Novel multi-attribute decision-making method based on Z-number grey relational degree

Liu, Ying; Rao, Congjun; Goh, Mark; Xiao, Xinping

doi:10.1007/s00500-022-07487-w

Cited by 10 publications

(5 citation statements)

References 53 publications

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“…Li et al [82] defined a generalized distance of Z-numbers to allow for the decisionmaker's preferences on different effects on the restriction and reliability parts of Z-numbers. Then, they defined the Z-number gray relational degree for the application in decisionmaking under the Z-number environment.…”

Section: Reference Methods Contributionmentioning

confidence: 99%

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

et al. 2023

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A Z-number is very powerful in describing imperfect information, in which fuzzy numbers are paired such that the partially reliable information is properly processed. During a decision-making process, human beings always use natural language to describe their preferences, and the decision information is usually imprecise and partially reliable. The nature of the Z-number, which is composed of the restriction and reliability components, has made it a powerful tool for depicting certain decision information. Its strengths and advantages have attracted many researchers worldwide to further study and extend its theory and applications. The current research trend on Z-numbers has shown an increasing interest among researchers in the fuzzy set theory, especially its application to decision making. This paper reviews the application of Z-numbers in decision making, in which previous decision-making models based on Z-numbers are analyzed to identify their strengths and contributions. The decision making based on Z-numbers improves the reliability of the decision information and makes it more meaningful. Another scope that is closely related to decision making, namely, the ranking of Z-numbers, is also reviewed. Then, the evaluative analysis of the Z-numbers is conducted to evaluate the performance of Z-numbers in decision making. Future directions and recommendations on the applications of Z-numbers in decision making are provided at the end of this review.

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Section: Reference Methods Contributionmentioning

confidence: 99%

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

et al. 2023

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“…If it is limited to if and only if the relative growth rate is equal to the perfect correlation, Y ¼ 10000X can be asserted as the unique expression; if it is limited to if and only if the relative absolute growth rate is equal to the perfect correlation, Y ¼ 1 3 X þ 999900 can be asserted as the unique expression. Therefore, in order to meet the needs of describing the diversity of correlation derived from the actual production, various incidence degrees emerged (Deng, 1993;Liu et al, 2010aLiu et al, , b, 2006Deng, 1985;Li, 2016;Xie and Liu, 2009;Dang et al, 2019;Chu and Xiao, 2023;Li et al, 2022;Geng et al, 2020;Zhang et al, 1996;Xiao et al, 1995;Luo and Zhang, 2020;Wu and Qu, 2020). These incidence degrees break through the limitation of linear range and realize that any two sequences can calculate incidence degrees without blind areas and are widely used in association clustering, association evaluation, association decision-making and play an extremely important role in traffic signal information processing, energy development, mineral mining, plant breeding and other aspects.…”

Section: Gray Incidence Degrees 527mentioning

confidence: 99%

“…Therefore, in order to meet the needs of describing the diversity of correlation derived from the actual production, various incidence degrees emerged (Deng, 1993; Liu et al. , 2010a, b, 2006; Deng, 1985; Li, 2016; Xie and Liu, 2009; Dang et al ., 2019; Chu and Xiao, 2023; Li et al ., 2022; Geng et al. , 2020; Zhang et al ., 1996; Xiao et al ., 1995; Luo and Zhang, 2020; Wu and Qu, 2020).…”

Section: Introductionmentioning

confidence: 99%

Equivalence class of complete correlation determination of several gray incidence degrees

Wei,

2024

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PurposeThis paper sets out to solve a common and crucial fundamental theoretical problem of gray incidence cluster analysis: to [X]={X|ρ(X,Y)≥1−ε0} constitute an approximate classification, it must first be proven that [X]={X|ρ(X,Y)=1} constitutes a rigorous classification.Design/methodology/approachThis paper does not study the concrete expressions of various incidence degrees but rather the perfect correlation essence of such incidence degrees, that is, sufficient and necessary conditions.FindingsFor any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree, it is proven that the perfect correlation relation is an equivalence relation. The set composed of all sequences Y that are equivalent to sequences X is studied, that is, the equivalence class of X. The structure and mutual relations of these equivalence classes are discussed, and the topological homeomorphism concept of incidence degree is introduced. The conclusion is obtained that the equivalence classes of the two incidence degrees must be the same when the topological homeomorphism is obtained.Research limitations/implicationsIn this paper, only the perfect correlation relation of any order difference incidence degree, the similarity incidence degree, the direct proportion incidence degree, the parallel incidence degree and the nearness incidence degree are studied as equivalent relations.Originality/valueNot only are the research results of several incidence degrees involved in this paper original but also many other effective incidence degrees have not done this basic research, so this paper opens up a research direction with theoretical significance.

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“…To jointly solve complex decision-making problems, the main purpose of the combined methods is to take full advantage of fusing different information by using other models and selecting the optimal solution by using GRA (Chu & Xiao, 2023). The combined methods include the combination of the information coverage grey numbers and GRA (Xiao et al, 2020a), the combination of the dynamic weighting operator and GRA (Jana & Pal., 2021), the combination of linguistic 2-tuples and GRA (Xiao et al, 2020b), and the combination of Z numbers and GRA (Li et al, 2022). Moreover, some scholars have also combined cloud models with other evaluation methods to build a comprehensive cloud model evaluation method.…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic Multi-Attribute Evaluation of Digital Economy Development in China: A Perspective From Interaction Effect

Xiao,

Gao,

Chen

et al. 2023

Technological and Economic Development of Economy

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This study aims to reflect the grey information coverage and complex interactions effect in digital economy development. Therefore, a multi-attribute decision making method based on the grey interaction relational degree of the normal cloud matrix (GIRD-NCM) model is proposed. First, the original information coverage grey numbers are transformed into normal cloud matrixes, and then a novel Minkowski distance between normal clouds is proposed by using different information principles. Second, the GIRD-NCM model is established according to the Choquet fuzzy integral and grey relational degree. Finally, the dynamic comprehensive evaluation of digital economy development in China from 2013 to 2020 is conducted. The implementation, availability, and feasibility of the GIRD-NCM model are verified by comparative analysis with three existing evaluation models. The empirical findings reveal a stable growth trend in China’s digital economy, with an annual growth rate of 7.87%, however, there are notable regional development disparities. The change in interaction degree has no effect on the rankings of provinces that are in the lead or have a moderately high level of digital economy development, but has a positive and negative impact on the rankings of these provinces with high and low levels of digital economy development, respectively.

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Novel multi-attribute decision-making method based on Z-number grey relational degree

Cited by 10 publications

References 53 publications

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

The Application of Z-Numbers in Fuzzy Decision Making: The State of the Art

Equivalence class of complete correlation determination of several gray incidence degrees

Dynamic Multi-Attribute Evaluation of Digital Economy Development in China: A Perspective From Interaction Effect

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