The method and its applications of determining possibility function of grey set

Abstract

PurposeGrey 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/approachFirst, 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.FindingsThe 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 implicationsThe 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/valueThe 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.

Hyperspectral estimation model of soil organic matter content based on principal gradient grey information

“…The whole of all the elements (grey elements) that have the nature of grey ⊗ P is called the grey set (Li and Li, 2021). Let all modelling samples form the modelling sample set X ¼ fx 1 ; x 2 ; Á Á Á ; x n g, if there is a grey concept ⊗ P on the domain U, that is, "soil organic matter content is abundant", then the modelling sample set can be regarded as a grey set, that is, ⊗ X ¼ f ⊗ x 1 ; ⊗ x 2 ; Á Á Á ; ⊗ x n g, where each modelling sample can be regarded as a grey element of the grey set.…”

“…However, due to various reasons, the research on grey set and grey mathematics is relatively weak, which affects the development of grey algebra and grey system theory. Therefore, to overcome the shortcomings of the existing definition of grey set, Li and Li (2021) proposed a new definition of grey set, and proposed to represent grey set by the possibility function, and unified the algorithm of ordinary set, fuzzy set and grey set. According to the decomposition theorem of grey set, Li and Li (2023) further proposed a method to determine the possibility function of grey set, that is, the method of increasing information and taking large.…”

“…Therefore, to overcome the shortcomings of the existing definition of grey set, Li and Li (2021) proposed a new definition of grey set, and proposed to represent grey set by the possibility function, and unified the algorithm of ordinary set, fuzzy set and grey set. According to the decomposition theorem of grey set, Li and Li (2023) further proposed a method to determine the possibility function of grey set, that is, the method of increasing information and taking large. This provides a theoretical basis for the study of estimation models from the perspective of information.…”

Use of AHP and grey fixed weight clustering to assess the maturity level of strategic communication management in Brazilian startups

“…The next step consists of defining the possibility functions. Possibility functions can be understood as ways of expressing grey set and (Li and Li, 2023) are utilized to calculate the degree of membership of alternatives to predefined classes, assigning each alternative to the class with the highest membership score (Delgado and Romero, 2016;Li et al, 2014;Wang et al, 2022). The possibility function formulation stemmed from debates among the researchers.…”

Multi-stage skewed grey cloud clustering model and its application

“…As a result, researchers and pertinent decision-making departments have recently shown a great deal of interest in the grey clustering model, which is a crucial component of the grey system theory. Many scholars have studied the nature and mechanism of the model (Xie et al ., 2019) and optimised the model from the improvement of possibility function (Li and Li, 2023; Sun et al ., 2022) and expansion of clustering principle (Qiang and Wang, 2015), which has been successfully applied in aviation (Delcea et al ., 2022), natural disasters (Zhang and Luo, 2023), finance (Yan et al ., 2022), information technology (Duan et al ., 2022) and other fields and greatly enriched the development of grey clustering model.…”