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A new approach for solving fully intuitionistic fuzzy transportation problems

Author

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  • Ali Ebrahimnejad

    (Islamic Azad University)

  • Jose Luis Verdegay

    (Universidad de Granada)

Abstract

In this paper, a well-known network-structured problem called the transportation problem (TP) is considered in an uncertain environment. The transportation costs, supply and demand are represented by trapezoidal intuitionistic fuzzy numbers (TrIFNs) which are the more generalized form of trapezoidal fuzzy numbers involving a degree of acceptance and a degree of rejection. We formulate the intuitionistic fuzzy TP (IFTP) and propose a solution approach to solve the problem. The IFTP is converted into a deterministic linear programming (LP) problem, which is solved using standard LP algorithms. The main contributions of this paper are fivefold: (1) we convert the formulated IFTP into a deterministic classical LP problem based on ordering of TrIFNs using accuracy function; (2) in contrast to most existing approaches, which provide a crisp solution, we propose a new approach that provides an intuitionistic fuzzy optimal solution; (3) in contrast to existing methods that include negative parts in the obtained intuitionistic fuzzy optimal solution and intuitionistic fuzzy optimal cost, we propose a new method that provides non-negative intuitionistic fuzzy optimal solution and optimal cost; (4) we discuss about the advantages of the proposed method over the existing methods for solving IFTPs; (5) we demonstrate the feasibility and richness of the obtained solutions in the context of two application examples.

Suggested Citation

  • Ali Ebrahimnejad & Jose Luis Verdegay, 2018. "A new approach for solving fully intuitionistic fuzzy transportation problems," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 447-474, December.
    • Handle: RePEc:spr:fuzodm:v:17:y:2018:i:4:d:10.1007_s10700-017-9280-1
    DOI: 10.1007/s10700-017-9280-1
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    References listed on IDEAS

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    1. Shu-Ping Wan & Feng Wang & Gai-li Xu & Jiu-ying Dong & Jing Tang, 2017. "An intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 269-295, September.
    2. Sujeet Kumar Singh & Shiv Prasad Yadav, 2016. "Intuitionistic fuzzy transportation problem with various kinds of uncertainties in parameters and variables," 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. 7(3), pages 262-272, September.
    3. Jimenez, F. & Verdegay, J. L., 1999. "Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach," European Journal of Operational Research, Elsevier, vol. 117(3), pages 485-510, September.
    4. Ali Ebrahimnejad, 2015. "A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(11), pages 2048-2060, August.
    5. 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.
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    1. Sumati Mahajan & S. K. Gupta, 2021. "On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions," Annals of Operations Research, Springer, vol. 296(1), pages 211-241, January.
    2. Bogdana Stanojević & Sorin Nǎdǎban, 2023. "Empiric Solutions to Full Fuzzy Linear Programming Problems Using the Generalized “min” Operator," Mathematics, MDPI, vol. 11(23), pages 1-15, 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. Shyamali Ghosh & Sankar Kumar Roy & Gerhard-Wilhelm Weber, 2023. "Interactive strategy of carbon cap-and-trade policy on sustainable multi-objective solid transportation problem with twofold uncertain waste management," Annals of Operations Research, Springer, vol. 326(1), pages 157-197, July.
    5. Chaube, Shshank & Joshi, Dheeraj Kumar & Ujarari, Chandan Singh, 2023. "Hesitant Bifuzzy Set (an introduction): A new approach to assess the reliability of the systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 98-107.
    6. 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.
    7. Raj Kumar Bera & Shyamal Kumar Mondal, 2022. "A multi-objective transportation problem with cost dependent credit period policy under Gaussian fuzzy environment," Operational Research, Springer, vol. 22(4), pages 3147-3182, September.
    8. Divya Sharma & Dinesh C. S. Bisht & Pankaj Kumar Srivastava, 2024. "Solution of fuzzy transportation problem based upon pentagonal and hexagonal fuzzy numbers," 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 4348-4354, September.
    9. M. Bagheri & A. Ebrahimnejad & S. Razavyan & F. Hosseinzadeh Lotfi & N. Malekmohammadi, 2022. "Fuzzy arithmetic DEA approach for fuzzy multi-objective transportation problem," Operational Research, Springer, vol. 22(2), pages 1479-1509, April.
    10. Soumen Kumar Das & Sankar Kumar Roy & Gerhard Wilhelm Weber, 2020. "Heuristic approaches for solid transportation-p-facility location problem," 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. 28(3), pages 939-961, September.
    11. 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.

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