IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i14p3123-d1194581.html
   My bibliography  Save this article

Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness

Author

Listed:
  • Pavan Kumar

    (School of Advanced Science and Languages, VIT Bhopal University, Sehore 466116, India)

  • Hamiden Abd El-Wahed Khalifa

    (Department of Mathematics, College of Science and Arts, Qassim University, Al-Badaya 51951, Saudi Arabia
    Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt)

Abstract

In real-life scenarios, there are many mathematical tools to handle incomplete and imprecise data. One of them is the fuzzy approach. The main issue with addressing nonlinear interval programming (NIP) problems is that the optimal solution to the problem is a decision made under uncertainty that has a risk of not satisfying the feasibility and optimality criteria. Some strategies handle this kind of problem using classical terminology such as optimal solution and feasible solution. These strategies are insufficient for efficient analysis since the properties of the solution in an uncertain environment are ignored. Therefore, in the proposed approach, more suitable terminologies were suggested for the analysis process. In addition, it combines parametric treatment and interactive methodology. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming (MODP) issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α -pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named the decomposition approach (DP), is presented for achieving a subset for the parametric space that contains the same α -pareto optimal solution. For a better understanding of the suggested concept, a numerical example is provided.

Suggested Citation

  • Pavan Kumar & Hamiden Abd El-Wahed Khalifa, 2023. "Enhancing Decomposition Approach for Solving Multi-Objective Dynamic Non-Linear Programming Problems Involving Fuzziness," Mathematics, MDPI, vol. 11(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3123-:d:1194581
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/14/3123/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/14/3123/
    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. Carraway, Robert L. & Morin, Thomas L. & Moskowitz, Herbert, 1990. "Generalized dynamic programming for multicriteria optimization," European Journal of Operational Research, Elsevier, vol. 44(1), pages 95-104, January.
    3. Cinthia Peraza & Fevrier Valdez & Juan R. Castro & Oscar Castillo, 2018. "Fuzzy Dynamic Parameter Adaptation in the Harmony Search Algorithm for the Optimization of the Ball and Beam Controller," Advances in Operations Research, Hindawi, vol. 2018, pages 1-16, August.
    4. Abo-Sinna, Mahmoud A. & Hussein, Mohammad L., 1994. "An algorithm for decomposing the parametric space in multiobjective dynamic programming problems," European Journal of Operational Research, Elsevier, vol. 73(3), pages 532-538, March.
    5. Abo-Sinna, Mahmoud A. & Hussein, Mohammad L., 1995. "An algorithm for generating efficient solutions of multiobjective dynamic programming problems," European Journal of Operational Research, Elsevier, vol. 80(1), pages 156-165, January.
    6. Hamiden Abd El-Wahed Khalifa & Pavan Kumar, 2023. "Multi-objective optimisation for solving cooperative continuous static games using Karush-Kuhn-Tucker conditions," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 46(1), pages 133-147.
    7. Osman, Mohamed S. & El-Banna, Abou-Zaid H., 1993. "Stability of multiobjective nonlinear programming problems with fuzzy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(4), pages 321-326.
    Full references (including those not matched with items on IDEAS)

    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. Li, Dengfeng & Cheng, Chuntian, 2004. "Stability on multiobjective dynamic programming problems with fuzzy parameters in the objective functions and in the constraints," European Journal of Operational Research, Elsevier, vol. 158(3), pages 678-696, November.
    2. Hamiden Abd El-Wahed Khalifa, 2020. "Goal programming approach for solving heptagonal fuzzy transportation problem under budgetry constraint," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 85-96.
    3. Mahmoud A. Abo-Sinna & Rizk M. Rizk-Allah, 2018. "Decomposition of parametric space for bi-objective optimization problem using neural network approach," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 502-531, June.
    4. 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.
    5. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Svajone Bekesiene & Serhii Mashchenko, 2023. "On Nash Equilibria in a Finite Game for Fuzzy Sets of Strategies," Mathematics, MDPI, vol. 11(22), pages 1-12, November.
    15. Qian-Yun Tan & Cui-Ping Wei & Qi Liu & Xiang-Qian Feng, 2016. "The Hesitant Fuzzy Linguistic TOPSIS Method Based on Novel Information Measures," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(05), pages 1-22, October.
    16. Hsiao, Tzy-yih, 2006. "Establish standards of standard costing with the application of convergent gray zone test," European Journal of Operational Research, Elsevier, vol. 168(2), pages 593-611, January.
    17. Zola, Fernanda Cavicchioli & Colmenero, João Carlos & Aragão, Franciely Velozo & Rodrigues, Thaisa & Junior, Aldo Braghini, 2020. "Multicriterial model for selecting a charcoal kiln," Energy, Elsevier, vol. 190(C).
    18. Adel Hatami-Marbini & Madjid Tavana & Kobra Gholami & Zahra Ghelej Beigi, 2015. "A Bounded Data Envelopment Analysis Model in a Fuzzy Environment with an Application to Safety in the Semiconductor Industry," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 679-701, February.
    19. Manuel Casal-Guisande & Alberto Comesaña-Campos & Alejandro Pereira & José-Benito Bouza-Rodríguez & Jorge Cerqueiro-Pequeño, 2022. "A Decision-Making Methodology Based on Expert Systems Applied to Machining Tools Condition Monitoring," Mathematics, MDPI, vol. 10(3), pages 1-30, February.
    20. James Liou & Mei-Ling Chuang, 2010. "Evaluating corporate image and reputation using fuzzy MCDM approach in airline market," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(6), pages 1079-1091, October.

    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:11:y:2023:i:14:p:3123-:d:1194581. 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.