Purpose

The purpose of this paper is to construct an interval grey number NGM(1,1) direct prediction model (abbreviated as IGNGM(1,1)), which need not transform interval grey numbers sequences into real number sequences, and the Markov model is used to optimize residual sequences of IGNGM(1,1) model.

Design/methodology/approach

A definition equation of IGNGM(1,1) model is proposed in this paper, and its time response function is solved by recursive iteration method. Next, the optimal weight of development coefficients of two boundaries is obtained by genetic algorithm, which is designed by minimizing the average relative error based on time weighted. In addition to that, the Markov model is used to modify residual sequences.

Findings

The interval grey numbers’ sequences can be predicted directly by IGNGM(1,1) model and its residual sequences can be amended by Markov model. A case study shows that the proposed model has higher accuracy in prediction.

Practical implications

Uncertainty and volatility information is widespread in practical applications, and the information can be characterized by interval grey numbers. In this paper, an interval grey numbers direct prediction model is proposed, which provides a method for predicting the uncertainty information in the real world.

Originality/value

The main contribution of this paper is to propose an IGNGM(1,1) model which can realize interval grey numbers prediction without transforming them into real number and solve the optimal weight of integral development coefficient by genetic algorithm so as to avoid the distortion of prediction results. Moreover, the Markov model is used to modify residual sequences to further improve the modeling accuracy.

中文翻译：

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基于区间灰数的直接 NGM(1,1) 预测模型的开发

目的

本文的目的是构建一个区间灰数NGM(1,1)直接预测模型（简称IGNGM(1,1)），不需要将区间灰数序列转化为实数序列，马尔可夫模型为用于优化 IGNGM(1,1) 模型的残差序列。

设计/方法/方法

提出了IGNGM(1,1)模型的定义方程，并采用递归迭代法求解其时间响应函数。接着，通过基于时间加权最小化平均相对误差的遗传算法得到两个边界发展系数的最优权重。除此之外，马尔可夫模型用于修改残差序列。

发现

IGNGM(1,1)模型可以直接预测区间灰数序列，马尔可夫模型修正其残差序列。案例研究表明，所提出的模型具有更高的预测精度。

实际影响

不确定性和波动性信息在实际应用中广泛存在，这些信息可以用区间灰数来表征。本文提出了一种区间灰数直接预测模型，为预测现实世界中的不确定性信息提供了一种方法。

原创性/价值

本文的主要贡献是提出了一种IGGNM(1,1)模型，该模型可以在不将其转化为实数的情况下实现区间灰度数预测，并通过遗传算法求解积分发展系数的最优权重，从而避免预测的失真。结果。此外，利用马尔可夫模型对残差序列进行修正，进一步提高建模精度。