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Article
Publication date: 1 August 2016

Ye Li, Shanli Zhu and San-dang Guo

The purpose of this paper is to propose the grey target decision method based on three-parameter interval grey number for dealing with multi-attribute decision-making…

Abstract

Purpose

The purpose of this paper is to propose the grey target decision method based on three-parameter interval grey number for dealing with multi-attribute decision-making problems under uncertain environment.

Design/methodology/approach

First, the kernel and ranking method of three-parameter interval grey number are defined, which is the basis of determining the positive and negative bull’s-eye. Next, a new distance measure of three-parameter interval grey number is defined in view of the importance of the “center of gravity” point. Furthermore, a new comprehensive bull’s-eye distance is proposed based on the kernel which integrates the distance between different attributes to the positive and negative bull’s-eye. Then attribute weights are obtained by comprehensive bull’s-eye distance minimum and grey entropy maximization.

Findings

The paper provides a grey target decision method based on three-parameter interval grey number and example analysis shows that the method proposed in this paper is more reasonable and effective.

Research limitations/implications

If we have a better understanding of the distribution characteristics of three-parameter interval grey number, it is possible to have a more reasonable measure of the distance of three-parameter interval grey number.

Practical implications

The paper provides a grey target decision method, which can help decision maker deal with multi-attribute decision-making problems under uncertain environment.

Originality/value

This paper proposed the kernel and ranking method of three-parameter interval grey number, and defined a new distance measure of three-parameter interval grey number and proposed a new comprehensive bull’s-eye distance, Furthermore, this paper structured a grey target decision method based on three-parameter interval grey number.

Details

Grey Systems: Theory and Application, vol. 6 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 1 August 2006

Yaoguo Dang, Sifeng Liu and Chuanmin Mi

Based on the characteristics of interval number, the distance of interval number is defined. And based on the grey incidence degree theory, the degree of interval number

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Abstract

Purpose

Based on the characteristics of interval number, the distance of interval number is defined. And based on the grey incidence degree theory, the degree of interval number incidence is defined. These extend grey incidence analysis theory from real number sequence to interval number sequence.

Design/methodology/approach

Studies the multi‐attribute incidence decision‐making problems for interval number and models the incidence decision‐making model of multi‐attribute interval number.

Findings

An application example is given based on grey incidence decision model with multi‐attribute interval number.

Research limitations/implications

This new model can avoid the difficulty of seeking the dummy optimal scheme and the negative optimal scheme, and it regards evaluated scheme as a whole to seek the optimal scheme.

Practical implications

It is easy to realizing on computer and the evaluated result is more objective than the results obtained by other methods.

Originality/value

Studies multi‐attribute decision‐making problems.

Details

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

Keywords

Article
Publication date: 5 February 2018

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

Article
Publication date: 15 July 2021

Sandang Guo and Yaqian Jing

In order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati…

Abstract

Purpose

In order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati model (TGRM(1,1)) based on interval grey number sequences.

Design/methodology/approach

By combining grey Verhulst model and a special kind of Riccati equation and introducing a time-varying parameter and random disturbance term the authors advance a TGRM(1,1) based on interval grey number sequences. Additionally, interval grey number sequences are converted into middle value sequences and trapezoid area sequences by using geometric characteristics. Then the predicted formula is obtained by using differential equation principle. Finally, the proposed model's predictive effect is evaluated by three numerical examples of China's clean energy generation.

Findings

Based on the interval grey number sequences, the TGRM(1,1) is applied to predict the development trend of China's wind power generation, China's hydropower generation and China's nuclear power generation, respectively, to verify the effectiveness of the novel model. The results show that the proposed model has better simulated and predicted performance than compared models.

Practical implications

Due to the uncertain information and continuous changing of clean energy generation in the past decade, interval grey number sequences are introduced to characterize full information of the annual clean energy generation data. And the novel TGRM(1,1) is applied to predict upper and lower bound values of China's clean energy generation, which is significant to give directions for energy policy improvements and modifications.

Originality/value

The main contribution of this paper is to propose a novel TGRM(1,1) based on interval grey number sequences, which considers the changes of parameters over time by introducing a time-varying parameter and random disturbance term. In addition, the model introduces the Riccati equation into classic Verhulst, which has higher practicability and prediction accuracy.

Details

Grey Systems: Theory and Application, vol. 12 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: 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: 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: 11 June 2020

Ye Li, Sandang Guo and Juan Li

The purpose of this paper is to construct a prediction model of three-parameter interval grey number based on kernel and double information domains to expand the modeling…

Abstract

Purpose

The purpose of this paper is to construct a prediction model of three-parameter interval grey number based on kernel and double information domains to expand the modeling object of grey prediction model from interval grey number to three-parameter interval grey number.

Design/methodology/approach

First, the study decomposes the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point and defines the upper and lower information domains of the three-parameter interval grey number. Second, it calculates the kernel, the upper and lower information domains of the three-parameter interval grey number. Then, it constructs the prediction model for kernel sequence and upper and lower information domain sequences, respectively. By deducing the time response expressions of “center of gravity”, lower and upper limits of three-parameter interval grey number, a prediction model of three-parameter interval grey number based on kernel and double information domains is obtained.

Findings

This paper provides a prediction model of three-parameter interval grey number based on kernel and double information domains, and the example analysis shows that the method proposed in this paper has higher prediction accuracy and practicality.

Practical implications

In this paper, the modeling object of grey prediction model is extended to the three-parameter interval grey number, so it can be used for the prediction of uncertainty problems, such as stock changing trend, temperature and so on.

Originality/value

By decomposing the grey valued interval into upper and lower cells with the “center of gravity” as the dividing point, gives the definition of upper and lower information domains and then obtains a new method for whitening the three-parameter interval grey number.

Details

Grey Systems: Theory and Application, vol. 10 no. 4
Type: Research Article
ISSN: 2043-9377

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: 4 September 2018

Ye Li and Dongxing Zhang

The purpose of this paper is to propose a dynamic multi-attribute decision-making method based on the prospect theory for dealing with the dynamic multi-attribute…

Abstract

Purpose

The purpose of this paper is to propose a dynamic multi-attribute decision-making method based on the prospect theory for dealing with the dynamic multi-attribute decision-making problem with three-parameter interval grey number.

Design/methodology/approach

First, the kernel and comparison rule of three-parameter interval grey numbers are defined, which are the basis of collecting and sorting grey numbers. Next, the prospect value function is determined in view of the decision-making information with different time points as the reference points. Then, an optimal model for solving the attribute weight and time weight is constructed based on the grey entropy principle.

Findings

The paper provides a dynamic grey interrelation decision method based on the prospect theory with three-parameter interval grey number, and the example analysis shows that the method proposed in this paper has validity and rationality.

Research limitations/implications

If we have a better understanding of the weights of different reference points, it is possible to receive a more reasonable expression for the comprehensive prospect utility value function.

Practical implications

The paper provides a grey interrelation decision method based on the prospect theory, which can help the decision maker deal with the dynamic multi-attribute decision-making problems under the uncertain environment.

Originality/value

The paper proposes the kernel and ranking method of three-parameter interval grey number, and uses different time points as the reference points to define the prospect value function. Furthermore, this paper structures a dynamic grey interrelation decision method with three-parameter interval grey number based on the prospect theory.

Details

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

Keywords

1 – 10 of over 41000