Abstract
Purpose – The purpose of this paper is to extend a methodology for solving multi-objective linear programming (MOLP) problems, when the objective functions and constraints coefficients are stated as interval numbers.
Design/methodology/approach – The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from
optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods.
Findings – The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal.
Research limitations/implications – The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined.
Originality/value – The paper proposed a novel and well-defined algorithm to solve the considered problem.
Design/methodology/approach – The approach proposed in this paper for the considered problem is based on the maximization of the sum of membership degrees which are defined for each objective of multi objective problem. These membership degrees are constructed based on the deviation from
optimal solutions of individual objectives. Then, the final model based on membership degrees is itself an interval linear programming which can be solved by current methods.
Findings – The efficiency of the solutions obtained by the proposed method is proved. It is shown that the obtained solution by the proposed method for an interval multi objective problem is Pareto optimal.
Research limitations/implications – The proposed method can be used in modeling and analyzing of uncertain systems which are modeled in the context of multi objective problems and in which required information is ill defined.
Originality/value – The paper proposed a novel and well-defined algorithm to solve the considered problem.
| Original language | English |
|---|---|
| Pages (from-to) | 482-496 |
| Number of pages | 15 |
| Journal | Kybernetes |
| Volume | 42 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 22 Mar 2013 |
| Externally published | Yes |
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Bibliographical note
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Hajiagha, S. H. R., Amoozad Mahdiraji, H., & Hashemi, S. S. (2013). Multi‐objective linear programming with interval coefficients: A fuzzy set based approach. Kybernetes, 42(3), 482-496. https://doi.org/10.1108/03684921311323707