Relative Membership Degree Research Articles

Credit risk prediction based on an interpretable three-way decision method: Evidence from Chinese SMEs

Credit risk prediction can provide essential tools for use in commercial banking credit and credit-related decision-making. This paper proposes a three-way decision method based on prospect theory and evidence theory for predicting credit risk. The first problem in this study is determining the optimal classification boundary, and the second is effectively predicting the sample default status within an uncertain boundary. To address the limitation of the SVDD model, which is that it does not consider the aggregation degree, a new sample-weighted support vector data description (SW-SVDD) model is constructed by ranking samples according to their relative membership degree. The classification boundaries of the default and nondefault samples are determined according to the maximum prediction accuracy of the SW-SVDD model. The samples are divided into definite boundary nondefault, definite boundary default, and uncertain boundary samples. The default status of samples falling into definite boundaries is predicted by the SW-SVDD model. The three-way decision method combining prospect theory and evidence theory predicts the default status of samples falling into uncertain boundaries. This paper also proposes a new interpretability method based on the default probability, nondefault probability, and optimal threshold point obtained by the three-way decision model. The empirical results show that the proposed three-way decision method is a model that balances accuracy and interpretability. It has a higher classification performance than traditional models and can reveal the key features that lead to each customer's default. The proposed three-way decision method can enhance the accuracy and reliability of risk assessments, enabling financial institutions to make more informed lending decisions and more effectively manage credit portfolios.

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.

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.

Optimal Parameters of Gas Drainage and Carbon Dioxide Inerting Technology and Its Application in a High Gassy and Spontaneous Combustion Mine.

In the process of coupling disaster prevention and control of gas and coal spontaneous combustion in goaf, there is a great contradiction between the gas drainage and carbon dioxide inerting technology. The key performance indexes are put forward to solve the coupling disaster, such as the air quantity of the intake airway (A), the gas drainage rate (B), the carbon dioxide injection rate (C), and the injection depth (D). Using the numerical simulation method and the orthogonal test of four factors and three levels, we establish the coupling disaster model of the no. 7436 working face in the Kongzhuang coal mine. Using a combination of the relative membership degree method and range analysis, the optimal level of each factor is determined, which is AIIBIIICIIDII. Furthermore, the distribution law of the airflow field is obtained under the conditions of different gas drainage rates and carbon dioxide injection rates. The results show that the gas concentration decreases with an increase in gas drainage in the upper corner, but it has little impact on the width of the oxidation zone. The gas concentration can be reduced to 1%, while the gas drainage rate is higher than 35 m3/min. With an increase in gas injection rate, the carbon dioxide emission rate increases in the upper corner, but the width of the oxidation zone decreases. Also, the gas injection rate should be less than 800 m3/h. Moreover, with an increase in injection time in the upper corner during the injection process, the carbon dioxide and gas concentrations increase, and the maximum carbon dioxide concentration is 1.3%, and the maximum gas concentration is 0.42%, which is consistent with the results of numerical simulations.

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.

Development of Fuzzy Pattern Recognition Model for Underground Metal Mining Method Selection

Selection of underground metal mining method is a crucial task for the mining industry to excavate the ore deposit with proper safety and economy. The objective of the proposed study is to demonstrate the application of a fuzzy pattern recognition model for the decision-making of the most favourable underground metal mining method for a typical ore deposit. The model considers eight factors (shape, depth, dip, rock mass rating [RMR] of ore zone, RMR of footwall, RMR of hanging wall, thickness of the ore body, grade distribution), which influence the mining method, as input variables. The weights of these factors were determined using the analytic hierarchy process (AHP). The study used the pair-wise comparison method to determine the relative membership degrees of qualitative and quantitative criteria as well as weights of the criteria set. The model validation was done with the deposit characteristics of Uranium Corporation of India Limited (UCIL), Tummalapalle mine selected. The weighted distances for easiest to adopt are found to be 0.1436, 0.0230, 0.0497, 0.2085, 0.0952, 0.1228, and 0.1274, respectively, for block caving, sublevel stoping, sublevel caving, room and pillar, shrinkage stoping, cut and fill stoping, and squares set stoping. The results indicate that the room and pillar mining method is having the maximum weighted distance value for the given ore deposit characteristics and thus assigned the first rank. It was observed that the mining method selected using fuzzy pattern recognition model and the actual mining method adopted to extract the ore deposit are the same.

Evaluation of Precipitation Products by Using Multiple Hydrological Models over the Upper Yellow River Basin, China

In this study, 6 widely used precipitation products APHRODITE, CPC_UNI_PRCP, CN05.1, PERSIANN-CDR, Princeton Global Forcing (PGF), and TRMM 3B42 V7 (TMPA), were evaluated against gauge observations (CMA data) from 1998 to 2014, and applied to streamflow simulation over the Upper Yellow River basin (UYRB), using 4 hydrological models (DWBM, RCCC-WBM, GR4J, and VIC). The relative membership degree (u), as the comprehensive evaluation index in the hydrological evaluation, was calculated by the optimum fuzzy model. The results showed that the spatial pattern of precipitation from the CMA dataset and the other 6 precipitation products were very consistent with each other. The satellite-derived rainfall products (SDFE), like PSERSIANN-CDR and TMPA, depicted considerably finer and more detailed spatial heterogeneity. The SDFE and reanalysis (RA) products could estimate the monthly precipitation very well at both gauge and basin-average scales. The runoff simulation results indicated that the APHRODITE and TMPA were superior to the other 4 precipitation datasets, obtaining much higher scores, with average u values of 0.88 and 0.77. The precipitation estimation products tended to show better performance in streamflow simulation at the downstream hydrometric stations. In terms of performance of hydrological models, the RCCC–WBM model showed the best potential for monthly streamflow simulation, followed by the DWBM. It indicated that the monthly models were more flexible than daily conceptual or distributed models in hydrological evaluation of SDFE or RA products, and that the difference in precipitation estimates from various precipitation datasets were more influential in the GR4J and VIC models.

Research on the stiffness of Grillage Method in Virtual Cross Beam based on Fuzzy recognition

The stiffness of virtual cross beam is an important parameter which affects the calculation results when using beam grillage method to analyze the stress of bridge structure. In order to obtain a reasonable value of the stiffness about the virtual cross beam, it is necessary to make comparative analysis. On the basis of the comprehensive comparative analysis of the stress and deflection of the control section in hollow slab bridge and simply supported beam bridge with twin-box single cross section, the value range of the virtual cross beam stiffness is obtained. Based on the theory of fuzzy mathematics, a fuzzy recognition model for the stiffness of the virtual beam was proposed. By calculating the relative membership degree vector of the stiffness in each virtual beam, the length and width of the cross section of the virtual beam is obtained to be 0.7 times height of the beam. In order to further verify the reasonable of the value, the stress and deflection values of the control section have been compared. These values are taken from the single-box and double-chamber plexiglass box girder model and highway single-box three-chamber box beam. The compared results show that the solution of the grillage model with the stiffness of the virtual beam in this paper is in good agreement with shell solutions and solid solutions.

Evaluation of Dam Break Social Impact Assessments Based on an Improved Variable Fuzzy Set Model

In recent years attention has shifted from “dam safety” to “dam risk” due to the high loss characteristics of dam breaks. Despite this, there has been little research on social impact assessments. Variable fuzzy sets (VFSs) are a theoretical system for dealing with uncertainty that are used in many industries. However, the relative membership degree (RMD) calculations required for VFSs are complicated and data can be overlooked. Furthermore, the RMD is highly subjective when dealing with qualitative problems, which can seriously affect the accuracy of the results. This study introduces grey system theory (GST) which analyzes the RMD characteristics to improve traditional VFSs. A new method for calculating the social impact of a dam break is proposed based on the correlation between the core parameters of the two theories. The Liujiatai Reservoir is used as a test case and the new and traditional evaluation methods are compared. The results show that the proposed method has advantages when dealing with uncertainty that are consistent with the characteristics of the problems associated with dam break social impact assessments. Moreover, the evaluation results obtained using the proposed method are consistent with, or more accurate than, those obtained using the traditional method.

Risk Evaluation Based on Variable Fuzzy Sets and Information Diffusion Method

Risk evaluation is an effective way to reduce the impacts of natural hazards and it plays an increasingly important role in emergency management. Traditional methods of assessing risks mainly utilize Geographic Information System (GIS) to get risk map, and information diffusion method (IDM) to deal with incomplete data sets. However, there are few papers discuss the uncertainty of integrated hazards and consider dynamic risk under time dimension. The model proposed in this study combines the variable fuzzy set theory with information diffusion method (VFS-IDM) to solve the uncertainness of multiple hazards dynamic risk assessment when data sets are incomplete. This study employs fuzzy set theory (VFS) to calculate the relative membership degree and applies information entropy method (IEM) to obtain the weights of criteria indicators for multiple hazards evaluation. Then applies information diffusion method (IDM) to estimate condition probability distribution and vulnerability curve with the VFS-IEM model results, time data and multiple hazards losses. Then the expected value of multiple hazards dynamic risk can be calculated by using the normal information diffusion estimator so as to improve the accuracy of risk evaluation results.

Set Pair Analysis based on Similar Forecast model of Civil car ownership

It shows the important meaning that the accurate prediction of civil car ownership. The most important factor of civil car ownership are gotten from set pair analysis and correlation coefficient. Set pair analysis method can be used to quantificationally compute the similarity between main physics vectors from the view of identical, different and opposite sides. According to the weighted average of relative membership degree, obtain the set pair analysis based on similarity forecast model of civil car ownership, named SPA-SF. The forecast result of civil car ownership of 2015-2017 show that SPA-SF has certain application value in the prediction of civil car ownership.

An Algorithmic Model Building Scheme Based on Dynamic Programming Algorithms

Dynamic programming algorithm is a basic tool for solving multi-level decision-making problems, which is widely used in social economy, engineering technology and optimal control. Aiming at the incommensurability of multi-objective programming indices, the relative membership degree matrix of allocation schemes for quantitative and qualitative indices is established, and the analysis method of multi-objective and multi-stage dynamic programming problems is given by using vector and matrix unification. The decision maker determines the decision coefficients of each constraint indicator according to the specific problem and performs weighting processing. The weights of different state variables for different constraint indicators are integrated, the comprehensive weights of state variables are solved, and the original static constraint indicators are transformed into dynamic variables that can influence the decision results. The research shows that the algorithm transforms the multi-stage decision problem into a single-stage decision problem, and solves the optimal value of the expected value through the mixture of random expectation models in a single stage. As long as it is used properly, dynamic planning of this traditional method can be a better way to solve complex problems.

Comprehensive Prediction and Discriminant Model for Rockburst Intensity Based on Improved Variable Fuzzy Sets Approach

Rockburst intensity prediction is one of the basic works of underground engineering disaster prevention and mitigation. Considering the dynamic variability and fuzziness in rockburst intensity prediction, variable fuzzy sets (VFS) are selected for evaluation and prediction. Here, there are two problems in the application of traditional VFS: (i) the relative membership degree (RMD) calculation process is complex and time-consuming, and the RMD matrix of all indexes can be only obtained by using the RMD function repeatedly; (ii) unreasonable weights of indicators have great impact on the synthetic relative membership degree (SRMD), so it is difficult to guarantee the correctness of the final prediction result. In view of the above problem, this paper established three simplified feature relationship expressions of RMD based on VFS principle and used the SRMD function to establish a BP neural network model to optimize SRMD. The improved VFS method is more efficient and the prediction results are more stable and reliable than the traditional VFS method. The main advantages are as follows: (1) the improved VFS method has higher computational efficiency; (2) the improved VFS method can verify the correctness of RMD at all times; (3) the improved VFS method has higher prediction accuracy; and (4) the improved VFS method has higher fault tolerance and practicability.

A new method of the relative membership degree calculation in variable fuzzy sets for water quality assessment

The wide application of variable fuzzy sets theory (VFST) in water quality evaluation indicates that the calculation process of relative membership degree (RMD) is complicated and laborious. The traditional method of calculating RMD repeatedly reuses the relative membership degree function (RMDF), and lacks an effective means to estimate the reliability of the calculation. These problems increase the difficulty of water quality evaluation. Based on the principle of variable fuzzy sets, this research finds some data characteristics of RMD and further demonstrates its inevitability. A new method was developed using a combination of these data characteristics and the traditional method of RMD calculation. By empirical analysis of water quality evaluation, the new method exhibited stable reliability and efficient performance compared with the traditional method. The primary advantages include the following: (i) simplification of the calculation of RMD and reduction in the computation burden for RMDF, (ii) verification of the calculation result of RMD and development of a scientific basis for testing evaluation results, and (iii) improvement of the calculation accuracy of RMD.

Multi-Index Evaluation for Flood Disaster from Sustainable Perspective: A Case Study of Xinjiang in China.

The floods have undermined the sustainable construction of cities because of their sudden and destruction. To reduce the losses caused by floods, it is necessary to make a reasonable evaluation for historical floods and provide scientific guidance for future precaution. Previous research mainly used subjective/objective weights or barely made static analysis without considering the uncertainty and ambiguity of floods. Therefore, this study proposed a variable fuzzy recognition model, based on combined weights, to evaluate floods, including the determination of index weights and the choice of evaluation model. To make the index weights reflect both subjective experience and objective data, the combined weights were proposed and calculated based on the principle of minimum identification information. Then, the relative membership degree matrix and evaluation results can be worked out by the variable fuzzy recognition model. Conclusions indicated that the combined weights were more convincing than simply subjective or objective weights. Moreover, the variable fuzzy recognition model, by changing model parameters, got stable evaluation results of the sample data. Therefore, the model can improve the credibility of evaluation and the conclusions can provide reasonable suggestions for management departments.

AIS Data-based Decision Model for Navigation Risk in Sea Areas

The safety of maritime transportation has become increasingly important in recent decades. In this paper, a decision model (a multi-objective and multi-layer fuzzy optimisation model) for navigation risk in different sea areas is established. This is done according to the evaluation index system based on relative data extracted and analysed from Automatic Identification Systems (AIS) information and the multi-objective and multi-layer fuzzy optimisation theory. Then, sorted by an optimal relative membership degree vector and calculated from lower layer to higher layer, the sea areas which have higher navigation risk are selected. Finally, the decision model is shown to be scientific and practical since the results from it are basically consistent with real traffic in Chengshantou waters and the results from the fuzzy comprehensive evaluation model. With the decision model, navigation risk judgments in different sea areas can be offered. It can also provide decision making references to the design of ship routing systems, the layout of search and rescue sites, the configuration of rescue forces and the administration of navigation safety.

Relative Membership Degree Method for Fuzzy Multi-attribute Decision-making with Preference Information on Alternatives

The fuzzy multi-attribute decision-making (FMADM) problem that the attribute weights are interval numbers and the decision maker (DM) has avail preference information on alternatives is investigated. Firstly, a quadratic programming model based on the minimum sum of deviation squares between the subjective and objective decision-making preference information on alternatives is established, the attribute weights are obtained by solving the model and thus the overall values of every alternative are gained by using the additive weighting method. Secondly, The fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) of alternatives are introduced. Based on fuzzy sets theory, the relative membership degree of every alternative is obtained by means of the distance to which an alternative corresponds to the FPIS and FNIS, the alternatives are ranked by using the relative membership. The method not only avoids comparing for fuzzy numbers, but also has the advantages of simple operation and easy calculation. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Fuzzy Multi-objective Optimization of EMT Based on the Minimum Average Weighted Deviation Algorithm

The optimal control of the vehicles with electro-mechanical transmission is a problem of multi-objective optimization. In this paper, based on the working characteristics of the engine, the battery pack and the motor/generators (MGs) as well as their interactions, a multi-objective optimization model with the optimal objective functions which include drivability, electric supply performance and fuel consumption is established. Using the relative membership degree formulas, the multi-objective optimization is transformed to fuzzy multi-objective optimization, and the problem of multi-objective optimization is converted to single-objective optimization with the corresponding weights of the objective functions gained by the minimum average weighted deviation algorithm. The forward model based on Matlab is implemented. Compared with the rule-based method, this method had enabled the drivability, the electric supply performance and the fuel consumption to improve by 29.8%, 38.1% and 11.8%, respectively.

Multimedia Image Mining Method Based on Fuzzy Pixels Difference Iterative Clustering

The traditional multimedia image mining based on association rules, has a big flaw in mining time, thus a multimedia image mining method based on fuzzy pixel difference iterative clustering is proposed. In this method, multimedia image index characteristic value is converted into relative membership degree for fuzzy concept index. On the basis of the multimedia image samples and fuzzy pixel difference comprehensive tradeoff metric equations of different types, the Lagrange function is constructed to acquire fuzzy pixel difference iterative clustering loop iteration model. The model is adopted to analyze average divergence inside the cluster and average separation degree between clusters and choose the optimal clustering number value, so as to achieve mining of multimedia image. The results of simulation experiment show that the mining time and energy consumption of the proposed method are better than the traditional method, and the proposed method has a high value of application. Keywords: Fuzzy pixels, difference iterative clustering, multimedia image, mining.