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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| Published in | Fuzzy optimization and decision making Vol. 18; no. 4; pp. 433 - 449 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1568-4539 1573-2908 |
| DOI | 10.1007/s10700-019-09305-9 |
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| 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. |
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| AbstractList | 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. 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. |
| Author | Guu, Sy-Ming Chiu, Ya-Ling Wu, Yan-Kuen Yu, Jiajun |
| Author_xml | – sequence: 1 givenname: Ya-Ling surname: Chiu fullname: Chiu, Ya-Ling organization: College of International Business, Zhejiang Yuexiu University of Foreign Languages – sequence: 2 givenname: Sy-Ming surname: Guu fullname: Guu, Sy-Ming email: iesmguu@gmail.com organization: College of Management, Chang Gung University, Department of Neurology, Chang Gung Memorial Hospital LinKou – sequence: 3 givenname: Jiajun surname: Yu fullname: Yu, Jiajun organization: College of Management, Chang Gung University, School of Innovation and Entrepreneurship, Huashang College, Guangdong University of Finance & Economics – sequence: 4 givenname: Yan-Kuen surname: Wu fullname: Wu, Yan-Kuen organization: Department of Business Administration, Vanung University |
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| Cites_doi | 10.1007/s10700-008-9029-y 10.1016/S0165-0114(98)00417-5 10.1016/j.ins.2005.11.008 10.1007/978-94-017-1650-5 10.1016/j.ins.2011.03.004 10.1016/j.ins.2011.04.042 10.1109/TFUZZ.2007.902018 10.1016/j.fss.2005.02.010 10.1109/TFUZZ.2016.2593496 10.1016/S0165-0114(97)00184-X 10.1016/j.ins.2011.04.011 10.1109/TFUZZ.2015.2428716 10.1007/s00500-013-1152-1 10.1023/A:1022848114005 10.1016/j.ins.2010.10.024 10.1109/TFUZZ.2017.2771406 10.1016/0022-247X(85)90329-4 10.1016/S0019-9958(76)90446-0 10.1016/S0165-0114(98)00235-8 10.1016/j.fss.2014.04.007 10.1016/j.ins.2011.06.009 10.1016/j.fss.2013.03.009 10.1109/FSKD.2012.6233956 |
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| Snippet | 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... 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... |
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| SubjectTerms | 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 |
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| Title | A single-variable method for solving min–max programming problem with addition-min fuzzy relational inequalities |
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