Dempster-Shafer Research Articles

Safety risk assessment of reservoir dam structure: an empirical study in China

Reservoir dam structure is critical to protect public life and property and has always been attention worldwide. However, a systematic approach to assessing the safety risks of reservoir dam structure (RDS) is still required. This study presents a holistic framework for evaluating the safety risk of RDS and develops an evaluation index system. A risk assessment model is constructed based on the cloud and Dempster-Shafer (D-S) evidence theories. The model's validity is confirmed through an empirical analysis of the XY reservoir project. This study offers theoretical insights and practical solutions for managers to facilitate decision-making and supports the advancement of industry standards.

Decision with belief functions and generalized independence: Two impossibility theorems

Dempster-Shafer theory of evidence is a framework that is expressive enough to represent both ignorance and probabilistic information. However, decision models based on belief functions proposed in the literature face limitations in a sequential context: they either abandon the principle of dynamic consistency, restrict the combination of lotteries, or relax the requirement for transitive and complete comparisons. This work formally establishes that these requirements are indeed incompatible when any form of compensation is considered. It then demonstrates that these requirements can be satisfied in non-compensatory frameworks by introducting and characterizing a dynamically consistent rule based on first-order dominance.

CNN-ELMNet: fault diagnosis of induction motor bearing based on cross-modal vector fusion

Abstract As the primary driving equipment in industrial, accurate fault diagnosis and condition monitoring of induction motor is crucial for ensuring operational safety. This paper focuses on the bearing faults of induction motors, which have a substantial impact on both the mechanical and electromagnetic systems of the motors. However, in diagnostic tasks, we are faced with the challenges of multi-source, multi-modal data, significant influence from environmental noise, and minimal differentiation between fault data. This paper proposed a novel cross-modal vector fusion fault diagnosis and classification model (CNN-ELMNet), which includes a cross-modal vector fusion network (VF) based on D-S evidence theory, feature extraction layer (FE) and classification layer (CL). Specifically, the VF prioritizes the integration of diagnostic results from individual vibration signals or stator current signals within convolutional neural networks with the features of the input implicit vectors as decision-making evidence, followed by weighted vector fusion through D-S evidence theory at the decision level. The FE focuses on retaining the convolutional, pooling, and fully connected layers of the convolutional network and freezing the final fully connected layer, thus preserving training parameters and fully utilizing the network’s powerful FE capabilities. The CL includes an Extreme Learning Machine optimized for random hyperparameters using the snow ablation optimizer (SAO) algorithm, which offers rapid convergence and high classification recognition rates. The CNN-ELMNet model combines a convolutional network with an extreme learning machine optimized by the SAO algorithm, which not only preserves the model’s FE capability but also enhances the convergence speed and classification recognition rate of the model. Experimental results on real datasets demonstrate that the proposed model exhibits strong stability, generalization, and high accuracy in fault diagnosis, achieving accuracy rate of 99.29% and 98.75%. This provides a more feasible solution for the bearing fault diagnosis of induction motors and holds promising prospects for practical applications.

A Methodological Approach to Assembly Time Standard Estimation Based on Incomplete Characteristics of the Production Process and Using Small Databases

The problem solved in this article concerns assembly planning, which is time-consuming, but crucial in the development of mechanical products. At the product design stage there is no complete information about the manufacturing process, so it is necessary to develop an approach to help process the uncertain and incomplete information. In order to compare different product variants, the assembly time standard has to be estimated on the basis of the incomplete product and production process characteristics. This paper presents a method for estimating the assembly time standard using time classes, decision tree and evidence theory.

A Dempster–Shafer Enhanced Framework for Urban Road Planning Using a Model-Based Digital Twin and MCDM Techniques

Rapid urbanization in developing countries presents a critical challenge in the need for extensive and appropriate road expansion, which in turn contributes to traffic congestion and air pollution. Urban areas are economic engines, but their efficiency and livability rely on well-designed road networks. This study proposes a novel approach to urban road planning that leverages the power of several innovative techniques. The cornerstone of this approach is a digital twin model of the urban environment. This digital twin model facilitates the evaluation and comparison of road development proposals. To support informed decision-making, a multi-criteria decision-making (MCDM) framework is used, enabling planners to consider various factors such as traffic flow, environmental impact, and economic considerations. Spatial data and 3D visualizations are also provided to enrich the analysis. Finally, the Dempster–Shafer theory (DST) provides a robust mathematical framework to address uncertainties inherent in the weighting process. The proposed approach was applied to planning for both new road constructions and existing road expansions. By combining these elements, the model offers a sustainable and knowledge-based approach to optimize urban road planning. Results from integrating weights obtained through two weighting methods, the Analytic Hierarchy Process (AHP) and the Bayesian best–worst Method (B-BWM), showed a very high weight for the “worn-out urban texture” criterion and a meager weight for “noise pollution”. Finally, the cost path algorithm was used to evaluate the results from all three methods (AHP, B-BWM, and DST). The high degree of similarity in the results from these methods suggests a stable outcome for the proposed approach. Analysis of the study area revealed the following significant challenge for road planning: 35% of the area was deemed unsuitable, with only a tiny portion (4%) being suitable for road development based on the selected criteria. This highlights the need to explore alternative approaches or significantly adjust the current planning process.

A robust ensemble of hybrid and bivariate statistical models for flood prediction mapping in Lower Damodar River Basin of India

This research explores flood prediction in the Lower Damodar River Basin (LDRB) using a hybrid ensemble of a Naïve Bayes Tree (NBT) and five bivariate statistical models such as Evidential Belief Function (EBF), Index of Entropy (IOE), Frequency Ratio (FR), Statistical Index (SI), and Modified Information Value (MIV). A total of 348 flood locations and 15 conditioning factors including hydrological, topographical and land cover were considered for this analysis. To ensure the precision of model predictions, a multicollinearity assessment was executed. Receiver operating characteristic (ROC) curve, area under curve (AUC), mean absolute error (MAE), mean squared error (MSE), and root mean squared error (RMSE) were performed to compare and asses each of the models all. The results reveal that all models performed well in creating flood hazard maps with AUC >0.8 and RMSE <0.4. FR and EBF models demonstrated the highest predictive accuracy (AUC=0.85), followed by the IOE, SI, and MIV models. The ensemble of NBT with bivariate models shows promising results, showcasing reduced error metrics and improved accuracy for the IOE, SI, and MIV models. This study highlights the potential of ensemble models in flood hazard prediction, offering valuable insights for global flood risk management. The successful application of these data-driven models showcases their importance in forecasting flood risks, aiding decision-makers and planners in developing more effective flood mitigation strategies.

A novel multi-source information fusion method for emergency spatial resilience assessment based on Dempster-Shafer theory

In the midst of today's intricate and ever-changing natural and social landscape, this study is committed to proposing a novel multi-source information fusion method for assessing the spatial resilience of urban emergency evacuation and rescue. Its overarching aim is to uncover latent challenges and contribute to the enhancement of a city's capacity to respond to emergencies. To achieve this, we have devised a comprehensive assessment indicator system, capable of not only quantifying a city's spatial resilience but also offering indispensable guidance for urban emergency evacuation and rescue spatial planning. Furthermore, we have introduced an innovative evaluation methodology framework. This framework includes the establishment of the basic probability assignment (BPA) model, a pioneering method for generating BPA for observed values, and the novel application of hierarchical weighting and fusion techniques. By extending the Dempster-Shafer theory, we have not only enhanced the method's ability to express and integrate uncertain information but also significantly improved the precision of the evaluation. Ultimately, we conducted a quantitative assessment using Shenzhen, China, as a case study, identifying existing issues and proposing highly-targeted improvement strategies. These research findings not only provide robust support for the augmentation of urban emergency capabilities in Shenzhen but also offer pioneering insights for the quantitative assessment and advancement of emergency spatial resilience in cities across the globe.

Enhancing safety and reliability in multistory construction: A multi-state system assessment of shoring/reshoring operations using interval-valued belief functions

Ensuring safety and reliability in multistory concrete construction necessitates rigorous assessment methodologies capable of addressing the inherent uncertainties of the construction process. This paper introduces a novel reliability assessment methodology for shoring/reshoring (S/R) operations, framed within a multi-state parallel-series system (MSS). Our approach innovatively combines concrete slab capacities, forming system strengths, and construction quality, integrating cost and time efficiencies. Central to our method is the use of Interval Universal Generating Functions (IUGF), which leverage Dempster-Shafer (D-S) theory and interval analysis to robustly estimate system reliability under uncertainty. For instance, the model considers concrete strength ranging from 0.72 × 2.1D to 0.96 × 2.1D at different curing stages, producing a system reliability index between 0.63 and 0.76, against a desired threshold of 0.8. This methodology produces interval-valued belief functions that capture a comprehensive range of potential system states and their likelihoods, offering a refined perspective on system safety. An illustrative case study demonstrates the practical application of this methodology in optimizing formwork removal and S/R schedules, significantly enhancing decision-making in construction operations. This paper aligns with the core themes of reliability engineering and system safety by addressing critical safety and reliability issues in complex technological systems through advanced probabilistic safety assessment methods. It significantly enriches the professional discourse by presenting a robust method that can be adapted across various engineering fields facing similar reliability challenges.

Deep evidential fusion with uncertainty quantification and reliability learning for multimodal medical image segmentation

Single-modality medical images generally do not contain enough information to reach an accurate and reliable diagnosis. For this reason, physicians commonly rely on multimodal medical images for comprehensive diagnostic assessments. This study introduces a deep evidential fusion framework designed for segmenting multimodal medical images, leveraging the Dempster–Shafer theory of evidence in conjunction with deep neural networks. In this framework, features are first extracted from each imaging modality using a deep neural network, and features are mapped to Dempster–Shafer mass functions that describe the evidence of each modality at each voxel. The mass functions are then corrected by the contextual discounting operation, using learned coefficients quantifying the reliability of each source of information relative to each class. The discounted evidence from each modality is then combined using Dempster’s rule of combination. Experiments were carried out on a PET-CT dataset for lymphoma segmentation and a multi-MRI dataset for brain tumor segmentation. The results demonstrate the ability of the proposed fusion scheme to quantify segmentation uncertainty and improve segmentation accuracy. Moreover, the learned reliability coefficients provide some insight into the contribution of each modality to the segmentation process.

A new sine similarity measure based on evidence theory for conflict management

Evidence theory (ET) has gained significant attention in various fields due to its advantages over probability theory. However, highly conflicting evidence can sometimes yield counterintuitive results when using Dempster’s rule. This article aims to address this issue by introducing a new sine similarity measure that integrates the belief and plausibility functions in ET. The proposed sine similarity measure offers a comprehensive evaluation of the conflict between evidences. Importantly, the proposed measure satisfies several desirable properties, ensuring its effectiveness in capturing the similarity between evidences. Furthermore, a conflict management method is designed based on the proposed sine similarity measure and belief entropy. The validity of the proposed method is verified by some numerical examples and an application to target recognition.

Design and Optimization of a Cable-Driven Parallel Polishing Robot With Kinematic Error Modeling

Abstract This article presents the design and optimization of a cable-driven parallel polishing robot (CDPPR) with kinematic error modeling and introduces an improved nondominated sorting genetic algorithm II (NSGA-II) for multiobjective optimization. First, the mechanical design and kinematic and static modeling of the CDPPR are conducted. Subsequently, a kinematic error transfer model is established based on the evidence theory by considering the change of exit points of cables, and an error index is derived to measure the accuracy of the robot. Besides, another two performance indices including the workspace and static stiffness are proposed. Thus, a multiobjective optimization model is established to optimize the workspace, static stiffness, and error index, and an improved NSGA-II is developed. Finally, an experimental scaled prototype of the CDPPR is constructed, and numerical examples and experimental results demonstrate the effectiveness of the improved NSGA-II and the stability of the optimal configuration.

Modal semantics for reasoning with probability and uncertainty

Abstract This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the following: The latter allows us to adequately express belief functions (lower probabilities) over propositions, whereas the former does not. Thus, neighbourhood semantics is more expressive. The main part of the work is a section in which we study the modal equivalence between probabilistic Kripke models and a subclass of belief neighbourhood models, namely additive ones. We study how to obtain modally equivalent structures.

Application of artificial intelligence sensor and visual image technology in the analysis of hydrophilic space landscape characteristics

With the continuous development of intelligent sensor technology and artificial intelligence, the application of artificial intelligence feature recognition at the level of intelligent sensor information acquisition to urban landscape analysis has become a current research trend and hot spot, but also brings us new research directions and challenges. In this paper, the multi-sensor collaborative filtering algorithm is optimized, and a method based on evidence theory is proposed to deal with the fuzzy and unclear information generated in the process of multi-sensor collaboration. Then, the analysis and recognition of multi-sensor fusion information using AI technology are analyzed in detail. This paper discusses the problems in multi-sensor information fusion and related solutions. Combined with the key nodes of 3D object AI feature recognition, multi-sensor collaborative Dempster Shafer evidence theory and 3D convolutional neural network waterfront space landscape feature recognition sub-model are constructed, and the waterfront space landscape recognition analysis model is tested and analyzed. The results show that the multi-sensor information collection Kalman filtering fusion algorithm effectively realizes the recognition of landscape feature information and the filtering of irrelevant interference information combined with an artificial intelligence algorithm to build a landscape feature recognition model. Among all kinds of landscape recognition, the recognition effect of beach inflow is the best, and the recognition accuracy, recall, and F1 value are all above 95. However, the identification effect of hydrophilic plank roads and underwater breakwater is relatively poor. The recognition accuracy of the hydrophilic platform is the lowest at 83.16 % among the eight landscape types, and the recall rate of underwater breakwater is the lowest at 79.96 % among the eight landscape types. In general, the multi-sensor Kalman filtering algorithm information fusion model designed in this paper has higher recognition accuracy and better classification performance for the collection and classification of the entire landscape dataset. The work of this paper provides a new idea and direction for the design and application of waterfront landscape identification and analysis systems based on intelligent sensors and artificial intelligence technology and lays a certain foundation for the intelligent design of urban waterfront landscapes.

Group Consensus-Driven Energy Consumption Assessment Using Social Network Analysis and Fuzzy Information Fusion

With industrial development deepening, the share of industrial energy in overall consumption has notably risen. To assess industrial energy consumption accurately, this paper proposes a method employing interval type-2 fuzzy sets (IT2FSs) to represent assessment information effectively. Additionally, it analyzes decision-makers (DMs) as a social network to alleviate individual biases. IT2FSs are chosen to handle uncertainties in assessing industrial energy consumption. Addressing biases in DMs' opinions, a group consensus model aids the consensus reaching process (CRP). Industrial energy consumption is assessed using the MULTIMOORA method, yielding three results. These are fused via D-S evidence theory (DSET) to obtain the final assessment. Finally, the model's effectiveness is verified with a case study on energy consumption in the steel industry. In conclusion, this paper not only deepens the understanding of uncertainties in the energy consumption assessment process, but also provides a robust tool for various industries to optimize energy use and economic outcomes.

Distance and similarity measures on belief and plausibility under q-rung orthopair fuzzy sets with applications

Belief and plausibility functions based on evidence theory (ET) have been widely used in managing uncertainty. Various generalizations of ET to fuzzy sets (FSs) have been reported in the literature, but no generalization of ET to q-rung orthopair fuzzy sets (q-ROFSs) has been made yet. Therefore, this paper proposes a novel, simple, and intuitive approach to distance and similarity measures for q-ROFSs based on belief and plausibility functions within the framework of ET. This research addresses a significant research gap by introducing a comprehensive framework for handling uncertainty in q-ROFSs using ET. Furthermore, it acknowledges the limitations inherent in the current state of research, notably the absence of generalizations of ET to q-ROFSs and the challenges in extending belief and plausibility measures to certain aggregation operators and other generalizations including Hesitant fuzzy sets, Bipolar fuzzy sets, Fuzzy soft sets etc. Our contribution lies in the proposal of a novel approach to distance and similarity measures for q-ROFSs under ET, utilizing Orthopairian belief and plausibility intervals (OBPIs). We establish new similarity measures within the generalized ET framework and demonstrate the reasonability of our method through useful numerical examples. Additionally, we construct Orthopairian belief and plausibility GRA (OBP-GRA) for managing daily life complex issues, particularly in multicriteria decision-making scenarios. Numerical simulations and results confirm the usability and practical applicability of our proposed method in the framework of ET.

Fused Decision Rules of Multi-Intuitionistic Fuzzy Information Systems Based on the D-S Evidence Theory and Three-Way Decisions

Fused Decision Rules of Multi-Intuitionistic Fuzzy Information Systems Based on the D-S Evidence Theory and Three-Way Decisions

Belief Tsallis-Deng Structure Entropy and its uniform framework for analyzing multivariate time-series complexity based on evidence theory

In the framework of evidence theory, this paper proposes a new measure of uncertainty and introduces an entirely new unified framework for analyzing the complexity of multivariate time series. The theoretical foundation of this paper is random sets, viewing multivariate sequences as a new type of set variable, and using the belief theory framework to describe their behavior. Set variables are a natural extension of point variables, thus providing stronger universality in the analysis of multivariate time series. We tested our proposed new analytical framework on the logistic map and used the Tsallis-Deng Structure Entropy introduced in this paper to analyze the generated multivariate time series. Compared to the traditional Deng entropy, Tsallis-Deng Structure Entropy can adjust the sensitivity to time series complexity by tuning its structural parameter p. As the parameters of the logistic map change, the changes in Tsallis-Deng Structure Entropy show a high correlation with the Lyapunov exponent. In addition, we applied the proposed framework to analyze a multivariate epileptic EEG dataset. The results showed that using the novel evidence theory-based analysis framework for the 23-channel multivariate time series, the average classification accuracies of Deng entropy, Tsallis-Deng entropy, and Tsallis-Deng structural entropy for 24 epilepsy patients were 79 %, 74 %, and 82 %, respectively. In contrast, the average recognition accuracy using the traditional probabilistic framework based on multivariate embedding theory was 64 %. The evidence theory-based framework generally outperformed the multivariate embedding theory, with Tsallis-Deng structural entropy achieving the best performance. These results indicate that the proposed evidence theory-based framework not only avoids the dimensionality curse of the multivariate embedding theory but also better quantifies the complexity of multivariate time series from the same system and distinguishes different types of multivariate time series.

Multiple Unmanned Aerial Vehicle (multi-UAV) Reconnaissance and Search with Limited Communication Range Using Semantic Episodic Memory in Reinforcement Learning

Unmanned Aerial Vehicles (UAVs) have garnered widespread attention in reconnaissance and search operations due to their low cost and high flexibility. However, when multiple UAVs (multi-UAV) collaborate on these tasks, a limited communication range can restrict their efficiency. This paper investigates the problem of multi-UAV collaborative reconnaissance and search for static targets with a limited communication range (MCRS-LCR). To address communication limitations, we designed a communication and information fusion model based on belief maps and modeled MCRS-LCR as a multi-objective optimization problem. We further reformulated this problem as a decentralized partially observable Markov decision process (Dec-POMDP). We introduced episodic memory into the reinforcement learning framework, proposing the CNN-Semantic Episodic Memory Utilization (CNN-SEMU) algorithm. Specifically, CNN-SEMU uses an encoder–decoder structure with a CNN to learn state embedding patterns influenced by the highest returns. It extracts semantic features from the high-dimensional map state space to construct a smoother memory embedding space, ultimately enhancing reinforcement learning performance by recalling the highest returns of historical states. Extensive simulation experiments demonstrate that in reconnaissance and search tasks of various scales, CNN-SEMU surpasses state-of-the-art multi-agent reinforcement learning methods in episodic rewards, search efficiency, and collision frequency.

Disagreement serves an explainable ensemble model based on Dempster–Shafer evidence-fusion for an improved skin lesion classification

The ever-growing development of deep learning models for skin lesion classification yields consistently to exceptional performance. These models revealed remarkable accuracy and robustness in the diagnosis of various skin lesion classes. Although this advancement enables significant aids in early detection and diagnosis, selecting the most suitable model for a task is challenging especially when most models demonstrate high proficiency. Consequently, small performance variations among well-performing models become critical factors. These variations present an additional challenge especially when considering the black-box nature of the model, which may result in a lack of evidence and certainty when making critical decisions. In this study, we tackle the problem of selecting the most appropriate models for skin lesion classification among various well-performing, yet unexplainable deep learning models. In fact, by proposing an ensemble approach that leverages Dempster–Shafer theory and feature importance visualization, we aim to create a trustworthy and interpretable model for improved skin lesion classification. The proposed Dempster–Shafer evidence-fusion ensemble model, provides insights into evidence-based integration of multiple models allowing for enhanced trustworthiness in the decision-making process. This is accomplished through comparing the high performances between different deep learning models. Hence, metrics are extracted by performing statistical tests and explainable methods besides numerical assessment, from the failure cases to profile the disagreement from different perspectives. With these metrics, the classifiers’ complementary behaviors is then identified, accordingly making contribution in proposing an explainable ensemble model and leveraging the complementary strengths of the individual models. The proposed ensemble model has been exhaustively evaluated using the challenging HAM10000 dataset. The results obtained indicate that the proposed skin lesion classifier can provide useful decision support while significantly improving classification performance by 6% in terms of accuracy compared with the best-performing individual model, and achieving 92% accuracy.

Measures of extended fractional Deng entropy and extropy with applications

Recently, Zhang and Shang introduced modifications to the concept of fractional entropy and proved some properties based on the inverse Mittag-Leffler function (MLF). The Deng entropy serves as a valuable measure in the Dempster-Shafer evidence theory (DST) to tackle uncertainty. In this study, we extend the fractional Deng entropy measure, introducing two distinct versions: E fd 1 α ( m ) and E fd 2 α ( m ) . We call this new measure the extended fractional Deng entropy, EFDEn. Additionally, we apply a similar approach to the fractional Deng extropy measure, resulting in E X fd 1 α ( m ) and E X fd 2 α ( m ) . We call this new measure the extended fractional Deng extropy, EFDEx. These two measures are complementary, leading to provide a deeper analysis of known and unknown information. Subsequently, we conduct a comparative analysis of these measures within the DST framework. We also propose the decomposable fractional Deng entropy, an extension of the decomposable entropy for Dempster–Shafer evidence theory, which effectively decomposes fractional Deng entropy. Finally, we delve into a pattern recognition classification problem to highlight the importance of these new measures.