Grey-fuzzy solution for multi-objective linear programming with interval coefficients

Purpose The purpose of this paper is to propose a method for solving multi-objective linear programming (MOLP) with interval coefficients using positioned programming and interactive fuzzy programming approaches. Design/methodology/approach In the proposed algorithm, first, lower and upper bounds of...

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Bibliographic Details
Published in:Grey systems Vol. 8; no. 3; pp. 312 - 327
Main Authors: Mahmoudi, Amin, Feylizadeh, Mohammad Reza, Darvishi, Davood, Liu, Sifeng
Format: Journal Article
Language:English
Published: Bingley Emerald Publishing Limited 02.07.2018
Emerald Group Publishing Limited
Subjects:
Coefficients
Decision making
Fuzzy sets
Linear programming
Mathematical models
Mathematical programming
Methods
Multiple objective analysis
Random variables
Sensitivity analysis
Upper bounds
Interactive fuzzy programming approach
Grey linear programming
Grey system
Multi-objective linear programming
Interval coefficient
ISSN:2043-9377, 2043-9385
Online Access:Get full text
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Summary:Purpose The purpose of this paper is to propose a method for solving multi-objective linear programming (MOLP) with interval coefficients using positioned programming and interactive fuzzy programming approaches. Design/methodology/approach In the proposed algorithm, first, lower and upper bounds of each objective function in its feasible region will be determined. Afterwards using fuzzy approach, considering a membership function for each objective function and finally using grey linear programming, the solution for this problem will be obtained. Findings According to the presented example, in this paper, the proposed method is both simple in use and suitable for solving different problems. In the numerical example mentioned in this paper, the proposed method provides an acceptable solution for such problems. Practical implications As in most real-world situations, the coefficients of decision models are not known and exact. In this paper, the authors consider the model of MOLP with interval data, since one of the solutions to cover uncertainty is using interval theory. Originality/value Based on using grey theory and interactive fuzzy programming approaches, an appropriate method has been presented for solving MOLP problems with interval coefficients. The proposed method, against the complex methods, has less effort and offers acceptable solutions.
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ISSN:2043-9377
2043-9385
DOI:10.1108/GS-01-2018-0007