Purpose

The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.

Design/methodology/approach

Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.

Findings

The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.

Practical implications

Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.

Originality/value

The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.

中文翻译：

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区间多变量灰色模型的矩阵形式及其应用

目的

本文的目的是使多变量灰色模型能够直接应用于区间灰度数序列，构造区间多变量灰色模型（IMGM(1,m,k)模型）的矩阵形式对原始数据进行模拟和预测。本文中的区间灰度数序列。

设计/方法/方法

首先，将区间灰度数作为一个三维列向量，将多变量灰度模型的参数用矩阵形式表示。基于动态灰度作用和优化背景值，构建区间多变量灰度模型。最后通过两个例子和对比验证了IMGM(1,m,k)模型的有效性。

发现

该模型分别用于模拟和预测专家价值、外商直接投资、汽车销售和钢铁产量。结果表明，所提出的模型比另外两个模型具有更好的模拟和预测性能。

实际影响

由于信息的不确定性和现实的不断变化，区间灰度数被用来表征原始数据的全部信息。而IMGM(1,m,k)模型不仅考虑了参数随时间变化的特性，还同时考虑了区间灰度数的下、中、上界信息，使其更适合实际应用。

原创性/价值

本文的主要贡献是提出了一种新的区间多变量灰色模型，该模型考虑了区间数下、中、上界之间的相互作用，不需要将区间灰数序列转化为实数序列。根据区间灰度数各界的不同特点，建立区间多变量灰度模型的矩阵形式，对区间灰度数进行模拟和预测。此外，模型引入了动态灰度作用来反映参数随时间的变化。代替经典 MGM(1,m) 的白色方程，差分方程直接用于求解模拟值和预测值。