Fuzzy Optimization and Decision Making

, Volume 18, Issue 4, pp 433–449 | Cite as

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

  • Ya-Ling Chiu
  • Sy-Ming GuuEmail author
  • Jiajun Yu
  • Yan-Kuen Wu


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.


Fuzzy relational inequalities Addition-min composition Min–max programming problem Single-variable method 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ya-Ling Chiu
    • 1
  • Sy-Ming Guu
    • 2
    • 3
    Email author
  • Jiajun Yu
    • 2
    • 4
  • Yan-Kuen Wu
    • 5
  1. 1.College of International Business, Zhejiang Yuexiu University of Foreign LanguagesShaoxin CityChina
  2. 2.College of ManagementChang Gung UniversityTaoyuan CityTaiwan, ROC
  3. 3.Department of NeurologyChang Gung Memorial Hospital LinKouTaoyuan CityTaiwan, ROC
  4. 4.School of Innovation and EntrepreneurshipHuashang College, Guangdong University of Finance & EconomicsGuangzhou CityChina
  5. 5.Department of Business AdministrationVanung UniversityTaoyuan CityTaiwan, ROC

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