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A single-variable method for solving min–max programming problem with addition-min fuzzy relational inequalities

Author

Listed:
  • Ya-Ling Chiu

    (College of International Business, Zhejiang Yuexiu University of Foreign Languages)

  • Sy-Ming Guu

    (Chang Gung University
    Chang Gung Memorial Hospital LinKou)

  • Jiajun Yu

    (Chang Gung University
    Huashang College, Guangdong University of Finance & Economics)

  • Yan-Kuen Wu

    (Vanung University)

Abstract

In this paper, we study the min–max programming problem with n addition-min fuzzy relational inequality constraints. We prove that when the problem is feasible, an optimal solution always exists with all variables being of the same value. Based on this result, the min–max programming problem can be simplified as a single-variable optimization problem with the same optimal objective value. To solve the corresponding single-variable optimization problem, we propose an analytical method and an iterative method by successively approximating the lower bound of the optimal value. Numerical examples are given to illustrate our methods.

Suggested Citation

  • Ya-Ling Chiu & Sy-Ming Guu & Jiajun Yu & Yan-Kuen Wu, 2019. "A single-variable method for solving min–max programming problem with addition-min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 433-449, December.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:4:d:10.1007_s10700-019-09305-9
    DOI: 10.1007/s10700-019-09305-9
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    Citations

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    Cited by:

    1. Yan-Kuen Wu & Ching-Feng Wen & Yuan-Teng Hsu & Ming-Xian Wang, 2022. "Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 21(3), pages 429-454, September.
    2. Yan-Kuen Wu & Ching-Feng Wen & Yuan-Teng Hsu & Ming-Xian Wang, 2022. "Finding minimal solutions to the system of addition-min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 581-603, December.
    3. Gang Xiao & Khizar Hayat & Xiaopeng Yang, 2023. "Evaluation and its derived classification in a Server-to-Client architecture based on the fuzzy relation inequality," Fuzzy Optimization and Decision Making, Springer, vol. 22(2), pages 213-245, June.
    4. Yan-Kuen Wu & Sy-Ming Guu & Ya-Chan Chang, 2024. "A Single-Variable Method for Solving the Min–Max Programming Problem with Addition–Overlap Function Composition," Mathematics, MDPI, vol. 12(20), pages 1-16, October.
    5. Jianjun Qiu & Xiaopeng Yang, 2022. "Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 291-317, June.

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