One ranking method of interval grey number based on generalised greyness

Abstract

PurposeIn order to reflect the essential characteristics of interval grey number and study the ranking method of interval grey number as a whole, this paper aims to establish a ranking method of interval grey number.Design/methodology/approachFirst, based on the generalised greyness of interval grey number, the definitions of referenced grey number and proximity degree are given. Second, based on the greyness distance of interval grey number, the proximity degree model is constructed and its properties are analysed. Finally, some examples are given to illustrate the effectiveness of the proximity degree model.FindingsThe results show that the index of proximity degree can better reflect the degree that the interval grey number is relatively close to the referenced grey number in different cases. The proximity degree model used to compare interval grey numbers is an extension of the model used to compare real numbers. The examples show that the proximity degree model of interval grey number proposed in this paper is feasible and effective.Practical implicationsThe research studies show that the proximity degree model can be used for the ranking of interval grey numbers or real numbers and also for the ranking of numbers where interval grey numbers coexist with real numbers. In addition, the proximity degree model provides a theoretical basis for the establishment of grey comprehensive evaluation model.Originality/valueThe paper succeeds in putting forward the conceptions of referenced grey number and proximity degree based on the generalised greyness of interval grey number and constructing the proximity degree model for the ranking of interval grey number.

Some properties of generalized greyness of interval grey number

“…The generalized greyness of interval grey number not only provides a new method for judging the greyness or information preservation of grey number transformation, but also can be applied in interval grey number ranking (Li and Li, 2023). Definition 3.…”

“…Definition 3. Li and Li (2023) Suppose the background domain is Ω ¼ ½p; q, for ∀⊗ i ∈ ½a i ; b i ∈ Ω, a i ; b i ; p; q are all real numbers, and p ≤ a i < b i ≤ q. If there are two interval grey numbers ⊗ ðuÞ; ⊗ ðvÞ, and their generalized greyness vectors are as follows respectively.…”

“…Li and Li (2023) Suppose the background domain is Ω=false[p,qfalse], for ∀⊗i∈false[ai,bifalse]∈Ω, ai,bi,p,q are all real numbers, and p≤ai<bi≤q. If there are two interval grey numbers ⊗false(ufalse),⊗false(vfalse), and their generalized greyness vectors are as follows respectively.…”

“…Li and Li (2023) Suppose the background domain is Ω=false[p,qfalse], for ∀⊗i∈false[ai,bifalse]∈Ω, ai,bi,p,q are all real numbers, and p≤ai<bi≤q. If the generalized greyness vector of interval grey number ⊗i is as follows.…”

Grey angle cosine relational degree model based on generalized greyness of interval grey number

“…If d(⊗1,⊗2) is the greyness distance between ⊗1 and ⊗2, then d(⊗13,⊗03)=d(⊗23,⊗03), so that γ01=γ02. In fact, if the method of ranking interval grey number based on generalized greyness (Li and Li, 2023a) is used, we can get the ranking result, that is ⊗23≺⊗03≺⊗13. Although the greyness distances between the interval grey numbers ⊗13,⊗23 and ⊗03 are the same, the increment from ⊗12 to ⊗13 is obviously different from the increment from ⊗22 to ⊗23, and the increment from ⊗13…”