Purpose

Grey set is the important foundation of the grey mathematics and grey system theory, and the possibility function is the way of expressing grey set. This paper aims to establish the method of determining the possibility function of grey set and discusses its extended applications.

Design/methodology/approach

First, the grey kernel and the grey support set of grey set are defined, and the properties of grey kernel are analyzed. Second, according to the decomposition theorem of grey set, a method of determining the possibility function of grey set is put forward in this paper, which is called the method of increasing information and taking maximum and minimum (IITMM), and then it is further simplified as the method of increasing information and taking maximum (IITM), and an simple example is given to illustrate the calculation procedure. Finally, the grey information cluster method (GICM) based on IITM is proposed and applied to the ecological and geographical environment analysis of pine caterpillar.

Findings

The results show that the grey kernel of grey set still has grey uncertainty; the method of IITM has simple calculation and strict mathematical basis, and it can synthesize the information of the research object and accords with the principle of using minimum information; the GICM and the fuzzy cluster method have the same classification effect.

Practical implications

The researches show that method of IITM can be used not only to determine the possibility function of the grey set effectively, but also be used for the evaluation and cluster analysis of connotative objects. The classification result of the GICM presented in this paper is more precise than that of the fuzzy cluster method.

Originality/value

The paper succeeds in realizing both the IITM method for determining the possibility function of grey set and the GICM based on IITM for the connotative objects.

中文翻译：

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确定灰集可能性函数的方法及其应用

目的

灰色集是灰色数学和灰色系统理论的重要基础，而可能性函数是灰色集的表达方式。本文旨在建立确定灰色集可能性函数的方法，并讨论其扩展应用。

设计/方法/途径

首先定义了灰色核和灰色集的灰色支持集，分析了灰色核的性质。其次，根据灰集分解定理，本文提出了一种确定灰集可能性函数的方法，称为信息递增取极大极小法（IITMM），进而进一步简化为信息递增取最大值法（IITM），并给出一个简单的例子来说明计算过程。最后，提出了基于IITM的灰色信息聚类方法（GICM），并将其应用于松毛虫的生态地理环境分析。

发现

结果表明，灰色集的灰色核仍然存在灰色不确定性；IITM方法计算简单，数学基础严密，能够综合研究对象的信息，符合使用最少信息的原则；GICM与模糊聚类方法具有相同的分类效果。

实际影响

研究表明，IITM方法不仅可以有效地确定灰色集的可能性函数，而且可以用于内涵对象的评价和聚类分析。本文提出的 GICM 的分类结果比模糊聚类方法的分类结果更精确。

原创性/价值

本文成功地实现了确定灰集可能性函数的IITM方法和基于IITM的内涵对象的GICM。