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Article
Publication date: 19 August 2011

Nai‐ming Xie and Si‐feng Liu

This paper aims to construct a novel grey relational model based on grey number sequences and to solve the problems which exist in traditional grey relational models, in…

Abstract

Purpose

This paper aims to construct a novel grey relational model based on grey number sequences and to solve the problems which exist in traditional grey relational models, in which the uncertain information cannot be described.

Design/methodology/approach

Based on the definition of traditional grey relational models, considering the limited information and knowledge, the algorithm of grey numbers was combined with the grey relational model. A general formula of grey operations and grey distance is defined. A novel grey relational model based on grey number sequences, named grey geometrical relational model, is proposed according to the definition of grey distance. Finally, several properties including parallel, multiple and order‐keeping about the proposed model are discussed.

Findings

The results show that the novel grey relational model satisfies the properties properly. It is useful to calculate the relational degree of two different grey number sequences. And the process of calculating is easier than traditional grey relational models.

Practical implications

The method exposed in the paper can be used to calculate every two sequences. The method can also be used to rank sequences of more than two.

Originality/value

The paper succeeds in constructing a novel grey relational model. The properties of novel model are studied and it is a new development in grey systems theory undoubtedly.

Details

Grey Systems: Theory and Application, vol. 1 no. 2
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 1 August 2016

Kunli Wen

Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications. However, in one article published in…

Abstract

Purpose

Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications. However, in one article published in 2007, which applied the previous grey relational grade to environmental protection fields and some results had been found. After studied it carefully, the author found that the grey relational grade in the paper was not the previous grey relational grade. According to the mathematics logic, it must first prove the proposed grey relational grade satisfies the four axioms in grey relational analysis, and then the author can say that the achieved results are reasonable and correct. The paper aims to discuss these issues.

Design/methodology/approach

The paper lists the rational and regular grey relational grade that had been published in the past, and used the four axioms in grey system theory to prove the Pai’s grey relational grade that satisfy the four axioms steps by steps.

Findings

Through the detail proof of the proposed grey relational grade in Pai’s paper, it indeed satisfies the four axioms in grey relational grade.

Research limitations/implications

The paper had enhanced the correctness and reasonableness of that paper, and let the grey relational grade, which appear in Pai’s paper is legitimate and correct grey relational grade in grey system theory.

Originality/value

The paper had identified that Pai’s grey relational grade is a rational and regular grey relational grade in grey system theory, and it proves that the results in Pai’s paper are correct and reasonable.

Details

Grey Systems: Theory and Application, vol. 6 no. 2
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 7 November 2016

Kunli Wen

Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications, which include ordinal grey relational

Abstract

Purpose

Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications, which include ordinal grey relational grade and cardinal grey relational grade. However, the most original and important formula is Deng’s grey relational grade. After careful study it was found that although it is an ordinal form of grey relational grade, a rational mathematics model can be used to transfer it from ordinal into cardinal. It not only can enhance the essential of Deng’s grey relational grade, but also can let Deng’s grey relational grade be used more widely. The paper aims to discuss these issue.

Design/methodology/approach

The paper uses fuzzy set theory to get the rational value of distinguish coefficient in Deng’s grey relational grade, then uses grey entropy method to decide the rational weighting for the analysis sequences in Deng’s grey relational grade.

Findings

Through the mathematics derivation, it indeed can transfer the Deng’s grey relational grade from ordinal form into cardinal form.

Practical implications

The paper has deeply enhanced the essential of Deng’s grey relational grade, and made Deng’s grey relational grade more available and more usable in grey system theory.

Originality/value

The paper has transferred the Deng’s grey relational grade from ordinal into cardinal, it can let Deng’s grey relational grade be used in a wider area.

Details

Grey Systems: Theory and Application, vol. 6 no. 3
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 26 February 2021

Baohua Yang, Junming Jiang and Jinshuai Zhao

The purpose of this study is to construct a gray relational model based on information diffusion to avoid rank reversal when the available decision information is…

Abstract

Purpose

The purpose of this study is to construct a gray relational model based on information diffusion to avoid rank reversal when the available decision information is insufficient, or the decision objects vary.

Design/methodology/approach

Considering that the sample dependence of the ideal sequence selection in gray relational decision-making is based on case sampling, which causes the phenomenon of rank reversal, this study designs an ideal point diffusion method based on the development trend and distribution skewness of the sample information. In this method, a gray relational model for sample classification is constructed using a virtual-ideal sequence. Subsequently, an optimization model is established to obtain the criteria weights and classification radius values that minimize the deviation between the comprehensive relational degree of the classification object and the critical value.

Findings

The rank-reversal problem in gray relational models could drive decision-makers away from using this method. The results of this study demonstrate that the proposed gray relational model based on information diffusion and virtual-ideal sequencing can effectively avoid rank reversal. The method is applied to classify 31 brownfield redevelopment projects based on available interval gray information. The case analysis verifies the rationality and feasibility of the model.

Originality/value

This study proposes a robust method for ideal point choice when the decision information is limited or dynamic. This method can reduce the influence of ideal sequence changes in gray relational models on decision-making results considerably better than other approaches.

Details

Grey Systems: Theory and Application, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 2043-9377

Keywords

Content available
Article
Publication date: 22 October 2019

Li Xuemei, Yun Cao, Junjie Wang, Yaoguo Dang and Yin Kedong

Research on grey systems is becoming more sophisticated, and grey relational and prediction analyses are receiving close review worldwide. Particularly, the application of…

Abstract

Purpose

Research on grey systems is becoming more sophisticated, and grey relational and prediction analyses are receiving close review worldwide. Particularly, the application of grey systems in marine economics is gaining importance. The purpose of this paper is to summarize and review literature on grey models, providing new directions in their application in the marine economy.

Design/methodology/approach

This paper organized seminal studies on grey systems published by Chinese core journal database – CNKI, Web of Science and Elsevier from 1982 to 2018. After searching the aforementioned database for the said duration, the authors used the CiteSpace visualization tools to analyze them.

Findings

The authors sorted the studies according to their countries/regions, institutions, keywords and categories using the CiteSpace tool; analyzed current research characteristics on grey models; and discussed their possible applications in marine businesses, economy, scientific research and education, marine environment and disasters. Finally, the authors pointed out the development trend of grey models.

Originality/value

Although researches are combining grey theory with fractals, neural networks, fuzzy theory and other methods, the applications, in terms of scope, have still not met the demand. With the increasingly in-depth research in marine economics and management, international marine economic research has entered a new period of development. Grey theory will certainly attract scholars’ attention, and its role in marine economy and management will gain considerable significance.

Details

Marine Economics and Management, vol. 2 no. 2
Type: Research Article
ISSN: 2516-158X

Keywords

Content available
Article
Publication date: 14 August 2018

Xuemei Li, Ya Zhang and Kedong Yin

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models…

Abstract

Purpose

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Design/methodology/approach

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

Findings

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

Originality/value

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

Details

Marine Economics and Management, vol. 1 no. 1
Type: Research Article
ISSN: 2516-158X

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Article
Publication date: 29 July 2020

Xiumei Hao, Mingwei Li and Yuting Chen

This paper takes the seven overcapacity industries such as the textile industry, electricity and heat, steel, coal, automobile manufacturing, nonferrous metals and…

Abstract

Purpose

This paper takes the seven overcapacity industries such as the textile industry, electricity and heat, steel, coal, automobile manufacturing, nonferrous metals and petrochemical industry as research objects and proposes a TOPSIS grey relational projection group decision method with mixed multiattributes, which is used for the ranking of the seven industries with overcapacity and provided relevant departments with a basis for decision-making.

Design/methodology/approach

First, an evaluation index system from four aspects is established. Secondly, the attributes of linguistic information are converted into two-dimensional interval numbers and triangular fuzzy numbers, and an evaluation matrix is constructed and normalized. This paper uses the AHP method to determine the subjective weights and uses the coefficient of variation method to determine the objective weights. Moreover, this paper sets up the optimization model with the largest comprehensive evaluation value to determine the combined weights. Finally, the TOPSIS grey relational projection method is proposed to calculate the closeness of grey relational projections and to rank them.

Findings

This paper analyzes the problem of overcapacity in seven industries with the TOPSIS grey relational projection method. The results show that the four industries of automobile manufacturing, textile, coal and petrochemical are all in serious overcapacity levels, while the three industries of steel, nonferrous metals and electric power are relatively in weak overcapacity level in the three years of 2016–2018. TOPSIS grey relational projection method ranks the overcapacity degree of the seven major overcapacity industries, making the relative overcapacity degree of each industry more clear and providing a reference for the government to formulate targeted policies and measures for each industry.

Practical implications

By using TOPSIS grey relational projection method to evaluate the overcapacity of the seven major overcapacity industries, on the one hand, it makes the relative overcapacity degree of each industry more clear, on the other hand, it can provides the basis for the government and decision-making departments. This helps them promote better the healthy and orderly economic development of the seven major industries and avoid resource waste caused by overcapacity.

Originality/value

This article solves the single evaluation method caused by the limited indicators in the past, combines TOPSIS and the grey relational projection method and applies it to the overcapacity evaluation of the industry, not only applies it to the evaluation of overcapacity for the first time but also involves novel problems and methods, which expands the scope of application of the model.

Details

Grey Systems: Theory and Application, vol. 11 no. 2
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 5 January 2015

Xianlong Cao, Hongda Deng and Wei Lan

The purpose of this study was to evaluate the grey relational analysis method as a way of determining quickly the important factors affecting the atmospheric corrosion of…

Abstract

Purpose

The purpose of this study was to evaluate the grey relational analysis method as a way of determining quickly the important factors affecting the atmospheric corrosion of Q235 carbon steel in one year.

Design/methodology/approach

Atmospheric corrosion exposure tests on Q235 steel were carried out at seven typical test sites in China. The test period lasted one year. The corrosion rate of the Q235 test panels was determined using the weight-loss method and environmental factors were monitored and recorded by standard methods. The importance of the various environmental factors was evaluated using the grey relational analysis method.

Findings

The results obtained by the grey relational analysis method showed that the ranking order of factors affecting the corrosion of Q235 carbon steel from “slightly” to “severely” was as follows: relative humidity > dew days > SO3 > pH value of rain > rain precipitation > temperature > rainy days > Cl− > H2S > NO2. Furthermore, the initial atmospheric corrosion of Q235 carbon steel was recognized as being the corrosion of the smooth surface by water medium, or acidic aqueous solution.

Originality/value

Materials corrosion can be defined as a grey system because corrosion has a clear outcome and complex but uncertain characteristics. The grey relational analysis method, a part of grey system theory, is an effective and quick data processing method that can be used to sort out the degree of correlation of environmental factors affecting atmospheric corrosion in terms of it being a grey system with a lot uncertain information.

Details

Anti-Corrosion Methods and Materials, vol. 62 no. 1
Type: Research Article
ISSN: 0003-5599

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Article
Publication date: 23 August 2013

Li Hong‐jun, Hu Wei, Xie Zheng‐guang and Wang Wei

The paper aims to do some further research on grey relational analysis applied in wavelet transform, and proposed a grey relational threshold algorithm for image…

Abstract

Purpose

The paper aims to do some further research on grey relational analysis applied in wavelet transform, and proposed a grey relational threshold algorithm for image denoising. This study tries to suppress the noise while retaining the edges and important structures as much as possible.

Design/methodology/approach

The paper analyzed the characters of noises and edges distribution in different subbands; then used the grey relational value to calculate the relationship of scale, direction and noise deviation. This paper used the grey relational value of scale, direction and noise deviation as influenced factors, and proposed a grey relational threshold algorithm.

Findings

Grey relational analysis used in threshold setting has the superiority in image denoising. The simulation results have already certified both in visual effect and peak signal to noise ratio (PSNR).

Originality/value

This paper applied grey relation theory into image denoising, and proposed a grey relational threshold algorithm. It provides a novel method for image denoising.

Details

Grey Systems: Theory and Application, vol. 3 no. 2
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 17 August 2012

Sanjeev Goyal and Sandeep Grover

Advanced manufacturing system (AMS) offers opportunities for industries to improve their technology, flexibility and profitability through a highly efficient and focused…

Abstract

Purpose

Advanced manufacturing system (AMS) offers opportunities for industries to improve their technology, flexibility and profitability through a highly efficient and focused approach to manufacturing effectiveness. Selecting a proper AMS is a complicated task for the managers as it involves large tangible and intangible selection attributes. Failure to take right decision in selecting proper AMS alternative may even lead industry to losses. The purpose of this paper, therefore, is to rank the AMS alternatives by using fuzzy grey relational analysis, which will help managers when choosing an appropriate AMS.

Design/methodology/approach

This research proposes a multi‐attribute decision‐making (MADM) method, fuzzy grey relational analysis (FGRA), for AMS selection. The methodology is explained as follows. AMS alternatives and selection attributes will be chosen. The qualitative attributes will be converted into quantitative using fuzzy conversion scale. Then these data will be pre‐processed to normalize every value. This step is done to convert all alternatives into a comparability sequence. According to these sequences a reference sequence (ideal target sequence) is defined. Then, the grey relational coefficient between all comparability sequences and the reference sequence is calculated. Finally, based on these grey relational coefficients, the grey relational grade between the reference sequence and every comparability sequences is calculated. If a comparability sequence translated from an alternative has the highest grey relational grade between the reference sequence and itself, then that alternative will be the best choice. Fuzzy logic is used here to convert linguistic data into crisp score.

Findings

The proposed method is validated and compared by taking two examples from literature. The traditional statistical techniques require large data sets for evaluating attributes while grey theory on the contrary solve the multi attribute decision making problems with small data sets. This methodology will significantly increase the efficiency of decision making and overall competitiveness for manufacturing industries. This approach will motivate more and more industries to invest in AMS.

Practical implications

This method will help managers to weigh the AMS alternatives before actually buying them, which will in turn save money and time. This will build confidence of the top management for investing in costly technology such as AMS.

Originality/value

From time to time, various researchers have proposed various techniques to select the AMS. However, a survey on current evaluation methods shows that they are all less objective, lack accurate data processing, involve large calculations because of their complexity. In this paper, the authors attempt to solve the problem of AMS selection with FGRA, which is more logical, axiomatic, generates results in fewer steps with less calculations and is easy to understand. This paper succeeds in getting AMS alternatives' ranking using fuzzy grey relational analysis.

Details

Grey Systems: Theory and Application, vol. 2 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

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