Purpose

The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The theoretical importance of the degree of greyness concept is also due to its application in a range of uncertainty modelling methods: predictive, relational and decision-making methods. Greyness, being a result of cognitive uncertainty, was recently subjected to axiomatization in the form of grey space with the use of the classical sets theory. The purpose of this article is to develop a new approach to the degree of greyness, being consistent with the grey space concept.

Design/methodology/approach

In order to realise the article’s goals, the research is divided into three stages described in particular sections. The first section of the article presents a theoretical framework of the degree of greyness and the grey space. The second part includes the assumptions of the new degree of greyness concept, along with the mathematical models for the first, the second and the third degree of greyness. The third section contains numerical examples for each degree of greyness.

Findings

As a result of the research, a concept of a degree of greyness was created and it was linked with a concept of grey space. This new approach to the issue of the degree of greyness has allowed the analysing of this category in three dimensions dependent on an accepted reference base. As a result, a concept of concrete and abstractive grey numbers was introduced and relationships between these categories of numbers and the degree of greyness were determined.

Originality/value

The proposed approach to the issue of the degree of greyness is a theoretical unification of the previous considerations in this area. The proposed three dimensions of greyness degree will be derived from the grey space, so they will also be a function of quantity. Thus, the degree of greyness was linked with a classical set theory. An original input in this article is also a differentiation of concrete and abstractive grey numbers, which give a basis for deliberations connected with interpretation of grey numbers in the context of real applications.

中文翻译：

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灰度等级的新方法

目的

灰色程度可被视为认知不确定性的量度。因此，它是灰色系统理论的认识论核心的一部分。灰色度概念的理论重要性也归因于其在一系列不确定性建模方法中的应用：预测，关系和决策方法。灰色是认知不确定性的结果，最近通过使用经典集合理论以灰色空间的形式进行了公理化处理。本文的目的是开发一种与灰色空间概念相一致的新方法来达到灰色程度。

设计/方法/方法

为了实现本文的目标，本研究分为三个阶段，在特定部分中进行了描述。本文的第一部分介绍了灰色程度和灰色空间的理论框架。第二部分包括新灰度等级概念的假设，以及第一，第二和第三灰度等级的数学模型。第三部分包含每个灰度等级的数值示例。

发现

研究的结果是，创建了一个灰色度的概念，并将其与灰色空间的概念联系在一起。这种解决灰度等级问题的新方法允许根据公认的参考基准在三个维度上对该类别进行分析。结果，引入了具体的和抽象的灰度数字的概念，并确定了这些数字类别与灰度程度之间的关系。

创意/价值

提出的解决灰度等级问题的方法是该领域先前考虑因素的理论统一。建议的灰度等级的三个维度将从灰色空间得出，因此它们也是数量的函数。因此，灰色度与经典集合论相关。本文的原始输入内容还包括具体的和抽象的灰度数的区别，这为与实际应用中的灰度数解释相关的审议提供了基础。