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Dempster–Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. However, the existing evidence theory is insufficient to consider the situations where it has no capability to express the fluctuations of data at a given phase of time during their execution, and the uncertainty and imprecision which are inevitably involved in the data occur concurrently with changes to the phase or periodicity of the data. In this paper, therefore, a generalized Dempster–Shafer evidence theory is proposed. To be specific, a mass function in the generalized Dempster–Shafer evidence theory is modeled by a complex number, called as a complex basic belief assignment, which has more powerful ability to express uncertain information. Based on that, a generalized Dempster’s combination rule is exploited. In contrast to the classical Dempster’s combination rule, the condition in terms of the conflict coefficient between the evidences [inline-graphic not available: see fulltext] is released in the generalized Dempster’s combination rule. Hence, it is more general and applicable than the classical Dempster’s combination rule. When the complex mass function is degenerated from complex numbers to real numbers, the generalized Dempster’s combination rule degenerates to the classical evidence theory under the condition that the conflict coefficient between the evidences [inline-graphic not available: see fulltext] is less than 1. In a word, this generalized Dempster–Shafer evidence theory provides a promising way to model and handle more uncertain information. Thanks to this advantage, an algorithm for decision-making is devised based on the generalized Dempster–Shafer evidence theory. Finally, an application in a medical diagnosis illustrates the efficiency and practicability of the proposed algorithm.

Several studies have shown that the Dempster-Shafer theory (DST) can be successfully applied to scenarios where model interpretability is essential. Although DST-based algorithms offer significant benefits, they face challenges in terms of efficiency. We present a method for the Dempster-Shafer Gradient Descent (DSGD) algorithm that significantly reduces training time-by a factor of 1.6-and also reduces the uncertainty of each rule (a condition on features leading to a class label) by a factor of 2.1, while preserving accuracy comparable to other statistical classification techniques. Our main contribution is the introduction of a \"confidence\" level for each rule. Initially, we define the \"representativeness\" of a data point as the distance from its class's center. Afterward, each rule's confidence is calculated based on representativeness of data points it covers. This confidence is incorporated into the initialization of the corresponding Mass Assignment Function (MAF), providing a better starting point for the DSGD's optimizer and enabling faster, more effective convergence. The code is available at https://github.com/HaykTarkhanyan/DSGD-Enhanced.

The process of delineating areas that are more susceptible to pollution from anthropogenic sources has become an important issue for groundwater resources management and land-use planning. In this study, an attempt was made to delineate aquifer vulnerability zones for nitrate contamination at Galal Badra basin, east of Iraq using Dempster–Shafer method of evidence in GIS platform. First, an inventory map of the wells with elevated nitrate concentration (>3 mg/L) was prepared. The map showed that there are 63 wells with elevated nitrate concentrations in the study area. These data were partitioned randomly into two sets, for training and testing. The partition criterion was 70/30, 44 wells for training and 19 wells for testing. Then, the most influencing evidential thematic factors in determining aquifer vulnerability were selected depending on the availability of data. These factors were groundwater depth, hydraulic conductivity, slope, soil, and land use land cover (LULC). The spatial association between well locations and evidential thematic layers was investigated by means of mass functions (belief, disbelief, uncertainty, and plausibility) of Dempster–Shafer method. The integrated belief function was used to produce groundwater aquifer vulnerability index (GVI) for the study area. The pixel values of GVI were reclassified into five categories: very low, low, moderate, high, and very high using Jenks classification scheme. The very low–low zones cover 32 % (209 km 2 ). These classes mainly concentrate on the eastern parts of the study area and occupy small zone in the central part. The moderate zone extends over an area of 42 % (279 km 2 ) and mainly encompasses the western part of the study area. The high–very high zones cover 26 % (170 km 2 ) and these zones concentrate on the central part of the study area. The results indicate that the aquifer system in the study area is moderately vulnerable to contamination by nitrate. The model was validated by using relative operating characteristic technique. The success and prediction rates for area under the curve (AUC) were 0.86 and 0.77, respectively, indicating that the model has good capability to delineate aquifer vulnerability zones for nitrate contamination in the study area.

Environmental assessment and decision making is complex leading to uncertainty due to multiple criteria involved with uncertain information. Uncertainty is an unavoidable and inevitable element of any environmental evaluation process. The published literatures rarely include the studies on uncertain data with variable fuzzy reliabilities. This research has proposed an environmental evaluation framework based on Dempster–Shafer theory and Z-numbers. Of which a new notion of the utility of fuzzy number is proposed to generate the basic probability assignment of Z-numbers. The framework can effectively aggregate uncertain data with different fuzzy reliabilities to obtain a comprehensive evaluation measure. The proposed model has been applied to two case studies to illustrate the proposed framework and show its effectiveness in environmental evaluations. Results show that the proposed framework can improve the previous methods with comparability considering the reliability of information using Z-numbers. The proposed method is more flexible comparing with previous work.

Modern artificial objects have become increasingly complex, and this complexity is mirrored in the design process itself. When critical design changes occur in downstream phases, there is a high risk of deterioration in quality, cost, and delivery owing to rework across related processes. Therefore, potential design changes must be predicted in the early stages of design and proactive measures should be taken. In the early design stage, the process is inherently based on fallible design hypotheses, and the fallibility of these hypotheses can lead to design changes in later stages. Accordingly, the certainty of each hypothesis must be evaluated by considering the evidence that supports it. However, design hypotheses are often supported by multiple heterogeneous pieces of evidence with varying degrees of support, and the information available in the early stage is typically incomplete. As a result, rationally evaluating the certainty associated with each hypothesis is not easy. To address this issue, this study proposes a transparent and systematic method to quantify the certainty of design hypotheses while accounting for incomplete evidential information in the early design phase. It first organizes the conceptual foundation of the evidence underlying hypothesis certainty and models it. Then, by applying Dempster–Shafer theory, a computational framework capable of determining proposition certainty from multiple evidence sources under incomplete information, we propose a method to quantify the certainty of design hypotheses. The proposed method is applied to hypotheses generated in a design experiment, and procedural validity and user evaluation were examined. This study introduces a new approach for managing fallible design knowledge based on Dempster–Shafer theory, suggesting a conceptual basis for the early detection and mitigation of risks associated with potential design changes.

This study presents DSClustering, a novel algorithm that merges clustering validity with interpretability using the Dempster-Shafer theory. Traditional clustering methods like K-means, DBSCAN, and agglomerative clustering, while widely used for their efficiency and accuracy, often fall short in transparency, creating barriers in critical fields such as healthcare, finance, and consumer analytics where decision-making requires clear, interpretable insights. DSClustering aims to bridge this gap by assigning clusters based on belief functions from Dempster-Shafer theory, which allows it to generate rule-based explanations for each data point's cluster assignment. Through detailed experiments on real-world datasets, including consumer behavior and airline satisfaction data, we evaluate DSClustering against traditional algorithms using key metrics such as Silhouette score, Rand index and Dunn's index for clustering validity. The results indicate that DSClustering not only performs competitively but also offers a clear interpretative layer, making it suitable for applications where understanding model outputs is as essential as the accuracy of the outputs themselves. This work underscores the increasing importance of interpretability in machine learning, particularly in unsupervised learning, where transparency is typically challenging to achieve. DSClustering demonstrates a promising approach for balancing robust clustering with user-oriented interpretability, potentially encouraging broader adoption of interpretable clustering models in data-critical industries.

Dempster-Shafer theory (DST), as a generalization of Bayesian probability theory, is a useful technique for achieving multi-source information fusion under uncertain environments. Nevertheless, when a high degree of conflict exists between pieces of evidence, unreasonable results are often generated using Dempster’s combination rule. How to fuse highly conflicting information is still an open problem. In this study, we first propose an improved belief Hellinger divergence measure, which can fully consider the uncertainty in basic probability assignments, to quantify the conflict level between evidence. Second, some properties (i.e., nonnegativity, nondegeneracy, symmetry, and trigonometric inequality) of the proposed divergence measure are discussed. Then, we present a novel multi-source information fusion strategy, in which the credibility of the evidence is determined based on external discrepancy and internal ambiguity. Additionally, we consider the decay of credibility when fusing evidence across different times. Finally, applications in fault diagnosis and Iris dataset classification are presented to demonstrate the effectiveness of our method. The results indicate that our approach is more reasonable and can identify the target with a higher belief degree.

Hybridised classification and prioritisation of patients with chronic heart diseases (CHDs) can save lives by categorising them on the basis of disease severity and determining priority patients. Such hybridisation is challenging and thus has not been reported in the literature on telemedicine. This paper presents an intelligent classification and prioritisation framework for patients with CHDs who engage in telemedicine. The emergency status of 500 patients with CHDs was evaluated on the basis of multiple heterogeneous clinical parameters, such as electrocardiogram, oxygen saturation, blood pressure and non-sensory measurements (i.e. text frame), by using wearable sensors. In the first stage, the patients were classified according to Dempster–Shafer theory and separated into five categories, namely, at high risk, requires urgent care, sick, in a cold state and normal. In the second stage, hybridised multi-criteria decision-making models, namely, multi-layer analytic hierarchy process (MLAHP) and technique for order performance by similarity to ideal solution (TOPSIS), were used to prioritise patients according to their emergency status. Then, the priority patients were queued in each emergency category according to the results of the first stage. Results demonstrated that Dempster–Shafer theory and the hybridised MLAHP and TOPSIS model are suitable for classifying and prioritising patients with CHDs. Moreover, the groups’ scores in each category showed remarkable differences, indicating that the framework results were identical. The proposed framework has an advantage over other benchmark classification frameworks by 33.33% and 50%, and an advantage over earlier benchmark prioritisation by 50%. This framework should be considered in future studies on telemedicine architecture to improve healthcare management.

Cold rolling chatter is one of the bottlenecks to improve the production quality and efficiency of high-strength thin strip, so it is very important to predict and identify the chatter states. The accumulation of industrial data from the rolling process and the development of machine learning technology have opened up a path to solve this problem. However, due to low density and uneven distribution of actual process data, knowledge learning and states identification of cold rolling chatter phenomena are confined. Therefore, based on the combination of actual production data and simulation data, a novel identification method is proposed and applied to identify the cold rolling chatter states. Firstly, the actual vibration signals are collected and the simulation data generated from chatter model are used to supplement data in chatter states. The sample space is constructed based on the semi-supervised transfer component analysis (SSTCA) to realize the fusion of actual production data and simulation data. Then, different cold rolling states are identified by particle swarm optimization-support vector machine (PSO-SVM) and back propagation neural network (BPNN), respectively. Finally, the identification results of PSO-SVM and BPNN are combined based on the Dempster-Shafer (D-S) theory. It can be drawn that SSTCA can effectively solve the problems of low density and uneven distribution of industrial data by fusion of multi-source data, and D-S theory can realize the connection of different machine learning methods. Furthermore, the presented method can more accurately identify different chatter states in the rolling process.

In some multi-criteria decision-making (MCDM) scenarios, decision makers must address challenges like handling uncertain and incomplete information, managing biases in criteria values, and assessing interrelationships among criteria based on their partitioning as per their characteristics. To tackle these challenges, a picture fuzzy set (PFS) can be utilized to quantify vague information, Hamy mean (HM) can be used to consider criteria interrelationships while the power average (PA) mitigates any kind of biasness. Also, to overcome the limitations of persistence and invariantess in algebraic operations, Dempster-Shafer theory (DST) is employed. By integrating the conventional HM with the traditional PA under partitioning, this paper first introduced the novel power partitioned Hamy mean ( P P t H M q ) operator. Then, this operator is extended for picture fuzzy numbers (PFNs) with DST and two novel operators are introduced, which are named as picture fuzzy power partitioned Hamy mean ( P F P P t H M DST q ) and picture fuzzy weighted power partitioned Hamy mean ( P F W P P t H M DST q ) with some desirable properties. Moreover, based on these operators, a new method for MCDM in the PFS environment has been designed. The paper illustrates their application in selecting the best hotel among four alternatives ( B 1 , B 2 , B 3 , B 4 ) based on five criteria, which are partitioned into two sets. Results indicate that the best and worst alternatives under these operators are hotels B 1 and B 4 , respectively. Sensitivity analysis explores the impact of granularity parameter variations, and comparative analysis demonstrates the effectiveness of the presented operators. Overall, the study concludes that these operators offer flexibility, generality, and consistency for analyzing MCDM problems in PFS environments.