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Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment

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  • P. Senthil Kumar

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

Abstract

When people solve real-life SAP they 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 SAP under uncertain environment. He formulates the IFSAP and utilizes the TIFN to deal with uncertainty and hesitation. The SAP has uncertainty and hesitation in cost/time/profit/production is known as FIFSAP. The PSK (P. Senthil Kumar) method for finding an optimal solution for FIFAP is extended to solve the FIFSAP and the optimal objective value of FIFSAP is obtained in terms of TIFN. The main advantage of this method is that the optimal solution/assignment of FIFSAP is obtained without using the Hungarian method and intuitionistic fuzzy reduction method. Moreover, the proposed method is computationally very simple and easy to understand. The numerical example is presented to demonstrate computing procedure. The results affirm efficiency of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:igg:jfsa00:v:9:y:2020:i:1:p:1-34
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    References listed on IDEAS

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    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. 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.
    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. 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.
    6. Egon Balas & Matthew J. Saltzman, 1991. "An Algorithm for the Three-Index Assignment Problem," Operations Research, INFORMS, vol. 39(1), pages 150-161, February.
    7. Ming S. Hung & Walter O. Rom, 1980. "Solving the Assignment Problem by Relaxation," Operations Research, INFORMS, vol. 28(4), pages 969-982, August.
    8. 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.
    9. 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.
    10. Crama, Yves & Spieksma, Frits C. R., 1992. "Approximation algorithms for three-dimensional assignment problems with triangle inequalities," European Journal of Operational Research, Elsevier, vol. 60(3), pages 273-279, August.
    11. 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.
    12. 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.
    13. 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.
    14. Magos, D. & Miliotis, P., 1994. "An algorithm for the planar three-index assignment problem," European Journal of Operational Research, Elsevier, vol. 77(1), pages 141-153, August.
    15. 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.
    16. Sujeet Kumar Singh & Shiv Prasad Yadav, 2016. "A new approach for solving intuitionistic fuzzy transportation problem of type-2," Annals of Operations Research, Springer, vol. 243(1), pages 349-363, August.
    17. 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.
    18. 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.
    19. Geetha, S. & Nair, K. P. K., 1993. "A variation of the assignment problem," European Journal of Operational Research, Elsevier, vol. 68(3), pages 422-426, August.
    20. William P. Pierskalla, 1968. "Letter to the Editor—The Multidimensional Assignment Problem," Operations Research, INFORMS, vol. 16(2), pages 422-431, April.
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    1. 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.
    2. 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.
    3. 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.
    4. 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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