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A Simple Method for Solving Fully Intuitionistic Fuzzy Real Life Assignment Problem

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  • P. Senthil Kumar

    (PG & Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu, India)

  • R. Jahir Hussain

    (PG & Research Department of Mathematics, Jamal Mohamed College (Autonomous), Tiruchirappalli, Tamil Nadu, India)

Abstract

In solving real life assignment problem we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representations for the data. So, in this paper, the authors consider the assignment problem having uncertainty and hesitation in cost/time/profit. They formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and hesitation. The authors propose a new method called PSK (P.Senthil Kumar) method for finding the intuitionistic fuzzy optimal cost/time/profit for fully intuitionistic fuzzy assignment problem (FIFAP). The proposed method gives the optimal object value in terms of TIFN. The main advantage of this method is computationally very simple, easy to understand. Finally the effectiveness of the proposed method is illustrated by means of a numerical example which is followed by graphical representation of the finding.

Suggested Citation

  • 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.
    • Handle: RePEc:igg:joris0:v:7:y:2016:i:2:p:39-61
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    References listed on IDEAS

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    3. Seyed Hadi Nasseri & Ali Ebrahimnejad, 2011. "Sensitivity Analysis on Linear Programming Problems with Trapezoidal Fuzzy Variables," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 2(2), pages 22-39, April.
    4. 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.
    5. H. W. Kuhn, 1955. "The Hungarian method for the assignment problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 2(1‐2), pages 83-97, March.
    6. Ali Ebrahimnejad & Seyed Hadi Nasseri & Sayyed Mehdi Mansourzadeh, 2011. "Bounded Primal Simplex Algorithm for Bounded Linear Programming with Fuzzy Cost Coefficients," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 2(1), pages 96-120, January.
    7. 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.
    8. Sarbjit Singh, 2012. "Note on Assignment Algorithm with Easy Method of Drawing Lines to Cover All Zeros," International Journal of Operations Research and Information Systems (IJORIS), IGI Global, vol. 3(3), pages 87-97, July.
    9. 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.
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    Cited by:

    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. "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.
    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Saeedeh Bazari & Alireza Pooya & Omid Soleimani Fard & Pardis Roozkhosh, 2023. "Modeling and solving the problem of scheduling university exams in terms of new constraints on the conflicts of professors' exams and the concurrence of exams with common questions," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 877-915, June.
    9. 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.
    10. 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.
    11. 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.
    12. 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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