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PSK Method for Solving Intuitionistic Fuzzy Solid Transportation Problems

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  • P.Senthil Kumar

    (Department of Humanities and Sciences, Navodaya Institute of Technology, Raichur, India)

Abstract

This article proposes a method for solving intuitionistic fuzzy solid transportation problems (IFSTPs) in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers (IFNs). The remaining parameters, namely: supply, demand and conveyance capacity, are all considered into crisp numbers. This type of STP is called a type-2 IFSTP. When solving the real life solid transportation problems (STPs) those tend to face the uncertainty state as well as hesitation due to many uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this article, the author tried to categorise the STPs under the uncertain environment. He formulates the intuitionistic fuzzy STPs and utilizes the triangular intuitionistic fuzzy number (TIFN) to deal with uncertainty and hesitation. The PSK (P.Senthil Kumar) method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem (FIFTP) is extended to solve the type-2 IFSTP and the optimal objective value of type-2 IFSTP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution of type-2 IFSTP is obtained without using the basic feasible solution and the method of testing optimality. Moreover, the proposed method is computationally very simple and easy to understand. A case study is presented to illustrate the procedure of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:igg:jfsa00:v:7:y:2018:i:4:p:62-99
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    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. P. Senthil Kumar, 2018. "A note on 'a new approach for solving intuitionistic fuzzy transportation problem of type-2'," International Journal of Logistics Systems and Management, Inderscience Enterprises Ltd, vol. 29(1), pages 102-129.
    3. 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.
    4. 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.
    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. P. Senthil Kumar & R. Jahir Hussain, 2016. "Computationally simple approach for solving fully intuitionistic fuzzy real life 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. 7(1), pages 90-101, December.
    7. P. Senthil Kumar, 2018. "Linear Programming Approach for Solving Balanced and Unbalanced Intuitionistic Fuzzy Transportation Problems," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 9(2), pages 73-100, April.
    8. K. B. Haley, 1962. "New Methods in Mathematical Programming---The Solid Transportation Problem," Operations Research, INFORMS, vol. 10(4), pages 448-463, August.
    9. P. Senthil Kumar, 2016. "PSK Method for Solving Type-1 and Type-3 Fuzzy Transportation Problems," International Journal of Fuzzy System Applications (IJFSA), IGI Global, vol. 5(4), pages 121-146, October.
    10. 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.
    11. P. Senthil Kumar, 2020. "Intuitionistic fuzzy zero point method for solving type-2 intuitionistic fuzzy transportation problem," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 37(3), pages 418-451.
    12. Debashree Guha & Debjani Chakraborty, 2010. "A Theoretical Development of Distance Measure for Intuitionistic Fuzzy Numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-25, March.
    13. 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.
    14. Deng-Feng Li & Shu-Ping Wan, 2017. "Minimum Weighted Minkowski Distance Power Models for Intuitionistic Fuzzy Madm with Incomplete Weight Information," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1387-1408, September.
    15. 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.
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    1. 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.
    2. 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.
    3. Abdelmalek Ouannou & Adil Brouri & Laila Kadi & Hafid Oubouaddi, 2022. "Identification of switched reluctance machine using fuzzy model," 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 2833-2846, December.
    4. 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.
    5. Zhi-Ming Chen & Cheng-Hsiung Lee & Hung-Lin Lai, 2022. "Speedup the optimization of maximal closure of a node-weighted directed acyclic graph," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1413-1437, December.
    6. 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.
    7. P. Senthil Kumar, 2019. "Intuitionistic fuzzy solid assignment problems: a software-based approach," 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. 10(4), pages 661-675, August.
    8. 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.

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