A modified combination rule in generalized evidence theory

Multisensor Data Fusion in IoT Environments in Dempster-Shafer Theory Setting: An Improved Evidence Distance-Based Approach

In IoT environments, voluminous amounts of data are produced every single second. Due to multiple factors, these data are prone to various imperfections, they could be uncertain, conflicting, or even incorrect leading to wrong decisions. Multisensor data fusion has proved to be powerful for managing data coming from heterogeneous sources and moving towards effective decision-making. Dempster-Shafer (D-S) theory is a robust and flexible mathematical tool for modeling and merging uncertain, imprecise, and incomplete data, and is widely used in multisensor data fusion applications such as decision-making, fault diagnosis, pattern recognition, etc. However, the combination of contradictory data has always been challenging in D-S theory, unreasonable results may arise when dealing with highly conflicting sources. In this paper, an improved evidence combination approach is proposed to represent and manage both conflict and uncertainty in IoT environments in order to improve decision-making accuracy. It mainly relies on an improved evidence distance based on Hellinger distance and Deng entropy. To demonstrate the effectiveness of the proposed method, a benchmark example for target recognition and two real application cases in fault diagnosis and IoT decision-making have been provided. Fusion results were compared with several similar methods, and simulation analyses have shown the superiority of the proposed method in terms of conflict management, convergence speed, fusion results reliability, and decision accuracy. In fact, our approach achieved remarkable accuracy rates of 99.32% in target recognition example, 96.14% in fault diagnosis problem, and 99.54% in IoT decision-making application.

Prediction of rock burst intensity based on multi-source evidence weight and error-eliminating theory

Rock burst is the main geological hazard in deep underground engineering. For the prediction of the intensity of rock burst, a model for prediction of rock burst intensity on the basis of multi-source evidence weight and error-eliminating theory was established. Four indexes including the ratio of rock's compressive-tensile strength [Formula: see text], the stress coefficient of rock [Formula: see text], the elastic energy index of rock Wet, and integrality coefficient Kv were chosen as the prediction variables of rock burst; the index weights are calculated by different weighting methods and fused with evidence theory to determine the final weight of each index. According to the theory of error-eliminating, taking "no rock burst" (I in classification standards of rock burst intensity) as the objective and using the error function to process 18 sets of typical rock burst data and the weight of evidence fusion as the normalized index limit loss value, a model for prediction of rock burst intensity was built. It is verified by the actual situation and three other models. Finally, the model has been applied to rock burst prediction of Zhongnanshan tunnel ventilation shaft. The results show that evidence theory fuses multi-source index weights and improves the method of determining index weights. The index value is processed by error-eliminating theory, and the limit value problem of index value normalization is optimized. The predicted results of the proposed model are consistent with the situation of Zhongnanshan tunnel. It improves the objectivity of the rock burst prediction process and provides a research idea for rock burst intensity prediction index.

A new correlation belief function in Dempster-Shafer evidence theory and its application in classification

Uncertain information processing is a key problem in classification. Dempster-Shafer evidence theory (D-S evidence theory) is widely used in uncertain information modelling and fusion. For uncertain information fusion, the Dempster's combination rule in D-S evidence theory has limitation in some cases that it may cause counterintuitive fusion results. In this paper, a new correlation belief function is proposed to address this problem. The proposed method transfers the belief from a certain proposition to other related propositions to avoid the loss of information while doing information fusion, which can effectively solve the problem of conflict management in D-S evidence theory. The experimental results of classification on the UCI dataset show that the proposed method not only assigns a higher belief to the correct propositions than other methods, but also expresses the conflict among the data apparently. The robustness and superiority of the proposed method in classification are verified through experiments on different datasets with varying proportion of training set.

A New Reliability Coefficient Using Betting Commitment Evidence Distance in Dempster-Shafer Evidence Theory for Uncertain Information Fusion

Dempster-Shafer evidence theory is widely used to deal with uncertain information by evidence modeling and evidence reasoning. However, if there is a high contradiction between different pieces of evidence, the Dempster combination rule may give a fusion result that violates the intuitive result. Many methods have been proposed to solve conflict evidence fusion, and it is still an open issue. This paper proposes a new reliability coefficient using betting commitment evidence distance in Dempster-Shafer evidence theory for conflict and uncertain information fusion. The single belief function for belief assignment in the initial frame of discernment is defined. After evidence preprocessing with the proposed reliability coefficient and single belief function, the evidence fusion result can be calculated with the Dempster combination rule. To evaluate the effectiveness of the proposed uncertainty measure, a new method of uncertain information fusion based on the new evidence reliability coefficient is proposed. The experimental results on UCI machine learning data sets show the availability and effectiveness of the new reliability coefficient for uncertain information processing.

Situation assessment in air combat considering incomplete frame of discernment in the generalized evidence theory

For situation assessment in air combat, there may be incomplete information because of new technologies and unknown or uncertain targets and threats. In this paper, an improved method of situation assessment for air combat environment considering incomplete frame of discernment in the evidence theory is proposed to get a more accurate fusion result for decision making in the battlefield environment. First, the situation in air combat is assessed with knowledge. Then, the incomplete frame of discernment in the generalized evidence theory, which is an extension of Dempster-Shafer evidence theory, is adopted to model the incomplete and unknown situation assessment. After that, the generalized combination rule in the generalized evidence theory is adopted for fusion of situations in intelligent air combat. Finally, real-time decision-making in situation assessment can be reached for actions to take. Experiments in situation assessment of air combat with incomplete and uncertain situations show the rationality and effectiveness of the proposed method.

Dynamic probability integration for electroencephalography-based rapid serial visual presentation performance enhancement: Application in nighttime vehicle detection

Background

Rapid serial visual presentation (RSVP) has become a popular target detection method by decoding electroencephalography (EEG) signals, owing to its sensitivity and effectiveness. Most current research on EEG-based RSVP tasks focused on feature extraction algorithms developed to deal with the non-stationarity and low signal-to-noise ratio (SNR) of EEG signals. However, these algorithms cannot handle the problem of no event-related potentials (ERP) component or miniature ERP components caused by the attention lapses of human vision in abnormal conditions. The fusion of human-computer vision can obtain complementary information, making it a promising way to become an efficient and general way to detect objects, especially in attention lapses.

Methods

Dynamic probability integration (DPI) was proposed in this study to fuse human vision and computer vision. A novel basic probability assignment (BPA) method was included, which can fully consider the classification capabilities of different heterogeneous information sources for targets and non-targets and constructs the detection performance model for the weight generation based on classification capabilities. Furthermore, a spatial-temporal hybrid common spatial pattern-principal component analysis (STHCP) algorithm was designed to decode EEG signals in the RSVP task. It is a simple and effective method of distinguishing target and non-target using spatial-temporal features.

Results

A nighttime vehicle detection based on the RSVP task was performed to evaluate the performance of DPI and STHCP, which is one of the conditions of attention lapses because of its decrease in visual information. The average AUC of DPI was 0.912 ± 0.041 and increased by 11.5, 5.2, 3.4, and 1.7% compared with human vision, computer vision, naive Bayesian fusion, and dynamic belief fusion (DBF), respectively. A higher average balanced accuracy of 0.845 ± 0.052 was also achieved using DPI, representing that DPI has the balanced detection capacity of target and non-target. Moreover, STHCP obtained the highest AUC of 0.818 ± 0.06 compared with the other two baseline methods and increased by 15.4 and 23.4%.

Conclusion

Experimental results indicated that the average AUC and balanced accuracy of the proposed fusion method were higher than individual detection methods used for fusion, as well as two excellent fusion methods. It is a promising way to improve detection performance in RSVP tasks, even in abnormal conditions.

Multi-Source Information Fusion Based on Negation of Reconstructed Basic Probability Assignment with Padded Gaussian Distribution and Belief Entropy

Multi-source information fusion is widely used because of its similarity to practical engineering situations. With the development of science and technology, the sources of information collected under engineering projects and scientific research are more diverse. To extract helpful information from multi-source information, in this paper, we propose a multi-source information fusion method based on the Dempster-Shafer (DS) evidence theory with the negation of reconstructed basic probability assignments (nrBPA). To determine the initial basic probability assignment (BPA), the Gaussian distribution BPA functions with padding terms are used. After that, nrBPAs are determined by two processes, reassigning the high blur degree BPA and transforming them into the form of negation. In addition, evidence of preliminary fusion is obtained using the entropy weight method based on the improved belief entropy of nrBPAs. The final fusion results are calculated from the preliminary fused evidence through the Dempster's combination rule. In the experimental section, the UCI iris data set and the wine data set are used for validating the arithmetic processes of the proposed method. In the comparative analysis, the effectiveness of the BPA determination using a padded Gaussian function is verified by discussing the classification task with the iris data set. Subsequently, the comparison with other methods using the cross-validation method proves that the proposed method is robust. Notably, the classification accuracy of the iris data set using the proposed method can reach an accuracy of 97.04%, which is higher than many other methods.

Hierarchical Analysis Process for Belief Management in Internet of Drones

Group awareness is playing a major role in the efficiency of mission planning and decision-making processes, particularly those involving spatially distributed collaborative entities. The performance of this concept has remarkably increased with the advent of the Internet of Things (IoT). Indeed, a myriad of innovative devices are being extensively deployed to collaboratively recognize and track events, objects, and activities of interest. A wide range of IoT-based approaches have focused on representing and managing shared information through formal operators for group awareness. However, despite their proven results, these approaches are still refrained by the inaccuracy of information being shared between the collaborating distributed entities. In order to address this issue, we propose in this paper a new belief-management-based model for a collaborative Internet of Drones (IoD). The proposed model allows drones to decide the most appropriate operators to apply in order to manage the uncertainty of perceived or received information in different situations. This model uses Hierarchical Analysis Process (AHP) with Subjective Logic (SL) to represent and combine opinions of different sources. We focus on purely collaborative drone networks where the group awareness will also be provided as service to collaborating entities.

A Methodology to Generate Integrated Land Cover Data for Land Surface Model by Improving Dempster-Shafer Theory

Land cover type is a key parameter for simulating surface processes in many land surface models (LSMs). Currently, the widely used global remote sensing land cover products cannot meet the requirements of LSMs for classification systems, physical definition, data accuracy, and space-time resolution. Here, a new fusion method was proposed to generate land cover data for LSMs by fusing multi-source remote sensing land cover data, which was based on improving Dempster-Shafer evidence theory with mathematical models and knowledge rules optimization. The new method has the ability to deal with seriously disagreement information, thereby improving the robustness of the theory. The results showed the new method can reduce the disagreement between input data and realized the conversion of multiple land cover classification systems to into a single land cover classification system. China Fusion Land Cover data (CFLC) in 2015 generated by the new method maintained the classification accuracy of the China land use map (CNLULC), which is based on visual image interpretation and further enriched land cover classes of input data. Compared with Geo-Wiki observations in 2015, the overall accuracy for CFLC is higher than other two global land cover data. Compared with the observations, the 0–10 cm soil moisture simulated by the CFLC in Noah–MP LSM during the growing season in 2014 had better performance than that simulated by initial land cover data and MODIS land cover data. Our new method is highly portable and generalizable to generate higher quality land cover data with a specific land cover classification system for LSMs by fusing multiple land cover data, providing a new approach to land cover mapping for LSMs.

A New Total Uncertainty Measure from A Perspective of Maximum Entropy Requirement

The Dempster-Shafer theory (DST) is an information fusion framework and widely used in many fields. However, the uncertainty measure of a basic probability assignment (BPA) is still an open issue in DST. There are many methods to quantify the uncertainty of BPAs. However, the existing methods have some limitations. In this paper, a new total uncertainty measure from a perspective of maximum entropy requirement is proposed. The proposed method can measure both dissonance and non-specificity in BPA, which includes two components. The first component is consistent with Yager's dissonance measure. The second component is the non-specificity measurement with different functions. We also prove the desirable properties of the proposed method. Besides, numerical examples and applications are provided to illustrate the effectiveness of the proposed total uncertainty measure.

Conflict Data Fusion in a Multi-Agent System Premised on the Base Basic Probability Assignment and Evidence Distance

The multi-agent information fusion (MAIF) system can alleviate the limitations of a single expert system in dealing with complex situations, as it allows multiple agents to cooperate in order to solve problems in complex environments. Dempster–Shafer (D-S) evidence theory has important applications in multi-source data fusion, pattern recognition, and other fields. However, the traditional Dempster combination rules may produce counterintuitive results when dealing with highly conflicting data. A conflict data fusion method in a multi-agent system based on the base basic probability assignment (bBPA) and evidence distance is proposed in this paper. Firstly, the new bBPA and reconstructed BPA are used to construct the initial belief degree of each agent. Then, the information volume of each evidence group is obtained by calculating the evidence distance so as to modify the reliability and obtain more reasonable evidence. Lastly, the final evidence is fused with the Dempster combination rule to obtain the result. Numerical examples show the effectiveness and availability of the proposed method, which improves the accuracy of the identification process of the MAIF system.

An Improved Approach of Incomplete Information Fusion and Its Application in Sensor Data-Based Fault Diagnosis

The Dempster–Shafer evidence theory has been widely used in the field of data fusion. However, with further research, incomplete information under the open world assumption has been discovered as a new type of uncertain information. The classical Dempster’s combination rules are difficult to solve the related problems of incomplete information under the open world assumption. At the same time, partial information entropy, such as the Deng entropy is also not applicable to deal with problems under the open world assumption. Therefore, this paper proposes a new method framework to process uncertain information and fuse incomplete data. This method is based on an extension to the Deng entropy in the open world assumption, negation of basic probability assignment (BPA), and the generalized combination rule. The proposed method can solve the problem of incomplete information under the open world assumption, and obtain more uncertain information through the negative processing of BPA, which improves the accuracy of the results. The results of applying this method to fault diagnosis of electronic rotor examples show that, compared with the other uncertain information processing and fusion methods, the proposed method has wider adaptability and higher accuracy, and is more conducive to practical engineering applications.

An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion

The Dempster–Shafer evidence theory has been widely applied in the field of information fusion. However, when the collected evidence data are highly conflicting, the Dempster combination rule (DCR) fails to produce intuitive results most of the time. In order to solve this problem, the base belief function is proposed to modify the basic probability assignment (BPA) in the exhaustive frame of discernment (FOD). However, in the non-exhaustive FOD, the mass function value of the empty set is nonzero, which makes the base belief function no longer applicable. In this paper, considering the influence of the size of the FOD and the mass function value of the empty set, a new belief function named the extended base belief function (EBBF) is proposed. This method can modify the BPA in the non-exhaustive FOD and obtain intuitive fusion results by taking into account the characteristics of the non-exhaustive FOD. In addition, the EBBF can degenerate into the base belief function in the exhaustive FOD. At the same time, by calculating the belief entropy of the modified BPA, we find that the value of belief entropy is higher than before. Belief entropy is used to measure the uncertainty of information, which can show the conflict more intuitively. The increase of the value of entropy belief is the consequence of conflict. This paper also designs an improved conflict data management method based on the EBBF to verify the rationality and effectiveness of the proposed method.

Improved Base Belief Function-Based Conflict Data Fusion Approach Considering Belief Entropy in the Evidence Theory

Due to the nature of the Dempster combination rule, it may produce results contrary to intuition. Therefore, an improved method for conflict evidence fusion is proposed. In this paper, the belief entropy in D–S theory is used to measure the uncertainty in each evidence. First, the initial belief degree is constructed by using an improved base belief function. Then, the information volume of each evidence group is obtained through calculating the belief entropy which can modify the belief degree to get the final evidence that is more reasonable. Using the Dempster combination rule can get the final result after evidence modification, which is helpful to solve the conflict data fusion problems. The rationality and validity of the proposed method are verified by numerical examples and applications of the proposed method in a classification data set.

A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy

Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.

A Novel Evidence Theory and Fuzzy Preference Approach-Based Multi-Sensor Data Fusion Technique for Fault Diagnosis

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.

Fuzzy Risk Evaluation in Failure Mode and Effects Analysis Using a D Numbers Based Multi-Sensor Information Fusion Method

Failure mode and effect analysis (FMEA) is a useful tool to define, identify, and eliminate potential failures or errors so as to improve the reliability of systems, designs, and products. Risk evaluation is an important issue in FMEA to determine the risk priorities of failure modes. There are some shortcomings in the traditional risk priority number (RPN) approach for risk evaluation in FMEA, and fuzzy risk evaluation has become an important research direction that attracts increasing attention. In this paper, the fuzzy risk evaluation in FMEA is studied from a perspective of multi-sensor information fusion. By considering the non-exclusiveness between the evaluations of fuzzy linguistic variables to failure modes, a novel model called D numbers is used to model the non-exclusive fuzzy evaluations. A D numbers based multi-sensor information fusion method is proposed to establish a new model for fuzzy risk evaluation in FMEA. An illustrative example is provided and examined using the proposed model and other existing method to show the effectiveness of the proposed model.

A Time-Space Domain Information Fusion Method for Specific Emitter Identification Based on Dempster-Shafer Evidence Theory

Specific emitter identification plays an important role in contemporary military affairs. However, most of the existing specific emitter identification methods haven’t taken into account the processing of uncertain information. Therefore, this paper proposes a time–space domain information fusion method based on Dempster–Shafer evidence theory, which has the ability to deal with uncertain information in the process of specific emitter identification. In this paper, radars will generate a group of evidence respectively based on the information they obtained, and our main task is to fuse the multiple groups of evidence to get a reasonable result. Within the framework of recursive centralized fusion model, the proposed method incorporates a correlation coefficient, which measures the relevance between evidence and a quantum mechanical approach, which is based on the parameters of radar itself. The simulation results of an illustrative example demonstrate that the proposed method can effectively deal with uncertain information and get a reasonable recognition result.

A Novel Single-Valued Neutrosophic Set Similarity Measure and Its Application in Multicriteria Decision-Making

The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems. The key to using neutrosophic sets in decision-making applications is to make a similarity measure between single-valued neutrosophic sets. In this paper, a new method to measure the similarity between single-valued neutrosophic sets using Dempster–Shafer evidence theory is proposed, and it is applied in multicriteria decision-making. Finally, some examples are given to show the reasonable and effective use of the proposed method.

A Reliability-Based Method to Sensor Data Fusion

Multi-sensor data fusion technology based on Dempster–Shafer evidence theory is widely applied in many fields. However, how to determine basic belief assignment (BBA) is still an open issue. The existing BBA methods pay more attention to the uncertainty of information, but do not simultaneously consider the reliability of information sources. Real-world information is not only uncertain, but also partially reliable. Thus, uncertainty and partial reliability are strongly associated with each other. To take into account this fact, a new method to represent BBAs along with their associated reliabilities is proposed in this paper, which is named reliability-based BBA. Several examples are carried out to show the validity of the proposed method.

Evidence conflict measure based on OWA operator in open world

Dempster-Shafer evidence theory has been extensively used in many information fusion systems since it was proposed by Dempster and extended by Shafer. Many scholars have been conducted on conflict management of Dempster-Shafer evidence theory in past decades. However, how to determine a potent parameter to measure evidence conflict, when the given environment is in an open world, namely the frame of discernment is incomplete, is still an open issue. In this paper, a new method which combines generalized conflict coefficient, generalized evidence distance, and generalized interval correlation coefficient based on ordered weighted averaging (OWA) operator, to measure the conflict of evidence is presented. Through ordered weighted average of these three parameters, the combinatorial coefficient can still measure the conflict effectively when one or two parameters are not valid. Several numerical examples demonstrate the effectiveness of the proposed method.

Zero-Sum Matrix Game with Payoffs of Dempster-Shafer Belief Structures and Its Applications on Sensors

The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be inexact or uncertain, which requires that the model of matrix games has the ability to represent and deal with imprecise payoffs. To meet such a requirement, this paper develops a zero-sum matrix game model with Dempster-Shafer belief structure payoffs, which effectively represents the ambiguity involved in payoffs of a game. Then, a decomposition method is proposed to calculate the value of such a game, which is also expressed with belief structures. Moreover, for the possible computation-intensive issue in the proposed decomposition method, as an alternative solution, a Monte Carlo simulation approach is presented, as well. Finally, the proposed zero-sum matrix games with payoffs of Dempster-Shafer belief structures is illustratively applied to the sensor selection and intrusion detection of sensor networks, which shows its effectiveness and application process.

Sensing Attribute Weights: A Novel Basic Belief Assignment Method

Dempster-Shafer evidence theory is widely used in many soft sensors data fusion systems on account of its good performance for handling the uncertainty information of soft sensors. However, how to determine basic belief assignment (BBA) is still an open issue. The existing methods to determine BBA do not consider the reliability of each attribute; at the same time, they cannot effectively determine BBA in the open world. In this paper, based on attribute weights, a novel method to determine BBA is proposed not only in the closed world, but also in the open world. The Gaussian model of each attribute is built using the training samples firstly. Second, the similarity between the test sample and the attribute model is measured based on the Gaussian membership functions. Then, the attribute weights are generated using the overlap degree among the classes. Finally, BBA is determined according to the sensed attribute weights. Several examples with small datasets show the validity of the proposed method.