Multi‐objective linear programming with interval coefficients A fuzzy set based approach
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 considere...
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| Vydáno v: | Kybernetes Ročník 42; číslo 3; s. 482 - 496 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.01.2013
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| ISSN: | 0368-492X |
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| 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. |
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| AbstractList | 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. |
| Author | Hossein Razavi Hajiagha, Seyed Amoozad Mahdiraji, Hannan Sadat Hashemi, Shide |
| Author_xml | – sequence: 1 givenname: Seyed surname: Hossein Razavi Hajiagha fullname: Hossein Razavi Hajiagha, Seyed – sequence: 2 givenname: Hannan surname: Amoozad Mahdiraji fullname: Amoozad Mahdiraji, Hannan – sequence: 3 givenname: Shide surname: Sadat Hashemi fullname: Sadat Hashemi, Shide |
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| CitedBy_id | crossref_primary_10_3846_20294913_2016_1275878 crossref_primary_10_1007_s40819_025_01947_1 crossref_primary_10_1080_10556788_2025_2549341 crossref_primary_10_1155_2020_9207650 crossref_primary_10_1108_JM2_07_2018_0107 crossref_primary_10_1007_s40010_017_0469_z crossref_primary_10_1007_s12597_021_00512_w crossref_primary_10_1080_0305215X_2023_2195645 crossref_primary_10_1108_BFJ_09_2020_0865 crossref_primary_10_1108_K_10_2014_0226 crossref_primary_10_1108_GS_01_2018_0007 crossref_primary_10_1108_K_06_2016_0132 crossref_primary_10_1515_math_2019_0048 crossref_primary_10_1007_s40815_015_0081_9 crossref_primary_10_1007_s40815_020_00800_5 crossref_primary_10_1108_K_02_2014_0027 |
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| SubjectTerms | Deviation Fuzzy logic Intervals Linear programming Mathematical models Maximization Methodology Optimization |
| Subtitle | A fuzzy set based approach |
| Title | Multi‐objective linear programming with interval coefficients |
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