Fuzzy Optimization and Decision Making

, Volume 18, Issue 4, pp 433–449

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

Article

## 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.

## Keywords

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

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## 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