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

Ya-Ling Chiu (), Sy-Ming Guu (), Jiajun Yu () and Yan-Kuen Wu ()
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Ya-Ling Chiu: College of International Business, Zhejiang Yuexiu University of Foreign Languages
Sy-Ming Guu: Chang Gung University
Jiajun Yu: Chang Gung University
Yan-Kuen Wu: Vanung University

Fuzzy Optimization and Decision Making, 2019, vol. 18, issue 4, No 2, 433-449

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10700-019-09305-9

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