A new algorithm to solve fully fuzzy linear programming problems using the MOLP problem
Recently, two new algorithms have been proposed to solve a fully fuzzy linear programming (FFLP) problem by Lotfi et al. [F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Model. 3...
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| Published in: | Applied mathematical modelling Vol. 39; no. 12; pp. 3183 - 3193 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier Inc
15.06.2015
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| Subjects: | |
| ISSN: | 0307-904X |
| Online Access: | Get full text |
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| Summary: | Recently, two new algorithms have been proposed to solve a fully fuzzy linear programming (FFLP) problem by Lotfi et al. [F.H. Lotfi, T. Allahviranloo, M.A. Jondabeha, L. Alizadeh, Solving a fully fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Model. 33 (2009) 3151–3156] and Kumar et al. [A. Kumar, J. Kaur, P. Singh, A new method for solving fully fuzzy linear programming problems, Appl. Math. Model. 33 (2011) 817–823]. In this paper, based on a new lexicographic ordering on triangular fuzzy numbers, a novel algorithm is proposed to solve the FFLP problem by converting it to its equivalent a multi-objective linear programming (MOLP) problem and then it is solved by the lexicographic method. By a theorem, it is shown that the lexicographic optimal solution of MOLP problem can be considered as an optimal solution of the FFLP problem. Then, a simple example and two real problems, as two case studies, will be used to illustrate our algorithm and compare it with the existing methods. |
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| ISSN: | 0307-904X |
| DOI: | 10.1016/j.apm.2013.03.014 |