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A modified fuzzy goal programming procedure to solve fully quadratic fractional optimization model

Author

Listed:
  • Namrata Rani

    (Maharishi Markandeshwar (Deemed to be University))

  • Vandana Goyal

    (Maharishi Markandeshwar (Deemed to be University))

  • Deepak Gupta

    (Maharishi Markandeshwar (Deemed to be University))

Abstract

This paper is written to produce and efficient procedure to solve fully quadratic fractional optimization model(FQFOM) involving Trapezoidal Fuzzy Number(TrFN) as fuzzy parameters. Initially, the Fuzzy model is remodelled into a crisp model using $$ \alpha $$ α -cut methodology. In the second phase, a new methodology is given to form non-fractional models for each objective function vector using the concept of normalisation of denominators. Then membership functions and corresponding fuzzy goals are formed using aspiration and tolerance levels. Tolerance level for decision variables is provided by decision-maker units(DMU) to seek a satisfying solution. An algorithm along with flowchart and numerical example is provided to illustrate effectiveness of the proposed methodology. A comparative study is also undertaken to support the feasibility of the approach.

Suggested Citation

  • Namrata Rani & Vandana Goyal & Deepak Gupta, 2024. "A modified fuzzy goal programming procedure to solve fully quadratic fractional optimization 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. 15(11), pages 5167-5181, November.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:11:d:10.1007_s13198-024-02505-6
    DOI: 10.1007/s13198-024-02505-6
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    References listed on IDEAS

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    2. Bijay Baran Pal & Debjani Chakraborti, 2013. "Using genetic algorithm for solving quadratic bilevel programming problems via fuzzy goal programming," International Journal of Applied Management Science, Inderscience Enterprises Ltd, vol. 5(2), pages 172-195.
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    4. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    5. Stanley Zionts, 1968. "Programming with linear fractional functionals," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 15(3), pages 449-451, September.
    6. Ritu Arora & Kavita Gupta, 2018. "Branch and bound algorithm for discrete multi- level linear fractional programming problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(2), pages 5-21.
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    More about this item

    Keywords

    $$alpha $$ α -cut methodology; Decision maker unit(DMU); Fuzzy goal programming(FGP); Membership function; Multi-level multi-objective fully quadratic fractional optimization problem(MLMOFQFOP); Multi-level Programming(MLP); Trapezoidal fuzzy number(TrFN);
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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