "A Fuzzy Prescriptive Analytics Approach to Power Generation Capacity Planning," Energies, MDPI, vol. 15(9), pages 1-26, April.
    16. Omer F. Baris, 2018. "Timing effect in bargaining and ex ante efficiency of the relative utilitarian solution," Theory and Decision, Springer, vol. 84(4), pages 547-556, June.
    17. Bo Cowgill & Jonathan M. V. Davis & B. Pablo Montagnes & Patryk Perkowski, 2024. "Stable Matching on the Job? Theory and Evidence on Internal Talent Markets," CESifo Working Paper Series 11120, CESifo.
    18. Víctor G. Alfaro-García & Anna M. Gil-Lafuente & Gerardo G. Alfaro Calderón, 2017. "A fuzzy approach to a municipality grouping model towards creation of synergies," Computational and Mathematical Organization Theory, Springer, vol. 23(3), pages 391-408, September.
    19. Aghayi, Nazila & Maleki, Bentolhoda, 2016. "Efficiency measurement of DMUs with undesirable outputs under uncertainty based on the directional distance function: Application on bank industry," Energy, Elsevier, vol. 112(C), pages 376-387.
    20. Wenyao Niu & Yuan Rong & Liying Yu & Lu Huang, 2022. "A Novel Hybrid Group Decision Making Approach Based on EDAS and Regret Theory under a Fermatean Cubic Fuzzy Environment," Mathematics, MDPI, vol. 10(17), pages 1-30, August.

    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:gam:jmathe:v:8:y:2020:i:9:p:1540-:d:410912. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.