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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

Keywords

Article
Publication date: 10 April 2009

Qiao‐Xing Li and Si‐Feng Liu

The purpose of this paper is to propose the input‐occupancy‐output analysis for grey situations and to manage the economic systems with missing information. The situation is…

376

Abstract

Purpose

The purpose of this paper is to propose the input‐occupancy‐output analysis for grey situations and to manage the economic systems with missing information. The situation is realistic in practice.

Design/methodology/approach

During the decision‐making process of an economic system, the managers often get some uncertain data for the missing information. Then, it becomes difficult to analyze the complex system by using the input‐occupancy‐output analysis. Since the uncertain data are grey numbers, the decision maker can control it by using grey system theory and the input‐occupancy‐output analysis.

Findings

Get the grey direct consumption and occupancy coefficient matrices and the computational formulas of their matrix‐covered sets. The grey model of input‐occupancy‐output analysis and its covered solution are also obtained.

Research limitations/implications

The chaos of the grey statistic data should satisfy a level of accuracy and it is key to get the number‐covered set that the true data belongs to.

Practical implications

A feasible approach to control the economic system that the accurate data are difficult to be obtained.

Originality/value

Give a new approach to study an economic system by using grey system theory.

Details

Kybernetes, vol. 38 no. 3/4
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: 2 November 2015

Si-feng Liu, Yingjie Yang, Zhi-geng Fang and Naiming Xie

The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster…

Abstract

Purpose

The purpose of this paper is to present two novel grey cluster evaluation models to solve the difficulty in extending the bounds of each clustering index of grey cluster evaluation models.

Design/methodology/approach

In this paper, the triangular whitenization weight function corresponding to class 1 is changed to a whitenization weight function of its lower measures, and the triangular whitenization weight function corresponding to class s is changed to a whitenization weight function of its upper measures. The difficulty in extending the bound of each clustering indicator is solved with this improvement.

Findings

The findings of this paper are the novel grey cluster evaluation models based on mixed centre-point triangular whitenization weight functions and the novel grey cluster evaluation models based on mixed end-point triangular whitenization weight functions.

Practical implications

A practical evaluation and decision problem for some projects in a university has been studied using the new triangular whitenization weight function.

Originality/value

Particularly, compared with grey variable weight clustering model and grey fixed weight clustering model, the grey cluster evaluation model using whitenization weight function is more suitable to be used to solve the problem of poor information clustering evaluation. The grey cluster evaluation model using endpoint triangular whitenization weight functions is suitable for the situation that all grey boundary is clear, but the most likely points belonging to each grey class are unknown; the grey cluster evaluation model using centre-point triangular whitenization weight functions is suitable for those problems where it is easier to judge the most likely points belonging to each grey class, but the grey boundary is not clear.

Details

Grey Systems: Theory and Application, vol. 5 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 10 April 2009

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 grey…

565

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 grey‐number 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

Article
Publication date: 28 January 2011

Si‐feng Liu, Nai‐ming Xie and Jeffrey Forrest

The purpose of this paper is to solve the problems existing in traditional grey incidence models and advance several new grey incidence models based on visual angle of similarity…

2570

Abstract

Purpose

The purpose of this paper is to solve the problems existing in traditional grey incidence models and advance several new grey incidence models based on visual angle of similarity and nearness.

Design/methodology/approach

Based on the definition of traditional grey incidence models, two novel grey incidence models, grey similar incidence model and grey close incidence model, are studied in this paper. The interrelations and influence can be measured by the new models with different visual angle of similarity and/or nearness, respectively. The grey similar incidence model is used mainly to measure the similitude degree of the geometric patterns of sequence curves. The grey close incidence model is used mainly to measure the nearness of the sequence curves in space. The properties of the new models are discussed. It is proved that the proposed models are simplified methods to calculate the similitude degree and the close degree of grey incidence models.

Findings

The results show that the two novel grey incidence models satisfy the grey incidence axiom properly. It is useful to calculate the similitude degree and the close degree of two different sequences, and the process of calculating is easier than with traditional grey incidence models.

Practical implications

The method exposed in the paper can be used to calculate every two sequences. The similitude degree and the close degree of two different sequences can be given out. The method can also be used to rank sequences of more than two.

Originality/value

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

Details

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

Keywords

Article
Publication date: 16 October 2009

Nai‐Ming Xie and Si‐Feng Liu

The purpose of this paper is to study the parameters' properties of GM(n, h) model on the basis of multiple transformation and the relationship of GM(n, h) model and other grey…

118

Abstract

Purpose

The purpose of this paper is to study the parameters' properties of GM(n, h) model on the basis of multiple transformation and the relationship of GM(n, h) model and other grey models.

Design/methodology/approach

Multiple transformation property of parameters is important to construct a grey model. However, there is no research on the property of GM(n, h) model, therefore it is meaningful to study the relationship between GM(n, h) model and other grey models.

Findings

The multiple transformation property of parameters of GM(n, h) model is recognized. The parameters' value is dependent on multiple transformation value. The values of simulative and predicative are only dependent to the multiple transformation of the main variable and independent to other variables.

Research limitations/implications

The properties of other grey models could be obtained by analyzing the property of GM(n, h) model.

Practical implications

It is a very useful result for constructing a grey model.

Originality/value

This paper discusses multiple transformation property of GM(n, h) model and the relationship between the GM(n, h) model and other grey models. These grey models are put into a common model and the affections that parameters' multiple transformation caused to the model are studied.

Details

Kybernetes, vol. 38 no. 10
Type: Research Article
ISSN: 0368-492X

Keywords

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 which the…

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

Keywords

Article
Publication date: 1 August 2006

Zhi‐geng Fang, Si‐feng Liu, Aiqing Ruan and Xuewei Zhang

A study is made of the payoff matrix which is made up of grey interval number because of asymmetry information, player's finite knowledge and bounded rationality and all sorts of…

Abstract

Purpose

A study is made of the payoff matrix which is made up of grey interval number because of asymmetry information, player's finite knowledge and bounded rationality and all sorts of stochastic and non‐stochastic factors.

Design/methodology/approach

On the base of concept of equipollent, superior and inferior potential degree, the paper designs determinant rules of interval grey number potential relations, opens out player's decision‐making laws in the conditions of finite knowledge and logos. And it designs the grey game decision‐making rules which player choices maximum potential degree of grey game value (the most favorableness situation) under the cases of that there are all likely to be minimum potential degree of grey game value (the most disadvantage situation), which is a reliable way for both sides to accept.

Findings

The paper recognizes and defines overrated and underrated risk of potential optimal pure strategy in the grey game, designs arithmetic for determining player's overrated and underrated risk under the situation of potential optimal pure strategy.

Practical implications

The presents system meets the requirement of judging pure strategy solutions in the grey potential situation.

Originality/value

This paper builds up the system of judgment for grey potential.

Details

Kybernetes, vol. 35 no. 7/8
Type: Research Article
ISSN: 0368-492X

Keywords

Content available
Article
Publication date: 17 August 2012

412

Abstract

Details

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

1 – 10 of 18