Purpose

Aim to the limitations of grey relational analysis of interval grey number, based on the generalized greyness of interval grey number, this paper tries to construct a grey angle cosine relational degree model from the perspective of proximity and similarity.

Design/methodology/approach

Firstly, the algorithms of the generalized greyness of interval grey number and interval grey number vector are given, and its properties are analyzed. Then, based on the grey relational theory, the grey angle cosine relational model is proposed based on the generalized greyness of interval grey number, and the relationship between the classical cosine similarity model and the grey angle cosine relational model is analyzed. Finally, the validity of the model in this paper is illustrated by the calculation examples and an application example of related factor analysis of maize yield.

Findings

The results show that the grey angle cosine relational degree model has strict theoretical basis, convenient calculation and is easy to program, which can not only fully utilize the information of interval grey numbers but also overcome the shortcomings of greyness relational degree model. The grey angle cosine relational degree is an extended form of cosine similarity degree of real numbers. The calculation examples and the related factor analysis of maize yield show that the model proposed in this paper is feasible and valid.

Practical implications

The research results not only further enrich the grey system theory and method but also provide a basis for the grey relational analysis of the sequences in which the interval grey numbers coexist with the real numbers.

Originality/value

The paper succeeds in realizing the algorithms of the generalized greyness of interval grey number and interval grey number vector, and the grey angle cosine relational degree, which provide a new method for grey relational analysis.

中文翻译：

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基于区间灰数广义灰度的灰角余弦关联度模型

目的

针对区间灰数灰色关联分析的局限性，基于区间灰数的广义灰度性，尝试从接近度和相似度的角度构建灰度角余弦关联度模型。

设计/方法论/途径

首先给出了区间灰数和区间灰数向量的广义灰度算法，并分析了其性质。然后，基于灰色关联理论，提出基于区间灰数广义灰度的灰度角余弦关系模型，并分析经典余弦相似度模型与灰度角余弦关系模型之间的关系。最后通过计算实例和玉米产量相关因素分析的应用实例说明了本文模型的有效性。

发现

结果表明，灰度角余弦关联度模型理论基础严格、计算方便、易于编程，不仅能充分利用区间灰数信息，而且克服了灰度关联度模型的缺点。灰角余弦关联度是实数余弦相似度的扩展形式。玉米产量的计算实例和相关因素分析表明本文提出的模型是可行和有效的。

实际影响

研究成果不仅进一步丰富了灰色系统理论和方法，而且为区间灰数与实数共存序列的灰色关联分析提供了基础。

原创性/价值

论文成功实现了区间灰数和区间灰数向量的广义灰度以及灰度角余弦关联度的算法，为灰色关联分析提供了一种新的方法。