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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: 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: 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: 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: 3 April 2018

Rafal Mierzwiak, Naiming Xie and Marcin Nowak

Considering current development of Grey Systems Theory (GST), we can come up with the following thesis: practical applications are a dominant subject of research. Thus…

Abstract

Purpose

Considering current development of Grey Systems Theory (GST), we can come up with the following thesis: practical applications are a dominant subject of research. Thus, what seems to be symptomatic for relatively young knowledge disciplines, the authors observe the presence of imbalance between the development of GST application tools and theory’s epistemological and methodological background. As for GST, epistemological and methodological problems are becoming visible especially in the issues of determining a clear criterion of demarcation of this kind of a theory from others. In other words, this problem can be reduced to the issue of a precise determination of what the category of a grey system and grey information is. This problem is of great importance for further development and popularisation of GST in the world of science. Realising its significance, the purpose of this paper is to create a general overview of Grey Systems epistemology and afterwards create axiomatic and formal frames for a category of greyness.

Design/methodology/approach

In order to achieve set goals, two research approaches were accepted. In the area of inference about epistemology of GST an approach characteristic of an analytical philosophy was used, whereas in the case of axiomatic and formal frames for a category of greyness the authors referred to terms of a set theory and the principles of a pragmatic logic.

Findings

The result of research is to formulate a concept of a grey system and a concept of grey information in the context of a process of cognition. Moreover, a function of greyness and other fundamental categories of GST will be defined in an axiomatic way.

Originality/value

The paper presents a new consistent frame for the issues of methodological and epistemological backgrounds of GST. An original concept is to refer in considerations to a newly proposed grey space. This space was used for a formal justification of such elementary categories as grey numbers, a weight function of whitenization or grey sequences. The value of achievements shown in the paper is underlined by the fact that proposed theoretical constructions require further development and they can potentially open up new research trends in the GST.

Details

Grey Systems: Theory and Application, vol. 8 no. 2
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

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Article
Publication date: 14 June 2019

Pingping Xiong, Zhiqing He, Shiting Chen and Mao Peng

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to…

Abstract

Purpose

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods.

Design/methodology/approach

This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness.

Findings

To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy.

Originality/value

This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

Details

Kybernetes, vol. 49 no. 3
Type: Research Article
ISSN: 0368-492X

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Article
Publication date: 20 August 2018

Wenjie Dong, Sifeng Liu and Zhigeng Fang

The purpose of this paper is to study the modelling mechanisms of several grey incidence analysis models with great influence, including Deng’s grey incidence model…

Abstract

Purpose

The purpose of this paper is to study the modelling mechanisms of several grey incidence analysis models with great influence, including Deng’s grey incidence model, absolute degree of grey incidence model, slope degree of incidence model, similitude degree of incidence model and closeness degree of incidence model; then analyse the problems to be solved in grey incidence analysis models; and clarify the applicable ranges of commonly used grey incidence models.

Design/methodology/approach

The paper comes to conclusions by means of comparable analysis. The authors compare several commonly used grey incidence analysis models, including Deng’s grey incidence model, absolute degree of grey incidence model, slope degree of incidence model, similitude degree of incidence model and closeness degree of incidence model and give several examples to clarify the reasons why quantitative analysis results of different models are not exactly the same.

Findings

As the intension of each kind of incidence model is clear and the extension is relatively obscure, grey incidence orders calculated by different incidence models are often different. When making actual decisions, incompatible results may appear. According to different characteristics of extraction, grey incidence analysis models can be divided into three types: incidence model based on closeness perspective, incidence model based on similarity perspective and incidence model based on comprehensive perspective.

Practical implications

The conclusions obtained in this paper can help people avoid some defects in the process of actual selection and choose the better incidence analysis model.

Originality/value

The conclusions can be used as a reference and basis for the selection of grey incidence analysis models, it can help to overcome the defects and shortcomings of models caused by themselves and screen out more excellent analytical models.

Details

Grey Systems: Theory and Application, vol. 8 no. 4
Type: Research Article
ISSN: 2043-9377

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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: 16 July 2019

Yong Liu, Jun-liang Du, Ren-Shi Zhang and Jeffrey Yi-Lin Forrest

This paper aims to establish a novel three-way decisions-based grey incidence analysis clustering approach and exploit it to extract information and rules implied in panel data.

Abstract

Purpose

This paper aims to establish a novel three-way decisions-based grey incidence analysis clustering approach and exploit it to extract information and rules implied in panel data.

Design/methodology/approach

Because of taking on the spatiotemporal characteristics, panel data can well-describe and depict the systematic and dynamic of the decision objects. However, it is difficult for traditional panel data analysis methods to efficiently extract information and rules implied in panel data. To effectively deal with panel data clustering problem, according to the spatiotemporal characteristics of panel data, from the three dimensions of absolute amount level, increasing amount level and volatility level, the authors define the conception of the comprehensive distance between decision objects, and then construct a novel grey incidence analysis clustering approach for panel data and study its computing mechanism of threshold value by exploiting the thought and method of three-way decisions; finally, the authors take a case of the clustering problems on the regional high-tech industrialization in China to illustrate the validity and rationality of the proposed model.

Findings

The results show that the proposed model can objectively determine the threshold value of clustering and achieve the extraction of information and rules inherent in the data panel.

Practical implications

The novel model proposed in the paper can well-describe and resolve panel data clustering problem and efficiently extract information and rules implied in panel data.

Originality/value

The proposed model can deal with panel data clustering problem and realize the extraction of information and rules inherent in the data panel.

Details

Kybernetes, vol. 48 no. 9
Type: Research Article
ISSN: 0368-492X

Keywords

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