Purpose

The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to build the model with a trapezoidal possibility degree function.

Design/methodology/approach

Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.

Findings

The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.

Practical implications

In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.

Social implications

Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of “power shortage” in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.

Originality/value

A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.

中文翻译：

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具有梯形可能性函数的GM(1,1,⊗b)模型的发展及其应用

目的

本文的目的是克服传统模型中灰色作用量为实数从而导致“唯一解”的弱点，建立具有梯形可能性度函数的模型。

设计/方法/方法

利用模型的系统输入输出框图，在系统影响因素不足的情况下恢复区间灰度作用量，形成梯形可能性度函数。在此基础上，构建了一个能够输出非唯一解的新模型。

发现

该模型在信息不足的情况下满足灰色理论的非唯一解原理。该模型在结构和建模结果上与传统模型兼容。将新模型应用于长江流域生态环境用水模拟，验证了新模型的有效性和实用性。

实际影响

本研究在系统影响因素不足的情况下，恢复了灰色作用量的区间灰数形式，解决了传统模型问题的唯一解。对丰富灰色预测模型的理论体系具有重要价值。

社会影响

以用电为例，未来用电水平的准确预测关系到电力基础设施投资的利用效率。如果用电水平预测过低，将导致电力基础设施建设不足，电力行业“缺电”现象频发。如果预测过高，将导致对电力基础设施的过度投资。因此，电力供应整体过剩将导致运营效率相对较低。因此，为正确的区间预测建立适当的模型是解决此类问题的更好方法。本研究提出的模型是解决此类问题的有效模型。

原创性/价值

首次提出了一种基于梯形可能性度函数的区间灰色动作量灰色预测模型。