IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i7p569-d242946.html
   My bibliography  Save this article

Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Author

Listed:
  • Hsien-Chung Wu

    (Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan)

Abstract

The numerical method for solving the fuzzy linear programming problems with fuzzy decision variables is proposed in this paper. The difficulty for solving this kind of problem is that the decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative real numbers. In other words, the decision variables are assumed to be membership functions. One of the purposes of this paper is to derive the analytic formula of error estimation regarding the approximate optimal solution. On the other hand, the existence of optimal solutions is also studied in this paper. Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

Suggested Citation

  • Hsien-Chung Wu, 2019. "Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables," Mathematics, MDPI, vol. 7(7), pages 1-105, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:569-:d:242946
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/7/569/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/7/569/
    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. Izaz Ullah Khan & Tahir Ahmad & Normah Maan, 2013. "A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 159(2), pages 536-546, November.
    3. Wu, Hsien-Chung, 2009. "The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions," European Journal of Operational Research, Elsevier, vol. 196(1), pages 49-60, July.
    4. U. M. Pirzada & V. D. Pathak, 2013. "Newton Method for Solving the Multi-Variable Fuzzy Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 867-881, March.
    5. Dipankar Chakraborty & Dipak Kumar Jana & Tapan Kumar Roy, 2016. "A new approach to solve fully fuzzy transportation problem using triangular fuzzy number," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 26(2), pages 153-179.
    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).

    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. 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.
    2. Hsien-Chung Wu, 2023. "Solving Fuzzy Optimization Problems Using Shapley Values and Evolutionary Algorithms," Mathematics, MDPI, vol. 11(24), pages 1-26, December.
    3. Bogdana Stanojević & Milan Stanojević & Sorin Nădăban, 2021. "Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers," Mathematics, MDPI, vol. 9(11), pages 1-16, June.
    4. 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.
    5. Hsien-Chung Wu, 2019. "Applying the concept of null set to solve the fuzzy optimization problems," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 279-314, September.
    6. 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.
    7. 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.
    8. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. de Andres-Sanchez, Jorge, 2007. "Claim reserving with fuzzy regression and Taylor's geometric separation method," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 145-163, January.
    16. Mikhailov, L., 2004. "A fuzzy approach to deriving priorities from interval pairwise comparison judgements," European Journal of Operational Research, Elsevier, vol. 159(3), pages 687-704, December.
    17. Hongyi Sun & Bingqian Zhang & Wenbin Ni, 2022. "A Hybrid Model Based on SEM and Fuzzy TOPSIS for Supplier Selection," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    18. Liu, Yong-Jun & Zhang, Wei-Guo, 2015. "A multi-period fuzzy portfolio optimization model with minimum transaction lots," European Journal of Operational Research, Elsevier, vol. 242(3), pages 933-941.
    19. Sakawa, Masatoshi & Kato, Kosuke, 1998. "An interactive fuzzy satisficing method for structured multiobjective linear fractional programs with fuzzy numbers," European Journal of Operational Research, Elsevier, vol. 107(3), pages 575-589, June.
    20. Sajid Ali & Sang-Moon Lee & Choon-Man Jang, 2017. "Determination of the Most Optimal On-Shore Wind Farm Site Location Using a GIS-MCDM Methodology: Evaluating the Case of South Korea," Energies, MDPI, vol. 10(12), pages 1-22, December.

    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:7:y:2019:i:7:p:569-:d:242946. 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.