期刊
APPLIED MATHEMATICAL MODELLING
卷 38, 期 5-6, 页码 1660-1672出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2013.09.006
关键词
Fuzzy linear programming; Trapezoidal fuzzy number; Triangular fuzzy number; Multi-objective linear programming
资金
- National Natural Science Foundation of China [71061006, 71171055, 70871117, 61263018]
- Program for New Century Excellent Talents in University (the Ministry of Education of China) [NCET-10-0020]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20113514110009]
- Humanities Social Science Programming Project of Ministry of Education of China [09YGC630107]
- Natural Science Foundation of Jiangxi Province of China [20114BAB201012]
- Science and Technology Project of Jiangxi province educational department of China [GJJ12265, GJJ12740]
- Excellent Young Academic Talent Support Program Of Jiangxi University of Finance and Economics
Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers. (C) 2013 Elsevier Inc. All rights reserved.
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