Purpose

The purpose of this paper is to propose an uncertainty representation and information measurement method for characterizing grey numbers, estimating their internal laws and solving how to generate them based on available information data in the real world.

Design/methodology/approach

This paper attempts to present a new mathematical methodology in the field of grey numbers. The generalized grey number is defined at first with the concept of information elements and information samples. Then, the probability function of a grey number is proposed to describe the internal law of the grey number. By finding the feasible information elements from information samples, the probability calculation method for the true value of a grey number is presented. Finally, some numerical examples and comparisons are carried out to assess the efficiency and performance.

Findings

The results show that the uncertainty representation and information measurement method is effective in characterizing and quantifying grey numbers based on available information data.

Practical implications

Uncertain information is widespread in practical applications. In this manuscript, the grey number is represented and its information is measured through some existing data in discrete or interval forms, which provides a grey information concept that utilizes information elements to represent uncertainty in the real world.

Originality/value

The proposal presents a novel data-driven method to generate a grey number representation from available data rather than the classical whitening weight function constructed from experience, and the dynamic evolution process of a grey number is measured by the increase of information samples.

中文翻译：

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灰数的不确定性表示和信息测量

目的

本文的目的是提出一种不确定性表示和信息测量方法，用于表征灰度，估计其内部定律并解决如何基于现实世界中的可用信息数据生成它们。

设计/方法/方法

本文试图提出一种灰色数字领域的新数学方法。首先用信息元素和信息样本的概念定义广义灰度数。然后，提出了灰度数的概率函数来描述灰度数的内在规律。通过从信息样本中找到可行的信息元素，提出了灰数真值的概率计算方法。最后，通过一些数值例子和比较来评估效率和性能。

发现

结果表明，不确定性表示和信息测量方法可有效地基于可用信息数据对灰度值进行表征和量化。

实际影响

不确定的信息在实际应用中很普遍。在此手稿中，代表了灰度数，并通过离散或间隔形式的一些现有数据来测量其信息，这提供了一种灰度信息概念，该概念利用信息元素来表示现实世界中的不确定性。

创意/价值

该提案提出了一种新的数据驱动方法，该方法可以从可用数据中生成灰度值表示，而不是根据经验构建经典的白化权重函数，并且灰度值的动态演变过程是通过信息样本的增加来衡量的。