Traditional Grey Relational Analysis Research Articles

A practical decision-making framework for highway transportation scheme selection based on the triangular fuzzy neutrosophic information

In recent years, due to the further development of the market economy, the internal competition in the large-cargo transportation industry has become increasingly fierce, and the profit space has been greatly compressed. Therefore, large-cargo logistics enterprises are paying more and more attention to the research of highway transportation route plan. The highway transportation scheme selection is looked as the multi-attribute decision-making (MADM). In this paper, the triangular fuzzy neutrosophic numbers (TFNN) grey relational analysis (TFNN-GRA) method is established based on the classical grey relational analysis (GRA) and triangular fuzzy neutrosophic sets (TFNSs) with completely unknown weight information. In order to obtain the weight values, the information Entropy is established to obtain the weight values based on the score and accuracy functions under TFNSs. Then, combining the traditional fuzzy GRA model with TFNSs information, the TFNN-GRA method is set up and the computing steps for MADM are established. Finally, a numerical example for highway transportation scheme selection was established and some comparisons are established to study the advantages of TFNN-GRA. The main contributions of this paper are established as follows: (1) the information Entropy is established to obtain the weight values based on the score and accuracy functions under TFNSs; (2) the TFNN-GRA method is established with completely unknown weight information. (2) the TFNN-GRA method is established and the computing steps for MADM are established. (3) Finally, a numerical example for highway transportation scheme selection was established and some comparisons is employed to study advantages of TFNN-GRA method.

Evaluation analysis and promotion paths of regional green innovation vitality in China

PurposeThe purpose of this work is to construct a grey entropy comprehensive evaluation model to measure the regional green innovation vitality (GIV) of 31 provinces in China.Design/methodology/approachThe traditional grey relational proximity and grey relational similarity degree are integrated into the novel comprehensive grey evaluation framework. The evaluation system of regional green innovation vitality is constructed from three dimensions: economic development vitality, innovative transformation power and environmental protection efficacy. The weights of each indicator are obtained by the entropy weight method. The GIV of 31 provinces in China is measured based on provincial panel data from 2016 to 2020. The ward clustering and K-nearest-neighbor (KNN) algorithms are utilized to explore the regional green innovation discrepancies and promotion paths.FindingsThe novel grey evaluation method exhibits stronger ability to capture intrinsic patterns compared with two separate traditional grey relational models. Green innovation vitality shows obvious regional discrepancies. The Matthew effect of China's regional GIV is obvious, showing a basic trend of strong in the eastern but weak in the western areas. The comprehensive innovation vitality of economically developed provinces exhibits steady increasing trend year by year, while the innovation vitality of less developed regions shows an overall steady state of no fluctuation.Practical implicationsThe grey entropy comprehensive relational model in this study is applied for the measurement and evaluation of regional GIV, which improves the one-sidedness of traditional grey relational analysis on the proximity or similarity among sequences. In addition, a three-dimensional evaluation system of regional GIV is constructed, which provides the practical guidance for the research of regional development strategic planning as well as promotion paths.Originality/valueA comprehensive grey entropy relational model based on traditional grey incidence analysis (GIA) in terms of proximity and similarity is proposed. The three-dimensional evaluation system of China's regional GIV is constructed, which provides a new research perspective for regional innovation evaluation and expands the application scope of grey system theory.

Operational efficiency evaluation of Urban and rural residents’ basic pension insurance system based on the triangular fuzzy neutrosophic GRA method

At present, the basic pension insurance system for urban and rural residents in China has played a positive role in guaranteeing the basic life of the elderly in urban and rural areas. At present, the basic pension insurance system for urban and rural residents is not perfect, and there is still a great lag in the formulation of cross-system and cross-regional policies. There are differences in treatment between groups, between regions and between urban and rural areas. The coverage is not comprehensive enough and there are still some people who are not included in the basic protection system, etc. People urgently need a social pension insurance system that can provide reliable and sustainable protection in their old age. The operational efficiency evaluation of urban and rural residents’ basic pension insurance systems is viewed as the multi-attribute decision-making (MADM). In this paper, the triangular fuzzy neutrosophic numbers grey relational analysis (TFNN-GRA) method is built based on the traditional grey relational analysis (GRA) and triangular fuzzy neutrosophic sets (TFNSs). Finally, a numerical example for operational efficiency evaluation of urban and rural residents’ basic pension insurance systems has been given and some comparisons are used to illustrate advantages of 2TLNN-GRA method.

The result greyness problem of the grey relational analysis and its solution

This paper discusses how to deal with the greyness problem in the system from the perspective of “result”. Aiming at the greyness problem of the traditional grey relational analysis result, an information fusion grey relational analysis method based on D-S evidence theory and multi solution information fusion is proposed, which mends the traditional grey relational analysis method. The results show that the method proposed in the study has better effect than the traditional grey relational analysis method, and has higher accuracy in the wear particle identification, which indicates that it can further expand the application scope of the grey relational analysis method.

Method for 2-tuple linguistic neutrosophic number MAGDM and applications to physical education teaching quality evaluation in colleges and universities

The quality of physical education (PE) teaching in colleges and universities is the basis for the development of PE disciplines in colleges and universities, so currently thinking about how to effectively improve the quality of PE teaching in colleges and universities has become the first and foremost problem for many college and university PE departments to solve. In order to solve this problem, it is necessary to build a reasonable and scientific evaluation and monitoring system of PE teaching quality, because only by establishing an effective evaluation and monitoring system of teaching quality can we evaluate and supervise all the PE operation properly and scientifically, and then give feedback in the process of evaluation and supervision, such evaluation and monitoring system can greatly promote the continuous improvement of PE teaching quality in colleges and universities. This is also one of the most effective means to improve the quality of PE and achieve the goal of PE in colleges and universities. The PE teaching quality evaluation in Colleges and Universities is frequently viewed as the multiple attribute group decision making (MAGDM) issue. In this paper, the 2-tuple linguistic neutrosophic number grey relational analysis (2TLNN-GRA) method is built based on the traditional grey relational analysis (GRA) and 2-tuple linguistic neutrosophic sets (2TLNNSs). Then, a numerical example for PE teaching quality evaluation in Colleges and Universities has been given and some comparisons is used to illustrate advantages of 2TLNN-GRA method.

Performance evaluation of family business strategic transition based on the 2-tuple linguistic neutrosophic number multiple attribute group decision making

Since 2010, China’s traditional industry has entered a critical stage of development and enterprise reform and development is imminent. Product homogenization is serious in this market, so that the competition among enterprises is fierce. At the same time, international brands continue to enter the Chinese consumption market, which intensifies the competition and seriously squeezes the market share of Chinese local brands. However, the popularization and development of the Internet and the change of people’s consumption concept and level make the market put forward higher requirements for the development of business operation and many traditional family enterprises have embarked on the road of transformation. It is of great significance and value to clarify the influence of internal factors of family enterprises on strategic transformation. The performance evaluation of family business strategic transition is really a multiple attribute group decision making (MAGDM) problems. In this paper, the 2-tuple linguistic neutrosophic number grey relational analysis (2TLNN-GRA) method is proposed along with on the traditional grey relational analysis (GRA) and 2-tuple linguistic neutrosophic sets (2TLNNSs). Firstly, the 2TLNNSs is introduced. Then, combine the traditional fuzzy GRA model with 2TLNNSs information, the 2TLNN-GRA method is established and the computing steps for MAGDM are built. Finally, a numerical example for performance evaluation of family business strategic transition has been given and some comparisons is used to illustrate advantages of 2TLNN-GRA method.

Grey relational analysis method for typhoon vulnerability assessment of civil engineering structures based on the 2-tuple linguistic neutrosophic number.

As one of the severe natural disasters, typhoon hazard brings tremendous tragedy to human beings. The foreland in the southeast of China is one of the most typhoon prone areas in the world. There are amount of damage of civil engineering structures induced by typhoon every year. Especially for the spacious villages, the low-rise buildings are vulnerable to typhoon so that many of them are destroyed regionally. The typhoon vulnerability assessment of civil engineering structures is a classical multiple attribute group decision making (MAGDM) issues. In this paper, the 2-tuple linguistic neutrosophic number grey relational analysis (2TLNN-GRA) method is built based on the grey relational analysis (GRA) and 2-tuple linguistic neutrosophic sets (2TLNSs) with incomplete weight information. For deriving the weight information of the attribute, an optimization model is built on the basis of the GRA, by which the attribute weights can be decided. Then, the optimal alternative is chosen through calculating largest relative relational degree from the 2-tuple linguistic neutrosophic number positive ideal solution (2TLNNPIS) which considers both the largest grey relational coefficient (GRC) from the 2TLNNPIS and the smallest GRC form 2-tuple linguistic neutrosophic number negative ideal solution (2TLNN NIS). Then, combine the traditional fuzzy GRA model with 2TLNNSs information, the 2TLNN-GRA method is established and the computing steps for MAGDM are built. Finally, a numerical example for typhoon vulnerability assessment of civil engineering structures has been given and some comparisons is used to illustrate advantages of 2TLNN-GRA method.

Private-Sector Partner Selection for Public-Private Partnership Projects Based on Improved CRITIC-EMW Weight and GRA -VIKOR Method

When the government decides to use the public-private partnership (PPP) in projects, such as infrastructure construction, selecting a private-sector partner that meets the project's needs is one of the key factors for successful implementation, but this is ignored in existing research. On this basis, this paper proposes a GRA-VIKOR method based on the combined weight of the improved CRITIC-entropy weight method (EWM). The traditional CRITIC method is improved by combining it with EWM. The combined weights are measured, which reduces the limitations of the single weight. Considering the inherent correlation of evaluation indicators, the VIKOR method is combined with the grey relational analysis (GRA), which makes the results of the selection assessment more reasonable. This paper carries out a case study of the first inland navigation PPP project in China. Through preliminary tracking studies, it tests the effectiveness of the proposed method, the superiority of which is demonstrated by comparing the evaluation results with those of the traditional GRA methods, VIKOR, and TOPSIS.

Comprehensive Evaluation Model and Empirical Research on Railway Freight Rates in a Competitive Environment

This study aims to establish criteria to evaluate performance in railway freight pricing policy and to strengthen the marketing ability of the railway freight enterprise. The evaluation method used in our study is known as the improved grey relation analysis evaluation. Fifteen factors that influence freight pricing strategy are selected in this paper to establish a freight rate evaluation index system and comprehensive evaluation index values for monthly freight rates are calculated. The improved grey relation analysis not only considers the relation between each index and freight rate but also examines the relationship between each index. We find that the comprehensive evaluation state using the improved grey relation analysis evaluation method can better fit the 2015–2017 changes in monthly railroad freight revenue than the traditional grey relation analysis evaluation. Furthermore, an optimal pricing model for freight shipping by train is built and calculated using the bi-level programming model. Finally, the S Railway Bureau’s actual coal transportation in 2017 is taken as an experiment to support the validity of the improved grey relation analysis method. We find that when the monthly results of improved grey evaluation grades are compared with the grade evaluation of the gap between the historical shipping coal rates and the optimal freight shipping rates, the comparison of results matches well. The research work is helpful to policymakers who need to judge the performance of the market price.

A New Medium and Long-Term Power Load Forecasting Method Considering Policy Factors

At present, China’s power load development is facing a new situation in which policies such as the new economic norm, industrial structure adjustment, energy conservation and emission reduction, etc. are being deeply promoted, load growth in some areas begin to ease, and volatility of load gradually become prominent, which increases the difficulty of medium and long-term load forecasting. In this context, in view of multi-correlation, uncertainty of influence of policy factors on power load, in order to improve the accuracy of load forecasting under the influence of policy factors, and solve the problem that policy factors are ambiguous, difficult to be quantified, and difficult to be integrated into load forecasting model, a medium and long-term load forecasting model considering policy factors is proposed. First, by analyzing the influence of various policies on power load, a hierarchical policy influencing factor index system that combines macro and micro levels is constructed to systematically reflect the influence of economy and policies on load under the new situation. Then, in view of the traditional grey relational analysis model’s insufficient consideration of the difference of historical data and future power development situation, by respectively weighting historical periods and factor indexes, a quantification analysis model of power load influencing factors based on two-way weighted grey relational analysis is proposed to quantify the influence of various policy factors on power load, achieve the combination of subjective weighting and objective weighting,and obtain quantification weights. Finally, the weighted fuzzy cluster analysis method combined with weights is used to predict load under the influence of policy factors. The proposed model can better solve the difficulty of medium and long-term load forecasting caused by the volatility of load under the influence of policy factors, and is suitable for medium and long-term load forecasting under the background of policy changes. The analysis of calculation examples shows that compared with traditional grey relational analysis model, the quantification results of proposed methods are more realistic, compared with traditional prediction methods such as time series extrapolation and elasticity coefficient, proposed method has better prediction accuracy and engineering application value.

Comprehensive Evaluation of Non-waste Cities Based on Two-Tuple Mixed Correlation Degree

Under the background of vigorously promoting the construction of ecological civilization, the importance of constructing the “non-waste cities” becomes increasingly prominent. Taking 39 cities in the Yangtze River Economic Zone as the research objects, this paper establishes a new evaluation index system for “non-waste cities,” and proposes a multi-source, heterogeneous and multi-attribute decision-making method for the comprehensive evaluation of “non-waste cities.” Specifically, the evaluation index system of “non-waste cities” is constructed from four aspects: economic level, environmental pollution, resource consumption, and waste utilization. Considering that there is the characteristic of multi-source heterogeneity for the attribute values (that is, real numbers, interval numbers, and fuzzy linguistic variables coexist), the multi-source heterogeneous data are uniformly converted into two-tuples, and then a new two-tuple entropy weight method is proposed to determine the weights of evaluation attributes. Moreover, combining the traditional grey relational analysis method with TOPSIS, a multi-source, heterogeneous and multi-attribute decision-making method based on two-tuple mixed correlation degree (TTMCD-MSHMADM) is proposed to evaluate the “non-waste cities,” and an empirical analysis is made for the 39 cities in the Yangtze River Economic Zone. The result gives a theoretical basis for the formulation of sustainable economic development policies in the Yangtze River Economic Zone, and provides a decision reference for selecting the demonstration cities of “non-waste cities.”

The main factors affecting Taiwan’s economic growth rate via dynamic grey relational analysis

Ever since the grey system theory was proposed about 40 years ago, its characteristics such as small samples, few data, and uncertainty have been used for study in the literature with increasingly wider scope. Recent studies on grey relation analysis have included static data analyses, and most of them have adopted initial values with only a relational order. Under the same study conditions, if different data preprocessing methods are used, then the relational order will be ranked differently. This study took Taiwan as the object to explore seven economic indices (birth rate (%), Taiwan’s total population (thousand people), unemployment rate (%), income per capita (USD), weighted average interest rate on deposits (%), Consumer Price Index (CPI), and national income (NI)) and how they affect the economic growth rate. The traditional static grey relational analysis treated the collected data with taking consideration of time effect which is irrational under some circumstance. An innovative dynamic grey relational analysis was carried out by shifting the raw data due to the time leading or lagging effect which is a mean to improve the capability of traditional grey relational analysis. The differences in analyses between static grey relational analysis and dynamic grey relational analysis via different data preprocessing methods were further discussed, finding that different data preprocessing methods generated a new set of relational orders through the latter. Finally, the prosperity index was used to identify the effects of all factors on economic growth (leading, synchronization, and lagging indices).

Phase Identification of Low-Voltage Users with Novel Grey Relational Analysis Method

With the development of smart grid, the extensive use of advanced metering infrastructure (AMI) equipment further improves the lean management level of grid, which makes it possible to accurately analyse the power consumption information of low-voltage users. This paper proposes a novel algorithm for accurately identifying the phase of low voltage users. The algorithm is based on grey relational analysis (GRA). Data collected from independent users and buses are used for comparative analysis by proposed algorithm. In this paper, the algorithm and its experimental results in Hebei Province are introduced in detail. The results show encouraging results that the proposed algorithm can accurately identify the low-voltage users’ electricity phase, and the performance of the improved GRA algorithm is better than the traditional GRA. The proposed method also has better effect compared with other methods of phase identification.

Grey SWARA-FUCOM Weighting Method for Contractor Selection MCDM Problem: A Case Study of Floating Solar Panel Energy System Installation

Selection of the most appropriate contractor for the installation of solar panels is essential to maximizing the benefit of this renewable, sustainable energy source. Solar energy is one of the 100% renewable energy sources, but implementation may not be very simple and cost-effective. A key phase in the implementation of renewable energy is the evaluation of contractors for the installation of solar panels, which is addressed as a multi-criteria decision-making (MCDM) problem. A new hybrid method is proposed that combines the stepwise weight analysis ratio assessment (SWARA) and full consistent method (FUCOM) weights that are represented as grey numbers used with traditional grey relational analysis (GRA) and evaluation based on distance from average solution (EDAS) methods. The ranking of contractors by both methods is the same, which confirmed the results presented in this research. The use of the grey SWARA-FUCOM weighting method combined with the GRA and EDAS methods increased the decision-makers’ (DMs) confidence in awarding the installation of the solar panel energy system to the top-ranked contractor.

Multi-response optimization of Ti-6Al-4V turning operations using Taguchi-based grey relational analysis coupled with kernel principal component analysis

Ti-6Al-4V has a wide range of applications, especially in the aerospace field; however, it is a difficult-to-cut material. In order to achieve sustainable machining of Ti-6Al-4V, multiple objectives considering not only economic and technical requirements but also the environmental requirement need to be optimized simultaneously. In this work, the optimization design of process parameters such as type of inserts, feed rate, and depth of cut for Ti-6Al-4V turning under dry condition was investigated experimentally. The major performance indexes chosen to evaluate this sustainable process were radial thrust, cutting power, and coefficient of friction at the tool-chip interface. Considering the nonlinearity between the various objectives, grey relational analysis (GRA) was first performed to transform these indexes into the corresponding grey relational coefficients, and then kernel principal component analysis (KPCA) was applied to extract the kernel principal components and determine the corresponding weights which showed their relative importance. Eventually, kernel grey relational grade (KGRG) was proposed as the optimization criterion to identify the optimal combination of process parameters. The results of the range analysis show that the depth of cut has the most significant effect, followed by the feed rate and type of inserts. Confirmation tests clearly show that the modified method combining GRA with KPCA outperforms the traditional GRA method with equal weights and the hybrid method based on GRA and PCA.

Reliability analysis of tractor multi‐way valves based on the improved weighted grey relational method

In order to analyse the influence of different performance indexes on the working reliability of a tractor multi-way valve. The grey correlation theory is introduced into the reliability analysis of multi-way valves. Combined with the multi-way valve failure mode, the reliability index is proposed, and then a grey relational model and the reliability evaluation sequence of multi-way valves are established. The reliability of multi-way valve is analysed by traditional grey relational analysis and improved weighted grey correlation analysis, respectively. Although both methods produced the same optimal prototype, the dynamic identification coefficient introduced by the latter can effectively suppress the influence of singular values on the correlation sequence in the prototype sequence. The analysis process is simplified, and the accuracy of calculation is improved. Meanwhile, the identification degree of the sequence of the prototype is increased. In addition, the improved weighted grey relational analysis method uses the entropy weight method to assign weight coefficients. This method can reflect the influence degree of different sequence points on the overall correlation degree objectively and improve the reliability of the analysis results. Finally, the correctness of the optimal prototype is verified by comparing the experimental data. The reliability evaluation standard of the tractor multi-way valve is obtained.

Interval-valued Pythagorean fuzzy GRA method for multiple-attribute decision making with incomplete weight information

In this paper, the concept of multiple-attribute group decision-making (MAGDM) problems with interval-valued Pythagorean fuzzy information is developed, in which the attribute values are interval-valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval-valued Pythagorean fuzzy sets is the generalization of interval-valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval-valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval-valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval-valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval-valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval-valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive-ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.

Research on Application of Sintering Basicity of Based on Various Intelligent Algorithms

Prediction of alkalinity in sintering process is difficult. Whether the level of the alkalinity of sintering process is successful or not is directly related to the quality of sinter. There is no good method, prediction of alkalinity by high complexity, the present nonlinear, strong coupling, high time delay, so the recent new technology, grey least square support vector machine have been introduced. In this paper, The weight of evaluation objectives has not given the corresponding consideration when solving the correlation degree by taking traditional grey relation analysis and it is with a lot of subjective factors, easily lead to mistakes in decision-making on program. What is more,a kind of alkaline grey support vector machine model, enables us to develop new formulations and algorithms to predict the alkalinity. In the model,

An integrated green supplier selection approach with analytic network process and improved Grey relational analysis

With increased worldwide awareness of environmental protection, green supply chain management (GSCM) has received much attention from both researchers and practitioners over the past decade. Traditionally, organizations have considered criteria such as cost, quality, and delivery to evaluate the performance of their suppliers. Although there is an abundance of studies considering the conventional criteria in supplier selection, there are a rather limited number taking into account the environmental issues. In this study, we use both economic and environmental criteria and propose a comprehensive green supplier selection model. The analytic network process (ANP) is used to deal with the interdependencies among the criteria, and the traditional Grey relational analysis (GRA) has been modified to better address the uncertainties inherent in supplier selection decisions. We utilize the ANP and an improved GRA to weight the criteria and rank the suppliers respectively. The proposed approach is novel, and allows decision-makers to participate in the assessment process and use linguistic evaluation in the green supplier selection process. A case study in the automotive industry is presented to demonstrate the effectiveness of the proposed approach.

A grey-based group decision-making methodology for the selection of hydrogen technologies in life cycle sustainability perspective

Abstract The objective of this research is to develop a grey-based group decision-making methodology for the selection of the best renewable energy technology (including hydrogen) using a life cycle sustainability perspective. The traditional grey relational analysis has been modified to better address the issue of uncertainty. The proposed methodology allows multi-person to participate in the decision-making process and to give linguistic evaluation on the weights of the criteria and the performance of the alternative technologies. In this paper, twelve hydrogen production technologies have been assessed using the proposed methodology, electrolysis of water technology by hydropower has been considered to be the best technology for hydrogen production according to the decision-making group.