IDEAS home Printed from https://ideas.repec.org/a/spr/ijsaem/v15y2024i9d10.1007_s13198-024-02433-5.html
   My bibliography  Save this article

An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems

Author

Listed:
  • P. Senthil Kumar

    (Amity University)

Abstract

It presents the type-2 intuitionistic fuzzy solid transportation problem (type-2 IFSTP) in a real-world situation and introduces an efficient technique based on software codes for solving type-2 IFSTP. It defines various types of intuitionistic fuzzy solid transportation problems (IFSTPs) and presents a mathematical model of full and type-2 IFSTPs. Additionally, the theorem, corollary, and their proof, as well as some results relevant to type-2 IFSTPs, are presented. Both the existing problem’s solution and the proposed type-2 IFSTP’s solution are compared using software (e.g., Matlab). In particular, solving IFSTPs using Matlab is new in the literature. Shortcomings in the existing results are pointed out and solved. Using the proposed approach, the optimal solution and optimal objective value of both the solid transportation problem (STP) and type-2 IFSTPs are obtained concurrently with one LP model, which is the key objective of this article. It also discusses the time complexity of the existing algorithms for solving STPs with different intuitionistic fuzzy numbers (IFNs). Both the proposed results and the benefits of the proposed methodology are thoroughly discussed. Finally, a sound conclusion and future research directions are provided.

Suggested Citation

  • P. Senthil Kumar, 2024. "An efficient approach for solving type-2 intuitionistic fuzzy solid transportation problems with their equivalent crisp solid transportation problems," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(9), pages 4370-4403, September.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:9:d:10.1007_s13198-024-02433-5
    DOI: 10.1007/s13198-024-02433-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13198-024-02433-5
    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/s13198-024-02433-5?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. P.Senthil Kumar, 2018. "PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 7(4), pages 62-99, October.
    2. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    3. Haridas Roy & Govind Pathak & Rakesh Kumar & Zahid Amin Malik, 2024. "Maximum modulus zero-suffix method for finding an optimal solution to fuzzy transportation problems," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 897-917, June.
    4. Muhammad Sam'an & Farikhin & Bayu Surarso, 2023. "Three-phase algorithms in solving full fuzzy transportation problem by using fuzzy analytical hierarchy process," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 48(4), pages 445-466.
    5. Dalbinder Kour & Sathi Mukherjee & Kajla Basu, 2017. "Solving intuitionistic fuzzy transportation problem using linear programming," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1090-1101, November.
    6. Ashutosh Choudhary & Shiv Prasad Yadav, 2022. "An approach to solve interval valued intuitionistic fuzzy transportation problem of Type-2," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(6), pages 2992-3001, December.
    7. K. B. Haley, 1962. "New Methods in Mathematical Programming---The Solid Transportation Problem," Operations Research, INFORMS, vol. 10(4), pages 448-463, August.
    8. S. K. Bharati & S. R. Singh, 2018. "A New Interval-Valued Intuitionistic Fuzzy Numbers: Ranking Methodology and Application," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 363-381, November.
    9. S. K. Bharati & Rita Malhotra, 2017. "Two stage intuitionistic fuzzy time minimizing transportation problem based on generalized Zadeh’s extension principle," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 1442-1449, November.
    10. Krishna Prabha Sikkannan & Vimala Shanmugavel, 2021. "Sorting Out Fuzzy Transportation Problems via ECCT and Standard Deviation," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 12(2), pages 1-14, April.
    11. Xie, Fanrong & Butt, Muhammad Munir & Li, Zuoan & Zhu, Linzhi, 2017. "An upper bound on the minimal total cost of the transportation problem with varying demands and supplies," Omega, Elsevier, vol. 68(C), pages 105-118.
    12. Jaroslav Ramík & Milan Vlach, 2016. "Intuitionistic fuzzy linear programming and duality: a level sets approach," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 457-489, December.
    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, 2018. "PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 7(4), pages 62-99, October.
    2. P. Senthil Kumar, 2019. "PSK Method for Solving Mixed and Type-4 Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 10(2), pages 20-53, April.
    3. P. Senthil Kumar, 2020. "Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(1), pages 189-222, February.
    4. P. Senthil Kumar, 2018. "A Simple and Efficient Algorithm for Solving Type-1 Intuitionistic Fuzzy Solid Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(3), pages 90-122, July.
    5. Sharmistha Halder (Jana) & Biswapati Jana, 2020. "Application of fuzzy programming techniques to solve solid transportation problem with additional constraints," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 30(1), pages 67-84.
    6. P. Senthil Kumar, 2020. "Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 9(1), pages 1-34, January.
    7. Pedro Huidobro & Pedro Alonso & Vladimír Janiš & Susana Montes, 2022. "Convexity and level sets for interval-valued fuzzy sets," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 553-580, December.
    8. Yanan Zhang & Zhaopeng Meng & Yan Zheng & Anca Ralescu, 2019. "Schedule optimization under fuzzy constraints of vehicle capacity," Fuzzy Optimization and Decision Making, Springer, vol. 18(2), pages 131-150, June.
    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. Gourav Gupta & Shivani & Deepika Rani, 2024. "Neutrosophic goal programming approach for multi-objective fixed-charge transportation problem with neutrosophic parameters," OPSEARCH, Springer;Operational Research Society of India, vol. 61(3), pages 1274-1300, September.
    11. 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.
    12. Collan, Mikael, 2008. "New Method for Real Option Valuation Using Fuzzy Numbers," Working Papers 466, IAMSR, Åbo Akademi.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:ijsaem:v:15:y:2024:i:9:d:10.1007_s13198-024-02433-5. 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.