IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v14y2022i12p7423-d841242.html
   My bibliography  Save this article

Close Interval Approximation of Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems

Author

Listed:
  • Z. A. M. S. Juman

    (Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya 20400, Sri Lanka)

  • Salama A. Mostafa

    (Faculty of Computer Science and Information Technology, Universiti Tun Hussein Onn Malaysia, Batu Pahat 86400, Johor, Malaysia)

  • A. P. Batuwita

    (Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya 20400, Sri Lanka)

  • Ali AlArjani

    (Department of Industrial Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 16273, Saudi Arabia)

  • Md Sharif Uddin

    (Department of Industrial Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 16273, Saudi Arabia
    Department of Mathematics, Jahangirnagar University, Savar, Dhaka 1342, Bangladesh)

  • Mustafa Musa Jaber

    (Department of Medical Instruments Engineering Techniques, Dijlah University College, Baghdad 10021, Iraq
    Department of Medical Instruments Engineering Techniques, Al-Farahidi University, Baghdad 10021, Iraq)

  • Teg Alam

    (Department of Industrial Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 16273, Saudi Arabia)

  • El-Awady Attia

    (Department of Industrial Engineering, Prince Sattam Bin Abdulaziz University, Al Kharj 16273, Saudi Arabia
    Department of Mechanical Engineering, Faculty of Engineering (Shoubra), Benha University, Cairo 11629, Egypt)

Abstract

Due to globalization in this modern age of technology and other uncontrollable influences, transportation parameters can differ within a certain range of a given period. In this situation, a managerial position’s objective is to make appropriate decisions for the decision-makers. However, in general, the determination of an exact solution to the interval data-based transportation problem (IDTP) becomes an NP-hard problem as the number of choices within their respective ranges increases enormously when the number of suppliers and buyers increases. So, in practice, it is difficult for an exact method to find the exact solution to the IDTP in a reasonable time, specifically the large-sized problems with large interval sizes. This paper introduces solutions to the IDTP where supply, demand, and cost are all in interval numbers. One of the best interval approximations, namely the closed interval approximation of pentagonal fuzzy number, is proposed for solving the IDTP. First, in the proposed closed interval approximation method (Method-1), the pentagonal fuzzification method converts the IDTP to a fuzzy transportation problem (FTP). Subsequently, two new ranking methods based on centroid and in-center triangle concepts are presented to transfer the pentagonal fuzzy number into the corresponding crisp (non-fuzzy) value. Thereafter, the optimal solution was obtained using Vogel’s approximation method coupled with the modified distribution method. The proposed Method-1 is reported against a recent method and shows superior performance over the aforementioned and a proposed Method-2 via benchmark instances and new instances.

Suggested Citation

  • Z. A. M. S. Juman & Salama A. Mostafa & A. P. Batuwita & Ali AlArjani & Md Sharif Uddin & Mustafa Musa Jaber & Teg Alam & El-Awady Attia, 2022. "Close Interval Approximation of Pentagonal Fuzzy Numbers for Interval Data-Based Transportation Problems," Sustainability, MDPI, vol. 14(12), pages 1-18, June.
    • Handle: RePEc:gam:jsusta:v:14:y:2022:i:12:p:7423-:d:841242
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/14/12/7423/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/14/12/7423/
    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. Zhu, Kai & Ji, Kaiyuan & Shen, Jiayu, 2021. "A fixed charge transportation problem with damageable items under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    3. Miomir Stanković & Željko Stević & Dillip Kumar Das & Marko Subotić & Dragan Pamučar, 2020. "A New Fuzzy MARCOS Method for Road Traffic Risk Analysis," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    4. Amit Kumar & Amarpreet Kaur, 2011. "Methods for Solving Fully Fuzzy Transportation Problems Based on Classical Transportation Methods," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 2(4), pages 52-71, October.
    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. 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.
    2. 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.
    3. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    4. 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.
    5. 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.
    6. 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.
    7. Sarfaraz Hashemkhani Zolfani & Ramin Bazrafshan & Fatih Ecer & Çağlar Karamaşa, 2022. "The Suitability-Feasibility-Acceptability Strategy Integrated with Bayesian BWM-MARCOS Methods to Determine the Optimal Lithium Battery Plant Located in South America," Mathematics, MDPI, vol. 10(14), pages 1-18, July.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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).
    17. 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.
    18. 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.
    19. 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.
    20. Tan, Raymond R. & Aviso, Kathleen B. & Barilea, Ivan U. & Culaba, Alvin B. & Cruz, Jose B., 2012. "A fuzzy multi-regional input–output optimization model for biomass production and trade under resource and footprint constraints," Applied Energy, Elsevier, vol. 90(1), pages 154-160.

    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:jsusta:v:14:y:2022:i:12:p:7423-:d:841242. 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.