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

Amin Mahmoudi (Department of Industrial Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran)
Davood Darvishi (Department of Basic Sciences-Mathematics, Payame Noor University, Tehran, Iran)
Sifeng Liu (Institute for Grey Systems Studies, Nanjing University of Aeronautics and Astronautics, Nanjing, China)

ISSN: 2043-9377

Article publication date: 25 May 2018

Issue publication date: 2 July 2018

156

## Abstract

### 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.

## Citation

Mahmoudi, A., Feylizadeh, M.R., Darvishi, D. and Liu, S. (2018), "Grey-fuzzy solution for multi-objective linear programming with interval coefficients", Grey Systems: Theory and Application, Vol. 8 No. 3, pp. 312-327. https://doi.org/10.1108/GS-01-2018-0007

## Publisher

:

Emerald Publishing Limited