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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Bibliographic Details
Published in:Kybernetes Vol. 42; no. 3; pp. 482 - 496
Main Authors: Hossein Razavi Hajiagha, Seyed, Amoozad Mahdiraji, Hannan, Sadat Hashemi, Shide
Format: Journal Article
Language:English
Published: 01.01.2013
Subjects:
Deviation
Fuzzy logic
Intervals
Linear programming
Mathematical models
Maximization
Methodology
Optimization
ISSN:0368-492X
Online Access:Get full text
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Summary: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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ISSN:0368-492X
DOI:10.1108/03684921311323707