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Article
Publication date: 26 October 2012

Sifeng Liu, Zhigeng Fang, Yingjie Yang and Jeffrey Forrest

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

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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

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.

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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

Article
Publication date: 7 November 2016

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

Article
Publication date: 18 September 2019

Davood Darvishi, Jeffrey Forrest and Sifeng Liu

Ranking and comparing grey numbers represent a very important decision-making procedure in any given grey environment. The purpose of this paper is to study the existing…

Abstract

Purpose

Ranking and comparing grey numbers represent a very important decision-making procedure in any given grey environment. The purpose of this paper is to study the existing approaches of ordering interval grey numbers in the context of decision making by surveying existing definitions.

Design/methodology/approach

Different methods developed for comparing grey numbers are presented along with their disadvantages and advantages in terms of comparison outcomes. Practical examples are employed to show the importance and necessity of using appropriate methods to compare grey numbers.

Findings

Most the available methods are not suitable for pointing out which number is larger when the nuclei of the grey numbers of concern are the same. Also, these available methods are also considered in terms of partial order and total order. Kernel and degree of greyness of grey numbers method is more advantageous than other methods and almost eliminates the shortcomings of other methods.

Originality/value

Different methods for ranking grey numbers are presented where each of them has disadvantages and advantages. By using different methods, grey interval numbers are compared and the results show that some methods cannot make grey number comparisons in some situations. The authors intend to find a method that can compare grey numbers in any situation. The findings of this research can prevent errors that may occur based on inaccurate comparisons of grey numbers in decision making. There are various research studies on the comparison of grey numbers, but there is no research on the comparison of these methods and their disadvantages, advantages or their total or partial order.

Details

Grey Systems: Theory and Application, vol. 9 no. 4
Type: Research Article
ISSN: 2043-9377

Keywords

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…

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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

Keywords

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

Article
Publication date: 28 January 2011

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

Keywords

Article
Publication date: 29 July 2014

Naiming Xie and Jianghui Xin

The purpose of this paper is to study a novel grey possibility degree approach, which is combined with multi-attribute decision making (MADM) and applied MADM model for…

Abstract

Purpose

The purpose of this paper is to study a novel grey possibility degree approach, which is combined with multi-attribute decision making (MADM) and applied MADM model for solving supplier selection problem under uncertainty information.

Design/methodology/approach

The supplier selection problem is a typical MADM problem, in which information of a series of indexes should be aggregated. However, it is relatively easy for decision makers to define information in uncertainty, sometimes as a grey number, rather than a precise number. By transforming linguistic scale of rating supplier selection attributes into interval grey numbers, a novel grey MADM method is developed. Steps of proposed model were provided, and a novel grey possibility degree approach was proposed. Finally, a numerical example of supplier selection is utilized to demonstrate the proposed approach.

Findings

The results show that the proposed approach could solve the uncertainty decision-making problem. A numerical example of supplier selection is utilized to demonstrate the proposed approach. The results show that the proposed method is useful to aggregate decision makers’ information so as to select the potential supplier.

Practical implications

The approach constructed in the paper can be used to solving uncertainty decision-making problems that the certain value of the decision information could not collect while the interval value set could be defined. Obviously it can be utilized for other MADM problem.

Originality/value

The paper succeeded in redefining interval grey number, constructing a novel interval grey number based MADM approach and providing the solution of the proposed approach. It is very useful to solving system forecasting problem and it contributed undoubtedly to improve grey decision-making models.

Details

Kybernetes, vol. 43 no. 7
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 7 August 2017

Jing Ye and Yaoguo Dang

Nowadays, evaluation objects are becoming more and more complicated. The interval grey numbers can be used to more accurately express the evaluation objects. However, the…

Abstract

Purpose

Nowadays, evaluation objects are becoming more and more complicated. The interval grey numbers can be used to more accurately express the evaluation objects. However, the information distribution of interval grey numbers is not balanced. The purpose of this paper is to introduce the central-point triangular whitenization weight function to solve the clustering process of this kind of numbers.

Design/methodology/approach

A new expression of the central-point triangular whitenization weight function is presented in this paper, in terms of the grey cluster problem based on interval grey numbers. By establishing the integral mean value function on the set of interval grey numbers, the application range of grey clustering model is extended to the interval grey number category, and, in this way, the grey fixed weight cluster model based on interval grey numbers is obtained.

Findings

The model is verified by a case which reveals a high distinguishability, validity and practicability.

Practical implications

This model can be used in many fields, such as agriculture, economy, geology and medical science, and provides a feasible method for evaluation schemes in performance evaluation, scheme selection, risk evaluation and so on.

Originality/value

The central-point triangular whitenization weight function is introduced. The method reflects the thought “make full use of the information” in grey system theory and further enriches the system of grey clustering theory as well as expands the application scope of the grey clustering method.

Details

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

Keywords

Article
Publication date: 23 August 2013

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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