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Article
Publication date: 13 April 2021

Shuliang Li, Ke Gong, Bo Zeng, Wenhao Zhou, Zhouyi Zhang, Aixing Li and Li Zhang

The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to…

Abstract

Purpose

The purpose of this paper is to overcome the weakness of the traditional model, in which the grey action quantity is a real number and thus leads to a “unique solution” and to build the model with a trapezoidal possibility degree function.

Design/methodology/approach

Using the system input and output block diagram of the model, the interval grey action quantity is restored under the condition of insufficient system influencing factors, and the trapezoidal possibility degree function is formed. Based on that, a new model able to output non-unique solutions is constructed.

Findings

The model satisfies the non-unique solution principle of the grey theory under the condition of insufficient information. The model is compatible with the traditional model in structure and modelling results. The validity and practicability of the new model are verified by applying it in simulating the ecological environment water consumption in the Yangtze River basin.

Practical implications

In this study, the interval grey number form of grey action quantity is restored under the condition of insufficient system influencing factors, and the unique solution to the problem of the traditional model is solved. It is of great value in enriching the theoretical system of grey prediction models.

Social implications

Taking power consumption as an example, the accurate prediction of the future power consumption level is related to the utilization efficiency of the power infrastructure investment. If the prediction of the power consumption level is too low, it will lead to the insufficient construction of the power infrastructure and the frequent occurrence of “power shortage” in the power industry. If the prediction is too high, it will lead to excessive investment in the power infrastructure. As a result, the overall surplus of power supply will lead to relatively low operation efficiency. Therefore, building an appropriate model for the correct interval prediction is a better way to solve such problems. The model proposed in this study is an effective one to solve such problems.

Originality/value

A new grey prediction model with its interval grey action quantity based on the trapezoidal possibility degree function is proposed for the first time.

Details

Grey Systems: Theory and Application, vol. 12 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 22 December 2020

Jia Shi, Pingping Xiong, Yingjie Yang and Beichen Quan

Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

Abstract

Purpose

Smog seriously affects the ecological environment and poses a threat to public health. Therefore, smog control has become a key task in China, which requires reliable prediction.

Design/methodology/approach

This paper establishes a novel time-lag GM(1,N) model based on interval grey number sequences. Firstly, calculating kernel and degree of greyness of the interval grey number sequence respectively. Then, establishing the time-lag GM(1,N) model of kernel and degree of greyness sequences respectively to obtain their values after determining the time-lag parameters of two models. Finally, the upper and lower bounds of interval grey number sequences are obtained by restoring the values of kernel and degree of greyness.

Findings

In order to verify the validity and practicability of the model, the monthly concentrations of PM2.5, SO2 and NO2 in Beijing during August 2017 to September 2018 are selected to establish the time-lag GM(1,3) model for kernel and degree of greyness sequences respectively. Compared with three existing models, the proposed model in this paper has better simulation accuracy. Therefore, the novel model is applied to forecast monthly PM2.5 concentration for October to December 2018 in Beijing and provides a reference basis for the government to formulate smog control policies.

Practical implications

The proposed model can simulate and forecast system characteristic data with the time-lag effect more accurately, which shows that the time-lag GM(1,N) model proposed in this paper is practical and effective.

Originality/value

Based on interval grey number sequences, the traditional GM(1,N) model neglects the time-lag effect of driving terms, hence this paper introduces the time-lag parameters into driving terms of the traditional GM(1,N) model and proposes a novel time-lag GM(1,N) model.

Details

Grey Systems: Theory and Application, vol. 11 no. 4
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 21 October 2020

Xiwang Xiang, Xin Ma, Minda Ma, Wenqing Wu and Lang Yu

PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the…

Abstract

Purpose

PM10 is one of the most dangerous air pollutants which is harmful to the ecological system and human health. Accurate forecasting of PM10 concentration makes it easier for the government to make efficient decisions and policies. However, the PM10 concentration, particularly, the emerging short-term concentration has high uncertainties as it is often impacted by many factors and also time varying. Above all, a new methodology which can overcome such difficulties is needed.

Design/methodology/approach

The grey system theory is used to build the short-term PM10 forecasting model. The Euler polynomial is used as a driving term of the proposed grey model, and then the convolutional solution is applied to make the new model computationally feasible. The grey wolf optimizer is used to select the optimal nonlinear parameters of the proposed model.

Findings

The introduction of the Euler polynomial makes the new model more flexible and more general as it can yield several other conventional grey models under certain conditions. The new model presents significantly higher performance, is more accurate and also more stable, than the six existing grey models in three real-world cases and the case of short-term PM10 forecasting in Tianjin China.

Practical implications

With high performance in the real-world case in Tianjin China, the proposed model appears to have high potential to accurately forecast the PM10 concentration in big cities of China. Therefore, it can be considered as a decision-making support tool in the near future.

Originality/value

This is the first work introducing the Euler polynomial to the grey system models, and a more general formulation of existing grey models is also obtained. The modelling pattern used in this paper can be used as an example for building other similar nonlinear grey models. The practical example of short-term PM10 forecasting in Tianjin China is also presented for the first time.

Details

Grey Systems: Theory and Application, vol. 11 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 9 December 2020

Wei Meng, Qian Li, Bo Zeng and Yingjie Yang

The purpose of this paper is to unify the expression of fractional grey accumulating generation operator and the reducing generation operator, and build the FDGM(1,1) model with…

Abstract

Purpose

The purpose of this paper is to unify the expression of fractional grey accumulating generation operator and the reducing generation operator, and build the FDGM(1,1) model with the unified fractional grey generation operator.

Design/methodology/approach

By systematically studying the properties of the fractional accumulating operator and the reducing operator, and analyzing the sensitivity of the order value, a unified expression of the fractional operators is given. The FDGM(1,1) model with the unified fractional grey generation operator is established. The relationship between the order value and the modeling error distribution is studied.

Findings

The expression of the fractional accumulating generation operator and the reducing generation operator can be unified to a simple expression. For −1<r < 1, the fractional grey generation operator satisfies the principle of new information priority. The DGM(1,1) model is a special case of the FDGM(1,1) model with r = 1.

Research limitations/implications

The sensitivity of the unified operator is verified through random numerical simulation method, and the theoretical proof was not yet possible.

Practical implications

The FDGM(1,1) model has a higher modeling accuracy and modeling adaptability than the DGM(1,1) by optimizing the order.

Originality/value

The expression of the fractional accumulating generation operator and the reducing generation operator is firstly unified. The FDGM(1,1) model with the unified fractional grey generation operator is firstly established. The unification of the fractional accumulating operator and the reducing operator improved the theoretical basis of grey generation operator.

Details

Grey Systems: Theory and Application, vol. 11 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 3 May 2016

Mehmet Onur Olgun, Sırma Zeynep Alparslan Gök and Gültekin Özdemir

– The purpose of this paper is to extend the results of Meca et al. (2004) depending on the grey information revealed by the individual firms.

Abstract

Purpose

The purpose of this paper is to extend the results of Meca et al. (2004) depending on the grey information revealed by the individual firms.

Design/methodology/approach

The authors introduce cooperative grey games and focus on sharing ordering cost rule (SOC-rule) to distribute the joint cost.

Findings

In this study, the authors introduce a model, where inventory costs are assumed as grey numbers instead of crisp or stochastic ones studied in literature. At first, grey numbers and classical cooperative inventory games are recalled. Then, cooperative grey games are introduced and related results are given. Finally, an application is performed for three shotgun companies in Turkey.

Originality/value

It is an effective approach for theoretical analysis of systems with imprecise information and incomplete samples. Therefore, grey system theory, rather than the traditional probability theory and fuzzy set theory, is better suited to model the inventory problems by using cooperative game theory. To the best of the knowledge no study exists modeling inventory situations by using cooperative grey games. From this point of view this study is a pioneering work on a promising topic.

Details

Kybernetes, vol. 45 no. 5
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 17 January 2023

Jintao Yu, Xican Li, Shuang Cao and Fajun Liu

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by…

Abstract

Purpose

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Design/methodology/approach

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

Findings

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R2 = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

Practical implications

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

Originality/value

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

Details

Grey Systems: Theory and Application, vol. 13 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 20 June 2019

Souleymane Diba and Naiming Xie

The purpose of this paper is to evaluate, analyse and select the best suppliers for Satrec Vitalait Milk Company, operating in Senegal, based on criteria obtained from economic…

Abstract

Purpose

The purpose of this paper is to evaluate, analyse and select the best suppliers for Satrec Vitalait Milk Company, operating in Senegal, based on criteria obtained from economic, environmental and social dimensions of sustainable supply chain management, through the application of Deng’s grey relational analysis (GRA) model, absolute GRA model (ADGRA) and a novel second synthetic GRA (SSGRA) model, combined with one decision making under the uncertainty-based model, namely, the Hurwicz criteria.

Design/methodology/approach

The research adopts a new synthetic GRA model and highlights its reliability on small sample gathered from four senior experts of the company who administered a total number of 28 specialists operating in four departments of the company, through the employment of a self-administered questionnaire designed based on criteria identified from the literature that were refined via a Q-sort model.

Findings

The outcomes of the research methodology designated that all the selected five suppliers present a degree of attaining sustainability due to the fact that supplying unprocessed milk does not require the use of polluting methods for stocking and transportation. The undertaken study specifies that all the socio-environmental criteria play a crucial role in shaping the sustainability level of Satrec Vitalait’s suppliers and demonstrates the accuracy of the results obtained through the second synthetic degree of grey relation analysis for ranking the suppliers. Supplier 2 was found to be the best supplier for the company and, as result, a model for other suppliers to mimic.

Research limitations/implications

Future researchers can replicate the GRA-based supply chain model proposed in the current study in different environments especially in the context of green supply chain. Also, in future the SSGRA model, while using the bidirectional ADGRA instead of the conventional ADGRA, should also be tested, especially when the data sequences associated with different supply chain parameters have inconsistent directions. Also, comparative analysis of SSGRA-based results with that of modern statistical methods like structural equation modelling can also be used for future explorations. Furthermore, the current study is built upon the data associated with the Satrec Vitalait Milk Company (Senegal); therefore, the findings should be generalised with caution.

Originality/value

The study can be seen as a first-stepping stone for gauging and selecting the best sustainable supplier for Satrec Vitalait using grey system theory. For purpose of attaining the research goal, the SSGRA was exploited as an innovative experimental approach to estimate relationships between criteria with regard to the sustainability level of the company’s suppliers. Under this scope, relationships between criteria themselves and their goal were depicted by Deng’s degree of GRA and AGRA, respectively. The research is innovative by means of the framework of its methodology and data analysis.

Details

Grey Systems: Theory and Application, vol. 9 no. 3
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 28 May 2021

Zainab Asim, Syed Aqib Aqib Jalil, Shakeel Javaid and Syed Mohd Muneeb

This paper aims to develop a grey decentralized bi-level multi-objective programming (MOP) model. A solution approach is also proposed for the given model. A production and…

Abstract

Purpose

This paper aims to develop a grey decentralized bi-level multi-objective programming (MOP) model. A solution approach is also proposed for the given model. A production and transportation plan for a closed loop supply chain network under an uncertain environment and different scenarios is also developed.

Design/methodology/approach

In this paper, we combined grey linear programming (GLP) and fuzzy set theory to present a solution approach for the problem. The proposed model first solves the given problem using GLP. Membership functions for the decision variables under the control of the leader and for the goals are created. These membership functions are then used to generate the final solutions.

Findings

This paper provides insight for fomenting the decision-making process while providing a more flexible approach in uncertain logistics problems. The deviations of the final solution from the individual best solutions of the two levels are very little. These deviations can further be reduced by adjusting the tolerances associated with the decision variables under the control of the leader.

Practical implications

The proposed approach uses the concept of membership functions of linear form, and thus, requires less computational efforts while providing effective results. Most of the organizations exhibit decentralized decision-making under the presence of uncertainties. Therefore, the present study is helpful in dealing with such scenarios.

Originality/value

This is the first time, formulation of a decentralized bi-level multi-objective model under a grey environment is carried out as per the best knowledge of the authors. A solution approach is developed for bi-level MOP under grey uncertainty.

Details

Journal of Modelling in Management, vol. 16 no. 3
Type: Research Article
ISSN: 1746-5664

Keywords

Article
Publication date: 16 December 2022

Nan Li, M. Prabhu and Atul Kumar Sahu

The main purpose of present study is to model the replacement policy under uncertainty for managerial application based on grey-reliability approach by considering the subjective…

Abstract

Purpose

The main purpose of present study is to model the replacement policy under uncertainty for managerial application based on grey-reliability approach by considering the subjective views of quality control circle (QCC). The study objectively links the optimality between individual replacement and group replacement policies for determining the minimum operational costs. The integrated framework between QCC, replacement theory, grey set theory and supply chain management is presented to plan replacement actions under uncertainty.

Design/methodology/approach

The study proposes the concept of grey-reliability index and built a decision support model, which can deal with the imprecise information for determining the minimum operational costs to plan subsequent maintenance efforts.

Findings

The findings of the study establish the synergy between individual replacement and group replacement policies. The computations related to the numbers of failures, operational costs, reliability index and failure probabilities are presented under developed framework. An integrated framework to facilitate the managers in deciding the replacement policy based on operational time towards concerning replacement of assets that do not deteriorate, but fails suddenly over time is presented. The conceptual model is explained with a numerical procedure to illustrate the significance of the proposed approach.

Originality/value

A conceptual model under the framework of such items, whose failures cannot be corrected by repair actions, but can only be set by replacement is presented. The study provides an important knowledge based decision support framework for crafting a replacement model using grey set theory. The study captured subjective information to build decision model in the ambit of replacement.

Details

Grey Systems: Theory and Application, vol. 13 no. 2
Type: Research Article
ISSN: 2043-9377

Keywords

Article
Publication date: 22 February 2021

Xueguang Yu, Xintian Liu, Xu Wang and Xiaolan Wang

This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.

Abstract

Purpose

This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function.

Design/methodology/approach

To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed.

Findings

The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results.

Originality/value

Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.

Details

Engineering Computations, vol. 38 no. 6
Type: Research Article
ISSN: 0264-4401

Keywords

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