Variable Fuzzy Set Research Articles

Spatiotemporal comprehensive evaluation of water quality based on enhanced variable fuzzy set theory: A case study of a landfill in karst area

Water quality assessment is a crucial step in water resource management and pollution prevention, and is essential for achieving sustainable development. Current methods for evaluating water quality often fall short of meeting the needs of water resource management due to the lacks of accuracy and applicability. In this paper, an enhanced water quality evaluation system was established by Principal Component Analysis / Factor Analysis (PCA/FA), Analytic Hierarchy Process / Entropy Weight Method / Game Theory (AHP/EWM/GT) and Variable Fuzzy Set Theory (VFST). The accuracy of this method was verified by evaluating the water quality of a landfill in a karst area and comparing with the conventional evaluation models. The results indicated that the highest influence on groundwater quality in the study area came from human factor, dissolved solid factor, biological factor, and nutritional factor. The quality of surface water and groundwater in the study area was primarily Grade Ⅱ, accounting for 62.5% and 75%, respectively. The predominant groundwater type was HCO3-Ca·Mg, which was strongly affected by karstification. The NH3-N and TP in the surface water had the highest variability, and the variation coefficients of K+, Na+, Ca2+, Cl−, NH3-N, NO3−, TDS, and TH in the groundwater were greater than 1. The surface water quality gradually improved between 2018 and 2019. Overall, the groundwater quality in the southern and central regions was inferior to that in the northern and surrounding areas. There could be a hydraulic link between the surface water and landfill in the research location, while karstification and leachate primarily impacted the groundwater. The water quality evaluation method established in this study can make a significant contribution to water resource management, which has important practical significance for environmental protection and indirect social value to the public.

The application of gray system-variable fuzzy sets coupling theory on the susceptibility assessment of debris flow hazards

The occurrence of debris flow hazards has significant destructive effects people’s safety and the safety of their property, so the risk assessment of debris flow hazards has great significance. The maximum amount of debris flow at one time (X1), the reserves of loose substance (X2), the watershed area (X3), the length of the ditch (X4), the relative height difference (X5), the gradient of side slope (X6), the longitudinal slope of main ditch (X7), the length ratio of replenishment section (X8), the daily maximum rainfall (X9), and Faults developed in the watershed (X10) are selected as the evaluation index at first. Then the gray system-variable fuzzy sets coupling model is introduced; secondly, the relative membership degree matrix about the fuzzy variable sets is established, and the weight coefficients considering the uncertainty of assessment indices are determined based on the entropy weight method; finally, the susceptibility level of debris flow hazards is determined using the mean ranking feature value. The conclusion is drawn that the results obtained based on the coupling technique are consistent with the current specification; its accuracy arrives at 83%, and the method is feasible for the susceptibility level assessment of debris flow hazards. Compared to the traditional variable fuzzy sets model, it avoids the uncertainty of magnitude in the standard analysis, it can ensure the objectivity and accuracy of the calculation result, and its calculation process is simple and efficient. In total, the findings of the proposed model provide an alternate way to assess the susceptibility level of debris flow hazards and improve the evaluation accuracy in the future.

A Multiple Model Approach for Flood Forecasting, Simulation, and Evaluation Coupling in Zhouqu County

Flood disasters are considered to be one of the ten natural disasters that threaten the survival of mankind. They occur frequently and have a serious impact on the national economy. For quicker response to the sudden flood, in this paper, the relevant characteristics of flood forecasting and disaster assessment are comprehensively studied to establish the corresponding models, and a multi-objective culture shuffled complex differential evolution (MOCSCDE) algorithm is proposed to optimize the model parameters. It can achieve better convergence and significantly improve the model accuracy. Then, a river hydrodynamic model is established to simulate the flooding process, and the characteristics of flood evolution, such as water depth, flow speed, duration, and submerged area, are analyzed. Third, based on the above-mentioned flood forecasting and flood evolution calculations, the relative membership function (VFS) is determined via the set pair analysis method (SPA), and the variable fuzzy set model (SPAVFS) is used for flood risk assessment. Finally, through the study of flow forecasting at Zhouqu hydrological station, it is found that the accuracy of the forecast result of the built model is best compared with LSTM and XAJ model, the mean relative error is only 7.6%, and the certainty coefficient can reach 0.96, which surpass the baselines by 20% and 7.9%.

Evaluation of mine water inflow quality based on multiple methods

To reduce the negative impact of mine water gushing on the environment, it is necessary to evaluate the water quality. Taking the Pingdingshan coalfield as the research object, six components – namely, chroma, turbidity, total dissolved solids, total hardness, chloride (Cl−) and sulfate (SO4 2−) – were selected as index factors. The composite weight was calculated using the variable-weight theory, and the water quality of mine gushing water was evaluated using the matter-element extension model, fuzzy variable set model, Bayesian theory and Nemerow index method. The deviation of the four evaluation methods was calculated based on the specially constructed mathematical model. The research results show that the order of the deviation of the evaluation method from small to large is as follows: fuzzy variable set method (5.5) < matter-element extension method (8) < Bayesian statistical method (10) < Nemerow index method (17). The fuzzy variable set method is more suitable for Pingdingshan coalfield mine gushing water quality assessment. The authors hope that this research can provide a certain reference value for the evaluation of mine water quality in the future.

Emergency risk assessment of sudden water pollution in South-to-North Water Diversion Project in China based on driving force–pressure–state–impact–response (DPSIR) model and variable fuzzy set

Emergency risk assessment of sudden water pollution in South-to-North Water Diversion Project in China based on driving force–pressure–state–impact–response (DPSIR) model and variable fuzzy set

Risk assessment method for controlled flight into terrain of airlines based on QAR data

PurposeThe purpose of this paper is to assess the risk of controlled flight into terrain (CFIT) for airlines and to develop a practical method for evaluating and predicting CFIT risk to ensure safe and efficient airline operations.Design/methodology/approachIn accordance with the monitoring project specification issued by the Flight Standards Department of the Civil Aviation Administration of China (CAAC), a preliminary draft of evaluation indicators for CFIT risk was developed based on the literature review and semi-structured interviews. Fifteen aviation experts were then selected and invited to participate in a Delphi method to revise the draft. Analytic hierarchy process (AHP) and entropy weight method were used to determine the combined weight of the indicators. The variable fuzzy set model and quick access recorder (QAR) data were applied to evaluate the CFIT risk of an airline from 2007 to 2018, and the classification results were compared with actual operational data.FindingsThe research findings reveal that the six most significant monitoring items affecting CFIT risk are incorrect configuration settings during landing, loss of altitude during climbing, ground proximity warning, G/S deviation, flap extension delay during landing and incorrect takeoff configuration. The CFIT risk of airlines has shown an increasing trend since 2015. The values in 2010, 2017 and 2018 were greater than 2 and less than 2.5, indicating that the CFIT risk is at Level 2, close to Level 3, and the risk is low but approaching medium.Practical implicationsUsing the combination weight determined by AHP and entropy weight method to rank the weight of 15 monitoring items, airlines can take necessary measures (simulator training, knowledge training) to reduce the occurrence of monitoring items with high weight to reduce CFIT risk. This risk assessment method can quantitatively evaluate the CFIT risk of airlines and provide theoretical guidance and technical support for airlines to formulate safety management measures and flight training programs, enabling the interconnection between QAR data and flight quality.Originality/valueThe proposed method in this study differs from traditional approaches by offering a quantitative assessment of CFIT risk for airlines and enabling the interconnection between QAR data and flight quality.

The risk assessment of rockburst intensity in the highway tunnel based on the variable fuzzy sets theory

Rockbursts have important influences on construction safety, so the risk assessment of rockburst intensity has great significance. Firstly, the depth of the rockburst, the uniaxial compressive strength, the stress concentration coefficients, the brittleness coefficients, and the elastic energy index are selected as the evaluation index. Secondly, an assessment model is developed based on the fuzzy variable theory. And the model is proposed to assess the rockburst intensity in the highway tunnel. Finally, the results demonstrate that the results derived from the proposed model are consistent with the current specifications; the accurate rate comes to 100%. The method can determine the risk level of rockburst intensity and provide an alternative scheme. Hence, the study can accurately present a new approach to assess the rockburst intensity in the future.

Hazard Assessment of Concrete Dam Cracks Based on Variable Fuzzy Sets and the Modified Analytic Hierarchy Process

Hazard Assessment of Concrete Dam Cracks Based on Variable Fuzzy Sets and the Modified Analytic Hierarchy Process

Electrical Fire Dynamic Risk Assessment for High‐Rise Buildings Based on Variable Fuzzy Set Theory and Bayesian Network

High‐rise buildings fires are far more harmful than ordinary fires. In this regard, fire risk assessment is an important way to control fire risk and reduce losses. This study presents a comprehensive model to electrical fire dynamic risk assessment of high‐rise buildings based on a Bayesian network (BN) and a variable fuzzy set theory (VFST). Firstly, electric system, safety management, and other factors were comprehensively analyzed based on three categories: hazard sources identification (HSI), fault tree (FT) analysis, and VFST. A high‐rise building electrical fire dynamic risk assessment model was established based on a BN. Secondly, the prior probability of BN root nodes was determined by VFST, and the conditional probability table (CPT) was determined by the analytic hierarchy process (AHP) and decomposition method. On that basis, the quantitative inference and sensitivity analysis can be performed on the electrical fire risks of high‐rise buildings in combination with the variable fuzzy Bayesian network (VFBN) inference. Finally, a high‐rise building in Wuhan, China, was used as an example for verification. The results show that the proposed method can realize dynamic risk assessment of electrical fires in high‐rise buildings. This study provides a new method for fire risk assessment of high‐rise buildings to reduce the possibility of fire.

Research on the Comprehensive Evaluation of Grouting Quality Based on Fuzzy Rock Engineering System and Variable Fuzzy Set Theory

Research on the Comprehensive Evaluation of Grouting Quality Based on Fuzzy Rock Engineering System and Variable Fuzzy Set Theory

A Three-Way Decision Approach for Water Resources System Resilience Evaluation and Its Application

Resilience is a significant uncertainty thought of water resources system security. Compared with risk analysis, resilience pays more attention to the ability of water resources system itself to deal with adverse events. However, a standard system of water resources system resilience’s concept and evaluation have not yet formed. In view of this, this study had attempted to decompose the process of resisting interference of water resources system and analyzed the characteristics and influencing factors of three sub processes of resistance, recovery and adaptation. Furtherly, a new resilience evaluation index system of water resources system was explored and a three-way dicision approach for water resources system resilience analysis based on variable fuzzy sets and partial connection number was developed. Specifically, a multi-grade quantitative evaluation of water resources resilience was carried out based on variable fuzzy sets method, and then the quantitative evaluation results were transformed into qualitative decision-making results using a new three-way decision model based on partial connection number of set pair analysis. Finally, a case study of China’s Yangtze River Economic Belt (YEB) in 2008–2017 was performed and the results show that the resilience of water resources system in the YEB does not show an obvious improvement trend, or even almost stagnant. Of the 110 samples, 83.6% were at the medium level. Only 6.4% are barely at the excellent level, but they are basically in Shanghai.

The risk assessment of landslide hazards in the Badong section of Three Gorges using the variable fuzzy set theory

The risk assessment of landslide hazards has a tremendous influence on people’s lives and property safety; therefore, its investigation is significant. The stratigraphic lithology, degree of weathering, relationship between the structural plane and slope direction, cohesive force, angle of internal friction, severity, average slope degree, height of slope, and type of landslide are adopted as the evaluation factors first. Second, an assessment model is developed based on the variable fuzzy set theory. In addition, the proposed model is utilized to assess the landslide hazards in the Badong section of Three Georges in China. Finally, the results demonstrate that the results derived from the proposed model are consistent with the current specifications; the accuracy rate reaches 83%. The method can determine the risk level of landslide hazards and provide an alternative scheme. Hence, this study can accurately present a new approach for assessing landslide hazards in the future.

Dynamic risk assessment of compound hazards based on VFS–IEM–IDM: a case study of typhoon–rainstorm hazards in Shenzhen, China

Abstract. Global warming has led to increased compound hazards, and an accurate risk assessment of such hazards is of great importance to urban emergency management. Due to the interrelations between multiple hazards, the risk assessment of a compound hazard faces several challenges: (1) the evaluation of hazard level needs to consider the correlations between compound hazard drivers, (2) usually only a small number of data samples are available for estimating the joint probability distribution of the compound hazard drivers and the loss caused by the hazards, and (3) the risk assessment process often ignores the temporal dynamics of compound hazard occurrences. This paper aims to address the mentioned challenges and develop an integrated risk assessment model VFS–IEM–IDM to quantify the dynamic risk of compound hazards based on variable fuzzy set theory (VFS), information entropy method (IEM), and information diffusion method (IDM). For the first challenge, VFS–IEM–IDM measures the effect of the compound hazard drivers via the use of relative membership degree and analyses the correlation between drivers with the entropy weight method, which is combined to evaluate compound hazard level. To address the second challenge, VFS–IEM–IDM applies the normal diffusion function to estimate the probability distribution of the compound hazard and the corresponding loss vulnerability curve. To deal with the third challenge, VFS–IEM–IDM assesses the risk of a compound hazard in different months based on the definition of probabilistic risk. In the end, this paper takes the typhoon–rainstorm disaster in Shenzhen, China, as an example to evaluate the effectiveness of the proposed VFS–IEM–IDM model. The results show that VFS–IEM–IDM effectively estimates the typhoon–rainstorm compound hazard level and assesses the dynamic risk of the compound hazards.

The Quality Assessment of Pavement Performance Using the Entropy Weight-Variable Fuzzy Sets Model

As the assessment of pavement performance has considerable repercussions for the construction quality of roads, the study of the assessment procedure used is extremely critical. Riding quality index (RQI), pavement condition index (PCI), pavement structure strength index (PSSI), skid resistance index (SRI), and antirutting index (ARI) are selected as the assessment indexes of pavement performance. Then, the entropy weight-variable fuzzy sets model is introduced. Second, a relative membership degree matrix for the variable fuzzy sets is established, and the entropy weight method is used to determine the weight coefficients considering the uncertainty in the assessment indices. Finally, the quality level of pavement performance is determined by using the mean ranking feature value. The conclusions demonstrate a very accurate rate for the quality assessment of the pavement performance based on the variable fuzzy sets model compared to that based on the current specification, and the proposed method is feasible for the quality assessment of pavement performance, thus providing a novel means of assessing the quality level of pavement performance in the future.

The Application of Variable Fuzzy Sets Theory on the Quality Assessment of Surrounding Rocks

The quality assessment of surrounding rocks has tremendous influences on engineering construction, so its investigation is significant. The uniaxial compressive strength of rocks σ c , the integrity coefficients of rock mass K V , the conditions of the structural plane S S , the seepage amount of groundwater W , and the intersection angle θ between the axis line and structural plane are selected as the quality assessment index of surrounding rocks at first. Then, the entropy weight-variable fuzzy sets model is introduced. Second, the relative membership degree matrix about the variable fuzzy sets is established, and the weight coefficients are determined based on the entropy weight method. Finally, the fracture behavior level of surrounding rocks is determined using the mean ranking feature value. The conclusions demonstrate that the results obtained based on the variable fuzzy sets method are consistent with the current specification; its accuracy arrives at 80%. Compared with the traditional way, its assessment process has higher reliability and efficiency. So, it could provide a new alternate way to assess the risk level in civil engineering accurately.

Security Check Mutual Recognition between High-Speed Railway and Urban Rail Transit Based on Variable Fuzzy Set Theory

At present, the secondary security check at the transfer station between high-speed railway and urban rail transit brings inconvenience to passengers. The aim of this study is to develop a methodology for evaluating the safety level of high-speed railway and subway stations by using variable fuzzy set theory, so as to determine the conditions for security check mutual recognition. In this research, considering transportation capacity, personnel and equipment, and environment and management, three aspects are considered to construct an evaluation index system for mutual recognition of high-speed railway and urban rail transit security check. Then, the variable fuzzy safety evaluation model has been established for high-speed railway and subway stations and their transport modes to analyse the feasibility of security check mutual recognition. Using the variable fuzzy set theory and the important consistency sorting theorem, the decision approach proposed in this study was tested for the high-speed rail station A and subway station B. As a result of using the methodology, the safety evaluation result of high-speed railway station A is 1.60, and the result of subway station B is 2.26. It is concluded that the safety of high-speed rail station A is higher than that of subway station B, and it is possible to enter the metro station without security check in one direction. The approach presented in this research can be used for judging the conditions for security check mutual recognition at interchange stations between high-speed railway and urban rail transit, which provides reference for the implementation of security check mutual recognition.

Coupling Variable Fuzzy Sets and Gini Coefficient to Evaluate the Spatial Equilibrium of Water Resources

Coupling Variable Fuzzy Sets and Gini Coefficient to Evaluate the Spatial Equilibrium of Water Resources

Evaluation on the Risk of Water Inrush Due to Roof Bed Separation Based on Improved Set Pair Analysis-Variable Fuzzy Sets.

To study and prevent bed separation water inrush accidents in coal mines, it is necessary to evaluate the risk according to the limited geological data correctly. In this work, based on hydrogeological and mining conditions, we established a risk evaluation model and selected seven important factors, including the aquifer thickness, aquifer water abundance, hydraulic pressure of the aquifer, effective aquifuge thickness, mining failure ratio, mining height of the working face, and advancing distance as evaluation indexes. The intuitionistic fuzzy analytic hierarchy process (IFAHP) and entropy weight method (EWM) were used to analyze the weights of the original data, and the minimum information entropy principle was used to further integrate the abovementioned calculation results. With the weight results, set pair analysis–variable fuzzy set (SPA-VFS) theory was applied to determine the risk grade of each working face, which provided scientific guidance for the safe mining of coal mines. For the working face where water inrush may occur, the risk of bed separation water inrush can be reduced by optimizing the parameters or changing the mining conditions through the model analysis.

Assessment of life loss due to dam breach using improved variable fuzzy method

In recent years, several factors, such as frequent extreme weather, disrepair of dams, and improper management, have caused frequent dam failures, posing a significant threat to people's lives downstream. At present, the life loss is evaluated using the empirical formula method, in which the recommended approximate and threshold results are obtained through linear regression or statistical analysis. However, this method is sometimes insufficient because of the lack of a historical dataset and low availability, and it tends to simplify or ignore the influence of some factors in regression. During the research, most objects are considered as individual cases, and thus, the universality and scientificity of the application of evaluation models or parameters need further discussion. The variable fuzzy set theory features rigorous mathematical clarity and fuzziness of things and is widely used in the optimal decision evaluation model. Although, the traditional variable fuzzy evaluation method is widely used to deal with the linear variation in the index, some indexes, such as dam storage capacity and downstream population at risk, can cause non-linear problems, directly affecting the accuracy of membership evaluation results. Therefore, an improved model was proposed, where the relative difference formula was improved through logarithmic transformation and boundary constraint. The improved method was applied to the sequencing of life loss risk consequences for four reservoirs. The evaluation result was consistent with the actual situation of the disaster and the actual mortality rate. The scientificity and practicability of the improved model were verified, providing a new perspective for reservoir risk ranking and enriching the risk management theory.

Flood risk assessment model combining hierarchy process and variable fuzzy set theory: a case study in Zhejiang province, China

Flood risk assessment model combining hierarchy process and variable fuzzy set theory: a case study in Zhejiang province, China