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

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...

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Bibliographic Details
Published inFuzzy optimization and decision making Vol. 18; no. 4; pp. 433 - 449
Main Authors Chiu, Ya-Ling, Guu, Sy-Ming, Yu, Jiajun, Wu, Yan-Kuen
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2019
Springer Nature B.V
Subjects
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Iterative methods
Lower bounds
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Probability Theory and Stochastic Processes
Programming
Fuzzy relational inequalities
Min–max programming problem
Single-variable method
Addition-min composition
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Summary: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.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-019-09305-9