Purpose

The purpose of this paper is to survey and express the advantages and disadvantages of the existing approaches for solving grey linear programming in decision-making problems.

Design/methodology/approach

After presenting the concepts of grey systems and grey numbers, this paper surveys existing approaches for solving grey linear programming problems and applications. Also, methods and approaches for solving grey linear programming are classified, and its advantages and disadvantages are expressed.

Findings

The progress of grey programming has been expressed from past to present. The main methods for solving the grey linear programming problem can be categorized as Best-Worst model, Confidence degree, Whitening parameters, Prediction model, Positioned solution, Genetic algorithm, Covered solution, Multi-objective, Simplex and dual theory methods. This survey investigates the developments of various solving grey programming methods and its applications.

Originality/value

Different methods for solving grey linear programming problems are presented, where each of them has disadvantages and advantages in providing results of grey linear programming problems. This study attempted to review papers published during 35 years (1985–2020) about grey linear programming solving and applications. The review also helps clarify the important advantages, disadvantages and distinctions between different approaches and algorithms such as weakness of solving linear programming with grey numbers in constraints, inappropriate results with the lower bound is greater than upper bound, out of feasible region solutions and so on.

中文翻译：

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灰色线性规划：关于解决方法和应用的调查

目的

本文的目的是调查和表达在决策问题中解决灰色线性规划的现有方法的优缺点。

设计/方法/方法

在介绍了灰色系统和灰色数字的概念之后，本文概述了解决灰色线性规划问题和应用的现有方法。此外，对解决灰色线性规划的方法和方法进行了分类，并表达了其优点和缺点。

发现

过去到现在已经表达了灰色编程的进展。解决灰色线性规划问题的主要方法可以分为最佳最差模型，置信度，增白参数，预测模型，定位解决方案，遗传算法，覆盖解决方案，多目标，单纯形和对偶理论方法。这项调查调查了各种求解灰色编程方法及其应用的发展。

创意/价值

提出了解决灰色线性规划问题的不同方法，其中每种方法在提供灰色线性规划问题的结果上都有缺点和优点。这项研究试图回顾35年来（1985-2020年）发表的有关灰色线性规划求解和应用的论文。这篇综述还有助于弄清不同方法和算法之间的重要优缺点，区别和区别，例如在约束条件下求解带有灰色数字的线性规划的弱点，下限大于上限的不适当结果，可行区域解决方案等等。 。