Search

Nanofiltration (NF) has become a widely used technology in water treatment due to its environmental friendliness, energy efficiency, cost-effectiveness, and operational simplicity. However, polyamide (PA) NF membranes still face challenges, including low permeate flux, limited resistance to organic pollutants, and inadequate resilience to residual chlorine. To address these issues, this study developed a thin-film composite (TFC) NF membrane featuring a separation layer of sandwich structure. Initially, a single separation layer of polyvinyl alcohol (PVA) NF membrane was prepared, followed by the fabrication of a PA layer on its surface, and ultimately, a second PVA layer was constructed on the PA layer. The experimental results show that the PVA/PA/PVA sandwich structure TFC exhibits high permeability to pure water and robust resistance to both pollution and residual chlorine. The PVA-0.20/PA/PVA-0.20 TFC, prepared with a 0.20%w/v PVA solution, achieved a pure water flux of up to 22.05 L m−2 h−1 bar−1 (LMH/bar), which was 2.92 times higher than that of the control TFC membrane. Additionally, it demonstrated a salt rejection rate exceeding 96% for Na2SO4 and over 99% for Congo Red (CR) and Victoria Blue B (VB). In comparison with the control TFC membrane, the PVA-0.20/PA/PVA-0.20 membrane exhibited significantly enhanced resistance to pollution. Following immersion in a 1000 ppm NaClO solution for 4 h, the rejection rate of the control TFC membrane decreased markedly and that of the PVA-0.20/PA/PVA-0.20 membrane decreased marginally, indicating excellent resistance to residual chlorine. Due to the robust overall performance of the PVA/PA/PVA membrane, it holds potential advantages for application in treating reclaimed water or slightly polluted water.

The high concentration of chloride ions in desulphurization wastewater is the primary limiting factor for its reusability. Monovalent anion selective electrodialysis (S-ED) enables the selective removal of chloride ions, thereby facilitating the reuse of desulfurization wastewater. In this study, different concentrations of NaCl and Na2SO4 were used to simulate different softened desulfurization wastewater. The effects of current density and NaCl and Na2SO4 concentration on ion flux, permselectivity (PSO42−Cl−) and specific energy consumption were studied. The results show that Selemion ASA membrane exhibits excellent permselectivity for Cl− and SO42−, with a significantly lower flux observed for SO42− compared to Cl−. Current density exerts a significant influence on ion flux; as the current density increases, the flux of SO42− also increases but at a lower rate than that of Cl−, resulting in an increase in permselectivity. When the current density reaches 25 mA/cm2, the permselectivity reaches a maximum of 50.4. The increase in NaCl concentration leads to a decrease in the SO42− flux; however, the permselectivity is reduced due to the elevated Cl−/SO42− ratio. The SO42− flux increases with the increase in Na2SO4 concentration, while the permselectivity increases with the decrease in Cl−/SO42− ratio.

Discount coefficient is an efficient method to address conflicting evidence combination in Dempster-Shafer evidence theory. However, how to determine the discount coefficient of each evidence is an open issue. In this paper, considering both the influence of the amount of information contained in the evidence itself and the fuzziness of the evidence based on the negation of basic belief assignment, a new discount coefficient is presented. The proposed discount coefficient is a fractional form. The numerator is Deng entropy, and the denominator is entropy difference between initial body of evidence (BOE) and its negation. The more information contained in the evidence, the more value is obtained. And the lower fuzziness of evidence, the less value is obtained. A numerical example is given to illustrate the application of this proposed method in the combination of highly conflicting evidence.

A multisensor system is used to improve the ability of monitoring and tracking accuracy of an engineering system since only one sensor is not enough, whereupon, faulty diagnosis, as a typical information fusion problem which is under multisensor environment, has attracted much attention in recent years. The evidence theory has been widely used to solve this problem. However, when there is a high level of conflict between the information gathered from different sensors, the counter-intuitive result could be obtained when using the classical Dempster’s combination rule. To address this problem, an improved multisensor data fusion method is proposed to fuse the data collected from multisensors. Some numerical examples are illustrated to show that the proposed method is effective and feasible. Moreover, the fusion results using different methods are analyzed, which indicate the superiority and stronger application of the proposed method in the field of fault diagnosis.

Dempster-Shafer evidence theory (D-S theory) is a developing theory to solve the uncertain problems and it has an important impact on many fields such as information fusion, expert systems, and machine learning. One of the main points of D-S theory is about how to generate a reliable basic belief assignment. Furthermore, the data collected from the multi-sources may be influenced by noise or other factors which cause conflicts in practical applications. Since the fuzzy number is useful to construct the target model for generating basic belief assignments, in this paper, an improved method to obtain basic belief assignment is proposed based on the triangular fuzzy number and k-means++ algorithm. First, the k-means++ clustering method is used to construct the target model. Then, the difference degree between the target model and sample model is calculated to generate the initial basic belief assignments. After that, the conflicts will be resolved by using the discount coefficient method. Finally, Dempster's combination rule is used to combine initial basic belief assignments to obtain the final result. The applications in recognition problems of the Iris data set and Wine Quality data set illustrate that the proposed method is effective to generate the basic belief assignments and keeps a high recognition rate even under a noisy environment.

Intuitionistic fuzzy sets (IFSs) are essential in the multi-criteria decision making (MCDM) under uncertain environment. However, how to reasonably aggregate them with considering the uncertainty contained in the IFSs is still an open issue. In this paper, a new method is proposed to solve such a problem based on the Dempster-Shafer evidence theory, belief entropy, and the weighted ordered weighted averaging (WOWA) operator. One of the advantages of the presented model is that the uncertainty contained in the IFSs is effectively modeled based on belief entropy and the conversion from the IFS to Dempster-Shafer evidence theory. In the framework of evidence theory, the uncertain information contained in the IFSs can be embodied effectively. Then, the belief entropy is calculated to determine the certainty weights for each IFS. With the various definitions of the regular increasing monotone (RIM) quantifier Q function, the preference relationship of a decision maker is considered. A numerical example is shown to illustrate the feasibility and effectiveness of the proposed method.

How to measure the similarity or distance between the basic probability assignment (BPA) in evidence theory is an open issue. The existing evidence distance function has the shortcoming that the cardinality of each subset is not reasonably considered. To address this issue, a new similarity coefficients matrix is presented to model the cardinality of each subset. Based on the proposed similarity coefficients matrix, a novel distance measure of belief function is presented. Some numerical examples are used to compare the proposed distance with existing evidence distance. The results show the new evidence distance has better performance. The application of the proposed measure in target recognition based on sensor data fusion illustrates the promising aspect of real engineering.

Evidence theory is widely used in information fusion. However, how to combine highly conflicting evidence is still an open issue. In this paper, a modified average method is proposed to address this issue based on the belief entropy and induced ordered weighted averaging operator. One of the advantages of the proposed method is that both the uncertainty and reliability of evidence are considered. In addition, it provides a right for the decision maker to combine the evidence based on the requirements for the precision of the results. A numerical example is shown to illustrate the use of the proposed method and an application based on sensor fusion in fault diagnosis is given to demonstrate the efficiency of our proposed method.

Time series data fusion has been widely used in practice and has received great attention in recent years. From the perspective of analyzing the correlation between data, this paper proposed a new accurate time series data fusion algorithm based on the decision making trial and evaluation laboratory (DEMATEL) model. With the analysis of various factors in DEMATEL and the combination of ordered weight aggregation operator (OWA) algorithms, the impact of time interval on the results of the fusion is reduced. The example given in this paper is a good illustration of the efficiency and feasibility of the new algorithm. We believe that the improvement work in this paper not only promotes the theoretical prediction of data fusion but also plays an important role in various fields.

Measuring the distance between two intuitionistic fuzzy sets (IFSs) is an open issue. Many types of distances for the IFSs have been proposed in previous studies. Some existing methods cannot satisfy the axioms of similarity or provide counterintuitive cases. Others ignore the relationship between three parameters characterizing the information carried by the IFS. To address these issues, a new distance is proposed by analyzing the similarity among the three parameters of the IFS. The comparison with some existing distances illustrates that the new distance has a higher sensitivity and can effectively measure the similarity between the IFSs. The results of the application of pattern recognition are also shown that the proposed method has better recognition ability.

The improvement in recognition accuracy of a multi-sensor system is inseparable from the sensors' dynamic reliability, especially in the case of highly conflicting information. Recent research on multi-sensor system has shown that a difficult problem for the system designer is to figure out what factors are crucial in determining the reliability of the sensor. However, the acquisition of sensor reliability is affected by multi-factors in practical applications. In this paper, a novel method for sensor dynamic reliability evaluation based on evidence theory and belief entropy has been developed, aimed at obtaining a reasonable reliability parameter. Through experimental analysis and practical applications, the results indicate that sensor weight distribution and information entropy value could be used as efficient elements for higher recognition rate to improve the robustness and recognition rate of the multi-sensor system.

Time series forecasting, especially from the perspective of the network, has been a hot research topic. In this paper, based on the analysis of complex network, a novel method is proposed for more accurate time series predictions. First, time series data are mapped into a network by visibility graph. Then, the link prediction method is adopted to calculate the similarity index. Considering that node distance is an important factor in the network, we take that into account to determine the weight coefficients and improve the predictive results. To fully verify the validity of the proposed method, it is applied to some representative time series data sets with different characteristics. The data values are recorded daily, monthly, and yearly. The error measurement and correlation analysis show that our method has a good prediction performance. It is believed that this paper will not only contribute to time series forecasting in theory but also take effect in practice.

Dynamic data fusion on time series plays an important role in real applications like target identification. The existing credibility decay models (CDM) may be too subjective for parameters setting and do not make full use of time series information. To address these issues, a new method based on visibility graph and Dempster-Shafer evidence theory are presented in this paper. With the assist of a visibility graph averaging aggregation operator (VGA), a structure revision basic belief assignment (SRBBA) which contains past time information can be obtained. Through this way, the judgment to past data credibility is data-driven without the interference of subjective factors and more reasonable because more time information is considered. Besides, a series of identification applications, including numerical simulation, sensitivity analysis, and practical Iris class identifying are executed to illustrate the efficiency of the proposed method. These applications can show that the proposed method has promising aspects in time series data fusion.

In the field of knowledge representation, negation has been introduced so that practical issues can be modelled more effectively. The negation of probability was first formally determined by Zadeh, with its basic properties proposed by Yager. Recent studies have extended the negation of probability to that of basic probability assignment (BPA) by introducing Dempster-Shafer theory which is believed to perform well in dealing with uncertainty problems. Besides, the negation model has been proved to have the maximum entropy allocation, which attracts studies on uncertainty measures that can be applied in the negation process. In this paper, we have mainly investigated the trend of dissimilarity between two BPAs in the negation process. In particular, an evidence distance proposed by Jousselme et al. is used to serve as a dissimilarity measure to help quantify the variation trends. Moreover, standard deviation is used in this study to represent the dispersion in a BPA. Through our analysis, we obtained some interesting properties finally with their generalizations discussed in a proposed framework of negation methods.

The existing approaches for fuzzy soft sets decision-making are mainly based on different types of level soft sets. How to deal with such kinds of fuzzy soft sets decision-making problems via decreasing the uncertainty resulting from human's subjective cognition is still an open issue. To address this issue, a hybrid method for utilizing fuzzy soft sets in decision-making by integrating a fuzzy preference relations analysis based on the belief entropy with the Dempster-Shafer evidence theory is proposed. The proposed method is composed of four procedures. First, we measure the uncertainties of parameters by leveraging the belief entropy. Second, with the fuzzy preference relations analysis, the uncertainties of parameters are modulated by making use of the relative reliability preference of parameters. Third, an appropriate basic probability assignment in terms of each parameter is generated on the modulated uncertainty degrees of parameters basis. Finally, we adopt Dempster's combination rule to fuse the independent parameters into an integrated one; thus, the best one can be obtained based on the ranking candidate alternatives. In order to validate the feasibility and effectiveness of the proposed method, a numerical example and a medical diagnosis application are implemented. From the experimental results, it is demonstrated that the proposed method outperforms the related methods, because the uncertainty resulting from human's subjective cognition can be reduced; meanwhile, the decision-making level can also be improved with better performance.

Dempster–Shafer evidence theory has been extensively applied in a variety of fields due to its ability to solve knowledge reasoning and decision-making problem under uncertain environments. Nevertheless, it is still an open issue about how to determine the basic probability assignment (BPA). In this paper, a new non-parametric method based on kernel density estimation is proposed to determine BPA. First, the probability density function of each attribute is calculated, which can be regarded as the probability model for the related attribute using the training sample. Then, a nested BPA function is constructed using the intersections point of test sample and probability models. Finally, Dempster’s combination rule is used to combine multiple BPAs to get the final BPA. Some classification experiments are conducted on several datasets. The experimental results demonstrate that the proposed method is more effective and reasonable in determining BPAs, which has a better classification performance than the existing method.

In human reliability analysis, dependence assessment is an important issue in risky large complex systems, such as operation of a nuclear power plant. Many existing methods depend on an expert's judgment, which contributes to the subjectivity and restrictions of results. Recently, a computational method, based on the Dempster–Shafer evidence theory and analytic hierarchy process, has been proposed to handle the dependence in human reliability analysis. The model can deal with uncertainty in an analyst's judgment and reduce the subjectivity in the evaluation process. However, the computation is heavy and complicated to some degree. The most important issue is that the existing method is in a positive aspect, which may cause an underestimation of the risk. In this study, a new evidential analytic hierarchy process dependence assessment methodology, based on the improvement of existing methods, has been proposed, which is expected to be easier and more effective.

Due to its efficiency to handle uncertain information, Dempster–Shafer evidence theory has become the most important tool in many information fusion systems. However, how to determine basic probability assignment, which is the first step in evidence theory, is still an open issue. In this article, a new method integrating interval number theory and k -means++ cluster method is proposed to determine basic probability assignment. At first, k -means++ clustering method is used to calculate lower and upper bound values of interval number with training data. Then, the differentiation degree based on distance and similarity of interval number between the test sample and constructed models are defined to generate basic probability assignment. Finally, Dempster’s combination rule is used to combine multiple basic probability assignments to get the final basic probability assignment. The experiments on Iris data set that is widely used in classification problem illustrated that the proposed method is effective in determining basic probability assignment and classification problem, and the proposed method shows more accurate results in which the classification accuracy reaches 96.7%.

Multisource information fusion has received much attention in the past few decades, especially for the smart Internet of Things (IoT). Because of the impacts of devices, the external environment, and communication problems, the collected information may be uncertain, imprecise, or even conflicting. How to handle such kinds of uncertainty is still an open issue. Complex evidence theory (CET) is effective at disposing of uncertainty problems in the multisource information fusion of the IoT. In CET, however, how to measure the distance among complex basis belief assignments (CBBAs) to manage conflict is still an open issue, which is a benefit for improving the performance in the fusion process of the IoT. In this paper, therefore, a complex Pignistic transformation function is first proposed to transform the complex mass function; then, a generalized betting commitment-based distance (BCD) is proposed to measure the difference among CBBAs in CET. The proposed BCD is a generalized model to offer more capacity for measuring the difference among CBBAs. Additionally, other properties of the BCD are analyzed, including the non-negativeness, nondegeneracy, symmetry, and triangle inequality. Besides, a basis algorithm and its weighted extension for multi-attribute decision-making are designed based on the newly defined BCD. Finally, these decision-making algorithms are applied to cope with the medical diagnosis problem under the smart IoT environment to reveal their effectiveness.

Sensor network–based application has gained increasing attention where data streams gathered from distributed sensors need to be processed and analyzed with timely responses. Distributed complex event processing is an effective technology to handle these data streams by matching of incoming events to persistent pattern queries. Therefore, a well-managed parallel processing scheme is required to improve both system performance and the quality-of-service guarantees of the system. However, the specific properties of pattern operators increase the difficulties of implementing parallel processing. To address this issue, a new parallelization model and three parallel processing strategies are proposed for distributed complex event processing systems. The effects of temporal constraints, for example, sliding windows, are included in the new parallelization model to enable the processing load for the overlap between windows of a batch induced by each input event to be shared by the downstream machines to avoid events that may result in wrong decisions. The proposed parallel strategies can keep the complex event processing system working stably and continuously during the elapsed time. Finally, the application of our work is demonstrated using experiments on the StreamBase system regardless of the increased input rate of the stream or the increased time window size of the operator.

Dempster−Shafer (DS) evidence theory is widely applied in multi-source data fusion technology. However, classical DS combination rule fails to deal with the situation when evidence is highly in conflict. To address this problem, a novel multi-source data fusion method is proposed in this paper. The main steps of the proposed method are presented as follows. Firstly, the credibility weight of each piece of evidence is obtained after transforming the belief Jenson−Shannon divergence into belief similarities. Next, the belief entropy of each piece of evidence is calculated and the information volume weights of evidence are generated. Then, both credibility weights and information volume weights of evidence are unified to generate the final weight of each piece of evidence before the weighted average evidence is calculated. Then, the classical DS combination rule is used multiple times on the modified evidence to generate the fusing results. A numerical example compares the fusing result of the proposed method with that of other existing combination rules. Further, a practical application of fault diagnosis is presented to illustrate the plausibility and efficiency of the proposed method. The experimental result shows that the targeted type of fault is recognized most accurately by the proposed method in comparing with other combination rules.

Time series data fusion is important in real applications such as target recognition based on sensors’ information. The existing credibility decay model (CDM) is not efficient in the situation when the time interval between data from sensors is too long. To address this issue, a new method based on the ordered weighted aggregation operator (OWA) is presented in this paper. With the improvement to use the Q function in the OWA, the effect of time interval on the final fusion result is decreased. The application in target recognition based on time series data fusion illustrates the efficiency of the new method. The proposed method has promising aspects in time series data fusion.

Failure Mode and Effects Analysis (FMEA) has been regarded as an effective analysis approach to identify and rank the potential failure modes in many applications. However, how to determine the weights of team members appropriately, with the impact factor of domain experts’ uncertainty in decision-making of FMEA, is still an open issue. In this paper, a new method to determine the weights of team members, which combines evidence theory, intuitionistic fuzzy sets (IFSs) and belief entropy, is proposed to analyze the failure modes. One of the advantages of the presented model is that the uncertainty of experts in the decision-making process is taken into consideration. The proposed method is data driven with objective and reasonable properties, which considers the risk of weights more completely. A numerical example is shown to illustrate the feasibility and availability of the proposed method.

The negation of probability provides a new way of looking at information representation. However, the negation of basic probability assignment (BPA) is still an open issue. To address this issue, a novel negation method of basic probability assignment based on total uncertainty measure is proposed in this paper. The uncertainty of non-singleton elements in the power set is taken into account. Compared with the negation method of a probability distribution, the proposed negation method of BPA differs becausethe BPA of a certain element is reassigned to the other elements in the power set where the weight of reassignment is proportional to the cardinality of intersection of the element and each remaining element in the power set. Notably, the proposed negation method of BPA reduces to the negation of probability distribution as BPA reduces to classical probability. Furthermore, it is proved mathematically that our proposed negation method of BPA is indeed based on the maximum uncertainty.

Bayesian update is widely used in data fusion. However, the information quality is not taken into consideration in classical Bayesian update method. In this paper, a new Bayesian update with information quality under the framework of evidence theory is proposed. First, the discounting coefficient is determined by information quality. Second, the prior probability distribution is discounted as basic probability assignment. Third, the basic probability assignments from different sources can be combined with Dempster’s combination rule to obtain the fusion result. Finally, with the aid of pignistic probability transformation, the combination result is converted to posterior probability distribution. A numerical example and a real application in target recognition show the efficiency of the proposed method. The proposed method can be seen as the generalized Bayesian update. If the information quality is not considered, the proposed method degenerates to the classical Bayesian update.

Conflict management in Dempster-Shafer theory (D-S theory) is a hot topic in information fusion. In this paper, a new weighted evidence combination on the basis of the distance between evidence and entropy function is presented. The proposed approach is identified as two procedures. First, the weight is determined based on the distance of evidence. Then, the obtained weight value in the first step is modified by making advantage of Deng entropy function. Our proposed method can efficiently cope with high conflicting evidences with better performance of convergence. A numerical example is provided to demonstrate that the proposed method is reasonable and efficient in the end.

Efficient matching of incoming events of data streams to persistent queries is fundamental to event stream processing systems in wireless sensor networks. These applications require dealing with high volume and continuous data streams with fast processing time on distributed complex event processing (CEP) systems. Therefore, a well-managed parallel processing technique is needed for improving the performance of the system. However, the specific properties of pattern operators in the CEP systems increase the difficulties of the parallel processing problem. To address these issues, a parallelization model and an adaptive parallel processing strategy are proposed for the complex event processing by introducing a histogram and utilizing the probability and queue theory. The proposed strategy can estimate the optimal event splitting policy, which can suit the most recent workload conditions such that the selected policy has the least expected waiting time for further processing of the arriving events. The proposed strategy can keep the CEP system running fast under the variation of the time window sizes of operators and the input rates of streams. Finally, the utility of our work is demonstrated through the experiments on the StreamBase system.

Dempster–Shafer evidence theory is widely applied in various fields related to information fusion. However, how to avoid the counter-intuitive results is an open issue when combining highly conflicting pieces of evidence. In order to handle such a problem, a weighted combination method for conflicting pieces of evidence in multi-sensor data fusion is proposed by considering both the interplay between the pieces of evidence and the impacts of the pieces of evidence themselves. First, the degree of credibility of the evidence is determined on the basis of the modified cosine similarity measure of basic probability assignment. Then, the degree of credibility of the evidence is adjusted by leveraging the belief entropy function to measure the information volume of the evidence. Finally, the final weight of each piece of evidence generated from the above steps is obtained and adopted to modify the bodies of evidence before using Dempster’s combination rule. A numerical example is provided to illustrate that the proposed method is reasonable and efficient in handling the conflicting pieces of evidence. In addition, applications in data classification and motor rotor fault diagnosis validate the practicability of the proposed method with better accuracy.

The multi-sensor data fusion technique plays a significant role in fault diagnosis and in a variety of such applications, and the Dempster–Shafer evidence theory is employed to improve the system performance; whereas, it may generate a counter-intuitive result when the pieces of evidence highly conflict with each other. To handle this problem, a novel multi-sensor data fusion approach on the basis of the distance of evidence, belief entropy and fuzzy preference relation analysis is proposed. A function of evidence distance is first leveraged to measure the conflict degree among the pieces of evidence; thus, the support degree can be obtained to represent the reliability of the evidence. Next, the uncertainty of each piece of evidence is measured by means of the belief entropy. Based on the quantitative uncertainty measured above, the fuzzy preference relations are applied to represent the relative credibility preference of the evidence. Afterwards, the support degree of each piece of evidence is adjusted by taking advantage of the relative credibility preference of the evidence that can be utilized to generate an appropriate weight with respect to each piece of evidence. Finally, the modified weights of the evidence are adopted to adjust the bodies of the evidence in the advance of utilizing Dempster’s combination rule. A numerical example and a practical application in fault diagnosis are used as illustrations to demonstrate that the proposal is reasonable and efficient in the management of conflict and fault diagnosis.

Sensor data fusion plays an important role in fault diagnosis. Dempster–Shafer (D-R) evidence theory is widely used in fault diagnosis, since it is efficient to combine evidence from different sensors. However, under the situation where the evidence highly conflicts, it may obtain a counterintuitive result. To address the issue, a new method is proposed in this paper. Not only the statistic sensor reliability, but also the dynamic sensor reliability are taken into consideration. The evidence distance function and the belief entropy are combined to obtain the dynamic reliability of each sensor report. A weighted averaging method is adopted to modify the conflict evidence by assigning different weights to evidence according to sensor reliability. The proposed method has better performance in conflict management and fault diagnosis due to the fact that the information volume of each sensor report is taken into consideration. An application in fault diagnosis based on sensor fusion is illustrated to show the efficiency of the proposed method. The results show that the proposed method improves the accuracy of fault diagnosis from 81.19% to 89.48% compared to the existing methods.