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Parameter Estimation of Integro-differential Equation-based Grey Predator-prey Model From Noisy Data  Zhaoya Zhang, Naiming Xie, Lu Yang, Xiaolei Wang The Journal of Grey System    2024, 36 (2): 79-89.   Abstract （85）            Knowledge map    The grey predator-prey model is widely applied in many fields for its effectiveness. While most of the research on the grey predator-prey model focuses on the different model forms, less attention has been paid to identifying parameters and initial value from noisy data. In this work, considering the measurement noise in practice, we propose a two-stage approach to estimate the structural parameters and initial value of the grey predator-prey model with integro-differential equations(IDEs). First, by introducing an integral operator, we propose another form of the grey predator-prey model, namely the IDE-based grey predator-prey model. Next, we develop a parameter estimation approach based on the idea of a two-stage in the presence of measurement noise, where in the first stage we smooth time series using cubic B-Spline and in the second stage estimate structural parameters and initial conditions by the separable nonlinear least squares. Then, the finite sample performance of the IDE-based model is investigated with Monte Carlo numerical experiments. Results demonstrate that the IDE-based model has better performance in terms of accuracy than the Cusum-based model. Finally, we use a case to further verify the accuracy and stability of the proposed method.   Related Articles | Metrics

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A Novel Logistic Multivariate Grey Prediction Model for Energy Consumption: A case study of China Coal  Sihao Chen, Yongshan Liu, Huiming Duan The Journal of Grey System    2023, 35 (4): 132-153.   Abstract （235）            Knowledge map    Coal consumption plays a pivotal role in the national economic growth, and the coal-based energy supply system as the main guarantee of China's energy is impossible to change in the short term. In order to ensure the security of China's energy supply, accurate coal consumption forecast can provide important theoretical basis for the development of scientific and effective energy planning and decision-making. Starting from the classical Logistic model, this paper introduces a variety of related factors such as energy consumption, economic growth rate and carbon dioxide emission growth rate to expand the modeling objects of the Logistic model and improve the performance of the model by relying on its ability to capture the historical trend of the data model and accurately predict the future value. At the same time, a new logistic multivariate grey prediction model of energy consumption is established by introducing the principle of grey variance information organically combined with the logistic model. The modeling steps of the model are obtained by using mathematical methods such as least squares estimation of parameters and number multiplication transformation. Finally, the new model is applied to the prediction of Chinese coal consumption, and the validity of the model is verified from different perspectives of three cases, showing that the fitted and predicted data of the new model have good consistency with the actual results. The new model has a high accuracy for China's coal short-term forecast, and uses simulation and prediction effects of 1.68220% and 1.29866%, respectively, to effectively forecast China's coal consumption in 2022-2026, and points out the development trend of Chinese coal consumption, and provides a basis for China to make scientific and effective energy planning and decision-making. Related Articles | Metrics

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Stock Movement Prediction With Sentiment Analysis Based on Grey Exponential Smoothing Method: A Case Study on Colombo Stock Exchange, Sri Lanka D.M. K. N. Seneviratna , M.V.D.H.P Malawana , R. M. K. T. Rathnayaka The Journal of Grey System    2023, 35 (4): 1-18.   Abstract （117）            Knowledge map    Sentiment  Analysis  is  an  innovative  development  technique  that  uses  natural language processing techniques to derive people's emotions under positive, negative,and neutral based on public opinions of information. The main objective of this study is  to  introduce  a  novel  stock  market  prediction  method  based  on  the  Grey Exponential Smoothing method for analyzing social media data within a big-data distributed environment. The empirical investigation of this study is mainly carried out based on the stock market price indices parallel to the extracted Tweets collected during the three selected politically important moments that happened in Sri Lanka during the past ten years; the first case study is based on the political background after  the  ending  of  the  thirty  years  of  civil  war  in  years  2009.  In  the  year  2015,Maithripala Sirisena ended the dynastic rule of Mahinda Rajapaksa. So, the second case  study  has  based  the Tweets  on  the  political  reforms  done  after  the  2015 presidential  election;  the  third  study  is  based  on  the  Sri  Lankan  political  and economic  background  after  the  Rajapaksas  rose  again  in  2020.  For  validations purpose, K Nearest Neighbour, Decision Tree Model, Support Vector Machine, Grey Exponential Smoothing model, and Multinomial Naïve Bayes machine learning were considered.  According  to  the  empirical  findings,  the  new  proposed  Hybrid  Grey Exponential Smoothing model is highly accurate with the lowest RMSE error values in one-head forecasting. Furthermore, the key finding of this research suggested that the  hybrid  Grey  Exponential  Smoothing  model  performs  well  in  sentiment classification-based financial predictions than traditional methods, especially with non-stationary behavioral backgrounds.  Related Articles | Metrics

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Study on the Strengthening Buffer Operators Based on Interpolation Functions Yanfang Wang , Xinyu Qi, Tao Chen, Hui Zhang, Zhengpeng Wu The Journal of Grey System    2023, 35 (2): 167-178.   Abstract （54）            Knowledge map    Based on the present theories of buffer operators, two kinds of strengthening buffer operators (SBOs) based on interpolation functions are established in this paper. Compared with the ones proposed by Dang, it shows that Dang's SBOs are, in our special case. The properties and the inner connections of different SBOs are discussed, which greatly extend the application range of the SBOs. The main function of the SBOs is to reduce or eliminate the impact of shock disturbed system, to restore the distorted "actual data" to its true state. This is the first time to connect the construction of strengthening buffer operators with interpolation functions, which provides a new routine for constructing SBOs.  Related Articles | Metrics

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Research on Grey Clustering Model Based on NDEA for Equipment System-of-Systems Configuration Selection Decision Jingru Zhang, Zhigeng Fang, Shuyu Xiao, Luyue Zhang The Journal of Grey System    2023, 35 (4): 91-107.   Abstract （102）            Knowledge map    Resources (e.g., development budget, equipment performance) is not infinite for the plan and development of equipment system-of-systems (ESoS). Decision makers (DMs) must determine the priority of the ESoS configuration scheme under many constraints. Aiming for this problem, a structure and operation logic modeling of ESoS is analyzed. The network DEA approach describes each ESoS as a n-phase network decision unit with inputs and outputs. Secondly, the performance and cost of single equipment and ESoS combat effect are all considered. Based on this, we calculate the input-output efficiency of ESoS and consider two situations regarding the development budget. Then, with phased efficiency as evaluation indexes, the grey clustering evaluation based on the possibility function is applied to measure the ESoS configuration from the perspective of DMs. Finally, a case study verifies the feasibility and efficacy of the proposed methodology via selection decision results. The proposed method can aid DMs throughout the decision process for ESoS.  Related Articles | Metrics

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Adaptive Fluctuation Grey Model withAK Fractional Derivative for Short-term Traffic Flow Prediction Quntao Fu, Shuhua Mao The Journal of Grey System    2023, 35 (4): 108-131.   Abstract （127）            Knowledge map    Short-term traffic flow prediction is an essential component of intelligent transportation systems. Shallow and deep pattern learning methods have been widely applied to short-term traffic flow prediction. However, shallow learning methods struggle with highly volatile data and models are usually constant-coefficient. On the other hand, deep learning methods require significant computational resources and time. In this paper, we propose a new adaptive fluctuation grey model for short-term traffic flow prediction. We combine the fractional differential equation and fractional accumulation generation operator, and expand the GM(1,1) model using trigonometric functions. Furthermore, we improve the Harris hawks algorithm by optimizing the distribution of the initial population with Cauchy mutation operator and introducing boundary constraint handling techniques to enhance the model parameter search capability. Finally, we apply the model to short-term traffic flow parameter prediction and compare it with the benchmark model. Results indicate that the new model shows better accuracy performance and better extraction of fluctuation information.  Related Articles | Metrics

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AGMC Model for Forecasting Carbon Dioxide Emission in Northwestern China Kedong Yin, Haolei Gu The Journal of Grey System    2023, 35 (2): 1-13.   Abstract （80）            Knowledge map    With economic and social development rapidly, carbon dioxide emission soared in the northwestern region. The importance of adopting emission reduction strategies cannot be overemphasized. Therefore, it is essential to accurately forecast carbon dioxide emission in northwestern China. The study used Lasso parameter estimation to select influential carbon dioxide emission features. FGM(1,1) model was used to forecast features trend. The adjacent accumulation grey multivariate convolution model (AGMC) model forecasts carbon dioxide emission trend. The future two years forecast result shows that Shaanxi province’s carbon dioxide emission will show a fluctuating trend. Qinghai autonomous regions will show a decreasing trend. Other regions will be in upward trend. The study suggests the central government should pay attention to the carbon emission problem in the northwestern region. Government increases science and technology investment and pays attention to urbanization spatial pattern rational layout.  Related Articles | Metrics

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The Impact of Claim Management on Selecting Contractors Using the Grey Ordinal Priority Approach (OPA-G) Hamid Asnaashari, Abbas Sheikh Aboumasoudi, Mohammad Reza Mozaffari, Mohammad Reza Feylizadeh The Journal of Grey System    2023, 35 (2): 14-40.   Abstract （47）            Knowledge map    This study aimed to explore the causes and origins of claims in the oil and gas industry. It also sought to find solutions, reduce or eliminate claims, and use them to select efficient contractors. In this paper, one of the new multi-attribute decision-making methods, called the grey ordinal priority approach, was used to rank criteria and alternatives. For dealing with uncertainty, grey systems theory was also applied. Finally, some criteria were proposed to identify and select more efficient contractors. The Grey systems theory can reduce the incidence of claims and increase productivity by ranking claim solutions to reduce costs and execution time, increase quality, and use these solutions in selecting contractors. The variations between the “grey ranks” and the “targeted changes observed” showed that an increase in distance between the ranks increases the effect of the top ranks. Besides, the increase of the grey range of the total weights from [0.8, 1.2] to [0.5, 1.5] made the scores fluctuations regular, and the rankings were shifted to weaker ranks with the closest competition. The contributions of this study are as follows: (1) Unlike previous research that focused on prioritizing the causes of claims, this study tried to identify and rank solutions to reduce the occurrence of claims; (2) The recognized solutions were presented as criteria for selecting more efficient contractors; (3) grey ordinal priority approach method has been used to compare and rank the proposed solutions to increase productivity, considering cost, time, and quality criteria; and (4) This method was first used in project claim management. This method showed that the criterion of “Employing a technical team with experienced and educated members” has the first, and the criterion of “Ensuring the contractor’s effective service records” has the second rank. Related Articles | Metrics

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A Novel Grey Incidence Analysis Model Based on Gamma Probability Density Function and Its Application Yu Feng, Yaoguo Dang, Deling Yang, Junjie Wang, Huimin Zhou The Journal of Grey System    2023, 35 (2): 41-54.   Abstract （93）            Knowledge map    Aiming at the problem that existing grey incidence analysis methods cannot effectively characterize the difference of development trends between sequences in line with the normativity axiom, a novel grey incidence analysis model based on the Gamma probability density function (GIAMG) is proposed. First, the projection factor is defined based on the geometric projection between sequences. Then, the grey incidence coefficient (GIC) is designed by combining the projection factor and the Gamma probability density function. According to the difference in development trends in different periods, the degree of grey incidence is constructed by summing up the GICs with variable weight. Finally, the GIAMG is used to identify the main air pollutants for respiratory diseases in Tianjin, China. Experimental results show that the proposed model is superior in the reliability and effectiveness of the related order over four traditional incidence models.  Related Articles | Metrics

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Forecasting Productive Inventory by Using Graphical Evaluation and Review Technique with Grey Number Representation Jing Zeng The Journal of Grey System    2023, 35 (2): 55-67.   Abstract （56）            Knowledge map    Quantitative forecasting of the inventory for key products can help to reduce the amount of inventory obsolescence and prevent production delays due to raw material stock-outs. Predicting productive inventory is beneficial to promote the sustainability of production management. In this work, a prediction model is constructed that predicts the pass rate of products and the processing path of unqualified products and simultaneously calculates the quantity, time, and probability of each path. Using the Graphical Evaluation and Review Technique (GERT), the manufacturing process of a square tube can be transformed into a stochastic network. Then, grey parameters are introduced into the GERT network to solve uncertainty in manufacturing. Finally, a numerical example is given to obtain a productive inventory prediction for beam square tubes using grey GERT(G-GERT). The main contribution of this work is the integration of inventory quantity, time, and probability. These three results can be predicted simultaneously, and the algorithm can be extended to any product production network. Related Articles | Metrics

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Grey Clustering Methods With Universal Possibility Functions Long Wang, Zhigeng Fang, Qin Zhang, Sifeng Liu The Journal of Grey System    2023, 35 (4): 19-33.   Abstract （114）            Knowledge map    The traditional possibility functions are always assumed to be linear functions. The preferences of decision-makers are not considered. It might not be proper to analyze all kinds of indicators with the traditional possibility functions. Therefore, we consider the preferences and first develop the universal possibility functions. The decision-makers can obtain the appropriate universal possibility functions by adjusting the clustering preference. Then, the related properties are revealed by the proof. Next, grey clustering methods with universal possibility functions are proposed. Finally, the effectiveness of the suggested methods is verified via the case illustration and comparative analysis. Related Articles | Metrics

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A Novel Modeling Method of Extended Grey EGM(1,1,∑e^(ck)) Model and Its Application in Predictions Maolin Cheng, Bin Liu The Journal of Grey System    2023, 35 (4): 55-75.   Abstract （101）            Knowledge map    In the grey models, the GM(1,1) model is an important type of prediction model. The traditional grey GM(1,1) model has good prediction results in the case the original data show exponential variations at a slow rate. However, in practical problems, although showing exponential variations or approximately exponential variations, original data vary very fast sometimes. In these cases, the traditional grey GM(1,1) model tends to have poor prediction accuracy, mainly because the data fails to meet the laws presented by the traditional model. Therefore, the paper makes improvements in the following two aspects: first, the paper transforms the traditional accumulated generating sequence of original data; second, the paper extends the traditional grey model's structure, i.e., building a grey EGM(1,1,∑e^(ck)) model. The paper offers the parameter optimization method of the grey EGM(1,1,∑e^(ck)) model. Using the novel modeling method proposed, the paper builds the grey EGM(1,1,∑e^(ck)) models for China's total electricity consumption and China's GDP per capita, respectively, in the final section. Results show that the models built with the proposed modeling method have high simulation precision and prediction precision. Related Articles | Metrics

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A Multi-attribute Decision-making Method Based on Grey Correlation Lirong Sun, Chi Zheng, Chenkai Jiang, Yinghua Tian, Yujing Ye The Journal of Grey System    2023, 35 (4): 76-90.   Abstract （164）            Knowledge map    Aiming at the grey feature problem of ' small sample and poor information ', this paper extends the traditional analytic hierarchy process, entropy method and ' vertical and horizontal ' scatter degree method to the field of grey number, and proposes a multi-attribute decision-making method based on grey correlation. Firstly, the applicable form of index weight is enriched, and the determination method of index weight in grey number form is given systematically. Secondly, aiming at the problem that the traditional evaluation method can not be directly applied to the comprehensive evaluation with grey characteristics, a comprehensive evaluation model in the form of grey number is proposed. Finally, through the interval grey number integration method and the ' kernel and grey number ' integration method, the evaluation values under each index are formed into a comprehensive evaluation value, and the evaluation results are sorted. Compared with the traditional evaluation method, the proposed method more reflects the rationality and dynamics of the evaluation results. Related Articles | Metrics

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A Conformable Fractional Non-homogeneous Grey Forecasting Model with Adjustable Parameters CFNGMA(1,1,k,c) and its Application  Wenqing Wu , Xin Ma , Bo Zeng , Peng Zhang The Journal of Grey System    2024, 36 (2): 1-12.   Abstract （178）            Knowledge map    The inconsistency between the whitening differential equation and the grey basic form of the non-homogeneous continuous grey model CFNGM(1,1,k,c) will result in internal errors. Thus this paper proposes a CFNGMA(1,1,k,c) model with adjustable parameters, which improves the accuracy of the CFNGM(1,1,k,c). This paper first elucidates reasons for the internal errors generated by the continuous grey model CFNGM(1,1,k,c), and explains the classic method, the discrete grey forecasting model, of eliminating internal errors. On the basis of an in-depth analysis of the modeling mechanism of CFNGM(1,1,k,c) model, a new parameter adjustable grey forecasting model is proposed by introducing parameter adjustment factors to modify model’s parameters. Finally, the new model is applied to explore the gross regional product of Chengdu and Deyang in the Chengdu metropolitan area. The calculation results indicate that the newly proposed model can obtain more accurate results.  Related Articles | Metrics

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Forecasting the Evolution of Public Opinion Using a Novel Improved Grey Model During Emergencies Hongchan Li, Yu Ma, Haodong Zhu The Journal of Grey System    2023, 35 (2): 87-104.   Abstract （67）            Knowledge map    Public opinion is an aggregate of people’s views, attitudes, and emotions about events that can spread through the Internet to generate online public opinion. Studying the evolution of online public opinion during emergencies can help relevant departments to take targeted measures to respond in advance. Tweets and Weibo texts with negative emotions are essential factors affecting the evolution of online public opinion. To this end, this paper proposes a novel improved grey model, SISGM(1,1), that optimizes initial conditions and background values for predicting the number of negative Weibo texts generated during emergencies. The model is improved as follows: First, the background value is reconstructed by the Simpson rule to achieve the effect of smoothing the data sequence. Second, the ISRU activation function is used to modify the initial condition, which can better reveal the characteristics of data growth and improve the model’s adaptability. Then, the modified background value is combined with the optimized initial condition to realize the double optimization. Finally, the PSO algorithm is used to calculate the introduced parameters to improve the prediction accuracy further. Additionally, the model is compared with five competing models to predict the evolution of online public opinion during emergencies. The experimental results demonstrate that the proposed model has apparent advantages compared to the other five competing models. Related Articles | Metrics

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A Grey Three-Way Decision Approach and Its Application Xuege Guo, Yong Liu, Huanhuan Zhao, Hanru Zhang, Gang Zhao, Zhiying Han The Journal of Grey System    2023, 35 (2): 105-129.   Abstract （73）            Knowledge map    The three-way decision offers new perspectives for solving uncertain decision problems, especially categorical decision-making. However, in reality, the preference information of the decision object may be vague and uncertain. To address this issue, we construct a grey relation analysis based three-way decision model in a grey system environment. First, based on an improved grey correlation similarity measure, we investigate how the conditional probabilities of decision events are constructed. Subsequently, according to the information entropy, we established the objective optimization model and calculated the optimal weight of each index. Considering the delay cost and the uncertainty of the loss function, the grey relative loss function matrix is constructed based on the uncertain information of decision objects. Based on this, we establish the optimal thresholds method with the relative loss function and devise the decision rules. Using the established decision rules, we can obtain the classification results of all decision objects. Finally, the proposed model is used to deal with the users’ classification problems in the movie recommendation system, which demonstrates the validity and feasibility of the model.   Related Articles | Metrics

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Grey Clustering Analysis of Provincial Scientific and Technological Innovation Capability Mainland Yuying Yang, Yuxuan Huang, Yichen Liu, Bin Liu The Journal of Grey System    2023, 35 (2): 130-148.   Abstract （96）            Knowledge map    The scientific and technological innovation capabilities of different provinces and cities in China are quite different. Comprehensive evaluation and analysis of provincial scientific and technological innovation capabilities are conducive to a more comprehensive and targeted understanding of different regional differences and put forward more effective policy recommendations for balanced and coordinated regional development. Firstly, this paper constructs the evaluation index system of scientific and technological innovation ability from four aspects: innovation input, innovation output, innovation carrier, and innovation environment; Secondly, using the method of combining subjectivity and objectivity, the indicators are weighted to reflect the importance of different indicators on scientific and technological innovation capability; Finally, the paper uses the grey weight clustering method to analyze the scientific and technological innovation capacity of 31 provinces and cities mainland from 2010 to 2020. The study found that there are significant geographical differences in China's scientific and technological innovation capabilities. The provinces and cities with strong scientific and technological innovation capabilities are mainly Beijing, Shanghai, Jiangsu, Zhejiang, and Guangzhou, which can enhance the scientific and technological innovation capabilities of surrounding provinces and cities through regional synergy.   Related Articles | Metrics

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Forecasting China’s Hydroelectric Power Generation Under the New Era Based on Grey Combination Model Shuliang Li, Nannan Song, Ke Gong, Bo Zeng, Yingjie Yang The Journal of Grey System    2023, 35 (2): 149-166.   Abstract （158）            Knowledge map    It's necessary to forecast hydroelectric power generation under the background of carbon peak. Firstly, based on the three-parameter whitening grey prediction model, the order of the accumulating-fractional-order in the real field and the coefficients of the background value are combined and optimized to establish a two-parameter optimized three-parameter whitening grey prediction model. The model is applied to predict China's hydroelectric power generation, and the comprehensive error is only 1.13%, indicating that the model has good performance. The results show that the carbon peak target can be achieved by 2030. Based on this, relevant countermeasures and suggestions are put forward.   Related Articles | Metrics

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Reinforcement Model for Unmanned Combat System of Systems Based on Multi-Layer Grey Target  Xueting Hao, Zhigeng Fang, Jingru Zhang, Fei Deng, Ankang Jiang, Shuyu Xiao The Journal of Grey System    2024, 36 (2): 54-66.   Abstract （150）            Knowledge map    In the future battlefield, unmanned combat mode will be crucial. Its attack strategy formulation is a significant and complex task. To address the issue of decisionmaking in unmanned combat system of systems(UCSoS) striking strategy, this paper begins by analyzing the characteristics of UCSoS. By utilizing the GERT concept, an unmanned combat A-GERT network is developed to provide parameter support for evaluating its effectiveness. Secondly, for effectiveness evaluation, a multi-layer gray target model built on the A-GERT network is proposed. This model is utilized to formulate the optimal striking scheme for the UCSoS. And Agent technology is employed to solve the intelligent learning decision-making problem for UCSoS based on multi-layer grey target model. Finally, a case study illustrates the efficiency and effectiveness of the reinforcement model for UCSoS based on multi-layer grey target. Related Articles | Metrics

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Improved Fractional Order Single Optimization Parameter Grey Model Jiangtao Wei, Yonghong Wu The Journal of Grey System    2023, 35 (4): 154-171.   Abstract （329）            Knowledge map    Some grey prediction models suffer from outliers and overfitting, and their prediction performance can be improved. Based on the fractional grey model (FGM) and the fractional time delayed grey model (FTDGM), an improved fractional single optimization parameter grey model (IFSGM) is proposed in this paper. A timetranslation power term is used to reduce model overfitting. The data is pre-processed to reduce the influence of outliers based on data transformation in cumulants and summations. The convolutional computational formulation is used to perform the prediction and improve the prediction effect. The genetic optimization algorithm is used to optimize the order of the fractional cumulants, find the optimal value of the order, and improve the model fit and prediction effect. In 6 data sets, the IFSGM and the 7 grey models are compared and tested. The experimental results show that IFSGM achieves excellent prediction performance.  Related Articles | Metrics