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Article
Publication date: 7 August 2017

San-dang Guo, Sifeng Liu and Zhigeng Fang

The purpose of this paper is to establish the algorithm rules of the interval grey numbers and propose a new ranking method of the interval grey numbers.

Abstract

Purpose

The purpose of this paper is to establish the algorithm rules of the interval grey numbers and propose a new ranking method of the interval grey numbers.

Design/methodology/approach

The definitions of “kernels” based on lower measure, upper measure or moderate measure are given according to the properties of the interval grey number problems. By means of the measurement error, the concept of the absolute degree of greyness and the relative degree of greyness corresponding to different “kernel” are given, and different simplified forms of the interval grey numbers are put forward.

Findings

The definitions of “kernel” and the degree of greyness in this paper not only take the upper limit, lower limit and the coverage of the interval grey numbers into account, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse.

Research limitations/implications

Though the method proposed in this paper has some deficiencies, such as the definition of relative degree of greyness is meaningless when the kernel of the interval grey number is 0, it provides a new idea for calculating and sorting the interval grey numbers and is conducive to the further development of the grey system theory.

Originality/value

The method proposed in this paper can not only distinguish interval grey numbers in different situations, but also avoid the inconsistency of the degree of greyness caused by the different universe of discourse. In this basis, the interval grey number algorithm is established and a new ranking method of interval grey numbers is given.

Details

Grey Systems: Theory and Application, vol. 7 no. 2
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 22 December 2020

Jia Shi, Pingping Xiong, Yingjie Yang and Beichen Quan

Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

Abstract

Purpose

Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

Design/methodology/approach

This paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.

Findings

In order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.

Practical implications

The proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.

Originality/value

Based on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

Details

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

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Article
Publication date: 26 May 2020

Rafał Mierzwiak, Marcin Nowak and Naiming Xie

The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The

Abstract

Purpose

The degree of greyness may be regarded as a measure of cognitive uncertainty. Therefore, it is a part of the epistemological core of the grey systems theory. The theoretical importance of the degree of greyness concept is also due to its application in a range of uncertainty modelling methods: predictive, relational and decision-making methods. Greyness, being a result of cognitive uncertainty, was recently subjected to axiomatization in the form of grey space with the use of the classical sets theory. The purpose of this article is to develop a new approach to the degree of greyness, being consistent with the grey space concept.

Design/methodology/approach

In order to realise the article’s goals, the research is divided into three stages described in particular sections. The first section of the article presents a theoretical framework of the degree of greyness and the grey space. The second part includes the assumptions of the new degree of greyness concept, along with the mathematical models for the first, the second and the third degree of greyness. The third section contains numerical examples for each degree of greyness.

Findings

As a result of the research, a concept of a degree of greyness was created and it was linked with a concept of grey space. This new approach to the issue of the degree of greyness has allowed the analysing of this category in three dimensions dependent on an accepted reference base. As a result, a concept of concrete and abstractive grey numbers was introduced and relationships between these categories of numbers and the degree of greyness were determined.

Originality/value

The proposed approach to the issue of the degree of greyness is a theoretical unification of the previous considerations in this area. The proposed three dimensions of greyness degree will be derived from the grey space, so they will also be a function of quantity. Thus, the degree of greyness was linked with a classical set theory. An original input in this article is also a differentiation of concrete and abstractive grey numbers, which give a basis for deliberations connected with interpretation of grey numbers in the context of real applications.

Details

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

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Article
Publication date: 24 September 2019

Shuaishuai Geng, Yu Feng, Yaoguo Dang, Junjie Wang and Rizwan Rasheed

This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness

Abstract

Purpose

This paper aims to propose an enhanced algorithm and used to decision-making that specifically focuses on the choice of a domain in the calculation of degree of greyness according to the principle of grey numbers operation. The domain means the emerging background of interval grey numbers, it is vital for the operational mechanism of such interval grey numbers. However, the criteria of selection of domain always remain same that is not only for the calculated grey numbers but also for the resultant grey numbers, which can be assumed as unrealistic up to a certain extent.

Design/methodology/approach

The existence of interval grey number operation based on kernel and the degree of greyness containing two calculation aspects, which are kernel and the degree of greyness. For the degree of greyness, it includes concepts of domain and calculation of the domain. The concepts of a domain are defined. The enhanced algorithm is also comprised of four deductive theorems and eight rules that are linked to the properties of the enhanced algorithm of the interval grey numbers based on the kernel and the degree of greyness.

Findings

Aiming to improve the algorithm of the degree of greyness for interval grey numbers, based on the variation of domain in the operation process, the degree of greyness of the operation result is defined in this paper, and the specific expressions for algebraic operations are given, which is relevant to the kernel, the degree of greyness and the domain. Then, these expressions are used to the algorithm of interval grey numbers based on the kernel and the degree of greyness, improving the accuracy of the operation results.

Originality/value

The enhanced algorithm in this paper can effectively reduce the loss of information in the operation process, so as to avoid the situation where the decision values are the same and scientific decisions cannot be made during the grey evaluation and decision-making process.

Details

Kybernetes, vol. 49 no. 6
Type: Research Article
ISSN: 0368-492X

Keywords

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Article
Publication date: 1 February 2013

Zheng‐Xin Wang

The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Abstract

Purpose

The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Design/methodology/approach

Based on the axiomatic definition of a grey number and its greyness degree in grey system theory, the whitenization mean, whitenization difference, whitenization covariance of sequences with interval grey numbers and their greyness degrees are defined in turn. In addition, the whitenization correlation coefficient and its greyness degree of sequences with interval grey numbers are also defined. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenization value and greyness degree of correlation coefficient to form of interval grey numbers are put forward further.

Findings

The whitenization value of correlation coefficient efficient of two arbitrary sequences with interval grey numbers have symmetry, with same greyness degree but without normalization in the interval [−1, 1]; the mean, difference, covariance and correlation coefficient defined in statistics are all the special cases of those in sequences with interval grey numbers.

Research limitations/implications

Due to the complexity of operation of grey numbers, the reliability of correlation coefficient of interval numbers sequence is difficult to be tested by constructing statistics at present. The further research is needed.

Practical implications

The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.

Originality/value

On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.

Details

Kybernetes, vol. 42 no. 2
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 6 February 2017

Wenxin Mao, Dang Luo and Huifang Sun

The purpose of this paper is to propose a multi-scale extended grey target decision method for dealing with multi-attribute decision-making problems with interval grey…

Abstract

Purpose

The purpose of this paper is to propose a multi-scale extended grey target decision method for dealing with multi-attribute decision-making problems with interval grey numbers whose value distribution information is asymmetrical.

Design/methodology/approach

First, the whitenization weight function (WWF) was adopted to show the value distribution information of interval grey numbers. The definitions of kernel, degree of greyness, relative kernel and whitenization standard deviation of interval grey numbers were given based on the WWF. Then, the relative kernel grey target and whitenization standard deviation grey target were constructed to take full advantage of the owned decision information. Finally, the relative bull’s-eye coefficient was proposed to rank the preference order of all alternatives.

Findings

The relative bull’s-eye coefficient reflects the influence of the decision information on decision results with respect to the mean level and value distribution of attribute values. Thus, the decision-maker could set the return and risk adjustment coefficient according to their preferences and select the optimal alternative with a high expected return and low risk.

Originality/value

The paper considers the valve distribution information of interval grey numbers, and a novel definition for kernels, degrees of greyness, relative kernels and whitenization standard deviations, which are given based on the WWF. The paper not only considers the influence of mean levels of decision information over decision results, but also takes the value distribution information into account.

Details

Grey Systems: Theory and Application, vol. 7 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

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Article
Publication date: 6 November 2017

Shi-quan Jiang, Si-feng Liu, Zhi-geng Fang and Zhong-xia Liu

The purpose of this paper is to study distance measuring and sorting method of general grey number.

Abstract

Purpose

The purpose of this paper is to study distance measuring and sorting method of general grey number.

Design/methodology/approach

First, the concept of generalised grey number based on grey system theory is given in this paper. Second, from the perspective of kernel and degree of greyness of general grey number, the method of measuring the distance of general grey number and its properties are given. At the same time, the concepts of the kernel expectation and the kernel variance of the general grey number are proposed.

Findings

Up to now, the method of measuring the distance and sorting of general grey number is established. Thus, the difficult problem for set up sorting of general grey number has been solved to a certain degree.

Research limitations/implications

The method exposed in this paper can be used to integrate information form a different source. Distance measuring and sorting method of general grey number could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers, etc.

Originality/value

The concepts of the kernel expectation and the kernel variance of the general grey number are proposed for the first time in this paper; the novel sorting rules of general grey numbers were also constructed.

Details

Grey Systems: Theory and Application, vol. 7 no. 3
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 1 February 2016

Sifeng Liu, Yingjie Yang, Naiming Xie and Jeffrey Forrest

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new…

Abstract

Purpose

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

Design/methodology/approach

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

Findings

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

Practical implications

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

Originality/value

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

Details

Grey Systems: Theory and Application, vol. 6 no. 1
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 17 September 2018

Lili Qian, Sifeng Liu and Zhigeng Fang

The purpose of this paper is to advance a new grey risky multi-attribute decision-making (RMADM) method from the perspective of regret aversion, which is based on the

Abstract

Purpose

The purpose of this paper is to advance a new grey risky multi-attribute decision-making (RMADM) method from the perspective of regret aversion, which is based on the general grey numbers (GGNs) taking the form of kernel and degree of greyness.

Design/methodology/approach

First, the normalised grey decision-making matrix is obtained on the basis of kernel and greyness degree of GGNs. Then the regret theory is integrated into the decision-making process by constructing the grey perceived utility function based on GGNs. Finally, the method of evaluation based on distance from average solution (EDAS) is applied to handle with the ranking problem because of its efficiency, stability as well as simplicity.

Findings

GGNs have more powerful capacity in expressing uncertainty than interval grey numbers, so the method can solve a larger number of RMADM problems in uncertain and imprecise environments. Meanwhile, the method fully considers the psychological behaviour of the decision makers, which is more applicable to the real world. It is the supplement and perfection of the existing RMADM methods.

Originality/value

The RMADM problem, the grey regret-rejoice function and the EDAS method are all introduced for the first time with GGNs in the form of kernel and degree of greyness. At the same time, the EDAS method is also the first time to be used in combination with the grey RMADM method based on the regret theory.

Details

Grey Systems: Theory and Application, vol. 9 no. 1
Type: Research Article
ISSN: 2043-9377

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Article
Publication date: 28 October 2014

Tooraj Karimi and Jeffrey Forrest

The purpose of this paper is to analyse the results of energy audit reports and defines most favourable characteristics of system, which is energy consumption of

Abstract

Purpose

The purpose of this paper is to analyse the results of energy audit reports and defines most favourable characteristics of system, which is energy consumption of buildings, and most favourable factors affecting these characteristics in order to modify and improve them.

Design/methodology/approach

Grey set theory has the advantage of using fewer data to analyse many factors, and it is therefore more appropriate for system study rather than traditional statistical regression which requires massive data, normal distribution in the data and few variant factors. So, in this paper grey clustering and entropy of coefficient vector of grey evaluations are used to analyse energy consumption in buildings of the Oil Ministry in Tehran. Grey clustering in this study has been used for two purposes: First, all the variables of building relate to energy audit cluster in two main groups of indicators and the number of variables is reduced. Second, grey clustering with variable weights has been used to classify all buildings in three categories named “no standard deviation”, “low standard deviation” and “non-standard”. Entropy of coefficient vector of grey evaluations is calculated to investigate greyness of results.

Findings

According to the results of the model, “the real building load coefficient” has been selected as the most important system characteristic and “uncontrolled area of the building” has been diagnosed as the most favourable factor which has the greatest effect on energy consumption of building.

Research limitations/implications

Clustering greyness of 13 buildings is less than 0.5 and average uncertainly of clustering results is 66 per cent.

Practical implications

It shows that among the 38 buildings surveyed in terms of energy consumption, three cases are in standard group, 24 cases are in “low standard deviation” group and 11 buildings are completely non-standard.

Originality/value

In this research, a comprehensive analysis of the audit reports is proposed. This analysis helps the improvement of future audits, and assists in making energy conservation policies by studying the behaviour of system characteristic and related factors.

Details

Grey Systems: Theory and Application, vol. 4 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

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