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Article

Sifeng Liu, Handan Rui, Zhigeng Fang, Yingjie Yang and Jeffrey Forrest

The purpose of this paper is to present the terms of grey numbers and its operations.

Abstract

Purpose

The purpose of this paper is to present the terms of grey numbers and its operations.

Design/methodology/approach

The definitions of elementary terms about grey numbers and its operations are presented one by one.

Findings

The reader could know the basic explanation about the important terms about grey numbers and its operations from this paper.

Practical implications

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

Originality/value

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

Details

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

Keywords

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Article

Yingjie Yang and Si‐feng Liu

The purpose of this paper is to advance new rules about operations of grey numbers based on kernels and greyness and analyze the reliability of these new operations.

Abstract

Purpose

The purpose of this paper is to advance new rules about operations of grey numbers based on kernels and greyness and analyze the reliability of these new operations.

Design/methodology/approach

A grey number is usually represented as a closed interval or a discrete set of numbers. Based on the definition of traditional grey number, novel rules that grey numbers can be represented as their kernels and associated degrees of greyness are proposed. In new rules, the operation between kernels of grey numbers has significance in the application of grey numbers. The reliability of operations of grey numbers using their kernels and the degrees of greyness derived from kernel operations and their corresponding interval operations are studied.

Findings

The results show that the novel rules about operation of grey numbers satisfy to the concept of grey system properly. It is useful to calculate the grey degree of grey numbers and the process of calculating is easier than traditional operation rules.

Practical implications

The method exposed in the paper can be used to calculate each two grey numbers. The grey degree and the calculating results of two grey numbers can be given out easily. The method can also be used to calculate grey numbers more than two.

Originality/value

The paper succeeds in constructing novel operation rules of grey numbers. The reliability of novel operation rules is studied and it is new development of grey systems theory, undoubtedly.

Details

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

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Article

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

Y. Yang, R. John and S. Liu

The purpose of this paper is to advance new rules about operations of grey sets based on grey numbers and greyness and investigate their capability in reducing uncertainty.

Abstract

Purpose

The purpose of this paper is to advance new rules about operations of grey sets based on grey numbers and greyness and investigate their capability in reducing uncertainty.

Design/methodology/approach

A grey set can have its characteristic function values restricted by grey numbers, and such a representation makes the operations of grey sets different from other sets. Based on the concept of whitenisation of grey sets, two extended operations of grey sets are defined and their properties are discussed.

Findings

The result demonstrates that the proposed meet operation can significantly reduce uncertainty in grey sets and that the novel rules about operation of grey sets can reduce uncertainty of the set significantly. The propagation of uncertainty under different operations is investigated.

Practical implications

The method exposed in the paper can be used to integrate information from different sources to reduce uncertainty in information.

Originality/value

The paper succeeds in constructing novel operation rules of grey sets. The capability of novel operation rules to reduce uncertainty is studied and it is a new development of grey systems theory.

Details

Kybernetes, vol. 41 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

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Article

Sifeng Liu, Zhigeng Fang, Yingjie Yang and Jeffrey Forrest

The purpose of this paper is to advance new rules about operations of grey numbers.

Abstract

Purpose

The purpose of this paper is to advance new rules about operations of grey numbers.

Design/methodology/approach

The paper first puts forward the definitions of basic element of grey number and general grey number. The operation axiom, operation rules of general grey numbers and a new algebraic system for general grey numbers are built based on the “kernel” and the degree of greyness of grey numbers.

Findings

Up to now, the operation of general grey numbers has been transformed to operation of real numbers; thus, the difficult problem for set up operation of general grey numbers has been solved to a certain degree.

Practical implications

The method exposed in the paper can be used to integrate information from a different source. The operation of general grey numbers could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers. The operation system of general grey numbers also opened a new passageway for research on grey input‐output and grey programming, etc.

Originality/value

The new conception of a basic element of grey number and general grey number was given for the first time in this paper. The novel operation rules of general grey numbers were also constructed.

Details

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

Keywords

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Article

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

Keywords

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Article

Qiao‐Xing Li and Si‐Feng Liu

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of…

Abstract

Purpose

The purpose of this paper is to explain the connotation of grey number, which is the basic unit of grey mathematics and the key to establish the mathematic framework of grey system theory.

Design/methodology/approach

From the grey hazy set, the paper re‐defines grey number and the operation of greynumber element, then some properties are obtained. Based on them, the operation of grey‐matrix element is given. The general definition of grey function and its operation are also proposed.

Findings

The connotation of grey number is elaborated and the elementary framework of grey mathematics can be established.

Research limitations/implications

The researched object, objective and techniques of grey system theory have not been logically proposed and they may influence the comprehension of grey system theory. The obtained results of grey mathematics may significantly promote its development.

Practical implications

The paper can enable managers to control the complex system with missing information by using the quantitative approaches.

Originality/value

Grey mathematics may become a branch of mathematics to deal with proximate calculation.

Details

Kybernetes, vol. 38 no. 3/4
Type: Research Article
ISSN: 0368-492X

Keywords

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Article

Nai‐ming Xie

The purpose of this paper is to redefine the concept of grey number with information background and to propose novel grey number algorithms.

Abstract

Purpose

The purpose of this paper is to redefine the concept of grey number with information background and to propose novel grey number algorithms.

Design/methodology/approach

As the basic element of a grey system, grey number is defined as a number of which the true value is unknown because of the limited information while the boundary or possible value set can be known. Grey number algorithms are key points for constructing grey system models and helping to calculate model results. The concept of grey number is redefined with information background in this paper. Novel grey number algorithms are defined considering all the different forms of grey number information background. Several illustrative examples are applied to state the process of the proposed algorithms.

Findings

The results show that the novel grey number algorithms can do the operations well no matter what the grey number's type. It is useful to create effective grey system models and to do system analysis, forecasting, decision making and control in grey systems.

Practical implications

The method exposed in the paper can be used to calculate different grey numbers and used in constructing new grey models.

Originality/value

The paper succeeds in defining new grey number algorithm. The concept and its remarks of grey number are discussed. The novel algorithm can be used in creating new grey models and solve the modelling parameters in of grey systems theory undoubtedly.

Details

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

Keywords

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Article

Naiming Xie

The purpose of this paper is to combine the interval grey number algorithm with a project scheduling model, so as to solve the interval grey number based project…

Abstract

Purpose

The purpose of this paper is to combine the interval grey number algorithm with a project scheduling model, so as to solve the interval grey number based project scheduling problem.

Design/methodology/approach

According to the grey system theory, if we could not clearly collect the right value of an activity while obtaining the upper and lower boundaries of the activity duration time, we can find activity duration time as interval grey number. This paper tries to combine interval grey number with project scheduling problem. The general definition of interval grey number was given. And then the linear operations of independent interval grey number and non-independent interval grey number were further defined. Interval grey number based project scheduling model and its algorithm were further proposed. Finally, a numerical case was adopted to test the effectiveness of the proposed method.

Findings

The results show that grey project scheduling and grey critical path method could be established under interval grey number measured activities.

Practical implications

Scheduling problem was widely used in project planning and control. This manuscript attempted to combine interval grey number with project scheduling so as to explain the flexible deadline in a special project. It is truly in accordance with the requirements for real applications.

Originality/value

This paper proposed linear operations of independent and non-independent interval grey numbers, and proposed a interval grey number based project scheduling model. Valuable contribution is to combine interval grey numbers with project scheduling and it is meaningful to make a useful strategy in a flexible condition of project scheduling.

Details

Grey Systems: Theory and Application, vol. 8 no. 1
Type: Research Article
ISSN: 2043-9377

Keywords

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Article

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

Keywords

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