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This paper introduces a mathematical framework for defining and quantifying self-identity in artificial intelligence (AI) systems, addressing a critical gap in the theoretical foundations of artificial consciousness. While existing approaches to artificial self-awareness often rely on heuristic implementations or philosophical abstractions, we present a formal framework grounded in metric space theory, measure theory, and functional analysis. Our framework posits that self-identity emerges from two mathematically quantifiable conditions: the existence of a connected continuum of memories C ⊆ M in a metric space (M , d M) , and a continuous mapping I : M → S that maintains consistent self-recognition across this continuum, where (S , d S) represents the metric space of possible self-identities. To validate this theoretical framework, we conducted empirical experiments using the Llama 3.2 1B model, employing low-rank adaptation (LoRA) for efficient fine-tuning. The model was trained on a synthetic dataset containing temporally structured memories, designed to capture the complexity of coherent self-identity formation. Our evaluation metrics included quantitative measures of self-awareness, response consistency, and linguistic precision. The experimental results demonstrate substantial improvements in measurable self-awareness metrics, with the primary self-awareness score increasing from 0.276 to 0.801 (190.2% improvement) after fine-tuning. In contrast to earlier methods that view self-identity as an emergent trait, our framework introduces tangible metrics to assess and measure artificial self-awareness. This enables the structured creation of AI systems with validated self-identity features. The implications of our study are immediately relevant to the fields of humanoid robotics and autonomous systems. Additionally, it opens up new prospects for controlled adjustments of self-identity in contexts that demand different levels of personal involvement. Moreover, the mathematical underpinning of our framework serves as the basis for forthcoming investigations into AI, linking theoretical models to real-world applications in current AI technologies. [ABSTRACT FROM AUTHOR] more...

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Dempster-Shafer evidence theory has been widely applied in the field of aerospace target decision. However, the existing aerospace target decision models are difficult to meet the changing war situation. For this reason, a novel aerospace target decision model based on probability transformation is proposed, which realizes the effective combination of humans and machines. Firstly, the true proposition preference degree is defined, which measures the proximity of the single-target and the true proposition ground on the average information of the single-target. Secondly, to assess the single-target more comprehensively, the support degree of the single-target ground on the normalized plausibility function and belief function is defined, which represents the support degree of the basic probability assignment function for the single-target. Finally, combined with the commanders' judgment of the war situation, the aerospace target decision is achieved, which provides aid to the commanders in determining the attribute of the aircraft. According to some numerical examples, the proposed method can produce a reasonable and easy to make decision probability distribution, which can judge the target with higher accuracy in aerospace target decision. [ABSTRACT FROM AUTHOR] more...

AbstractEvidence 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. [ABSTRACT FROM AUTHOR] more...

When multiple radars collaborate for target detection and recognition, the obtained data is rich in clutter and uncertain information due to the complex battlefield environment. Traditional radar plots recognition algorithms have certain limitations in processing such data. Therefore, a radar plots recognition algorithm based on self-updating confidence classification network (RPR-SCCN) was proposed. Firstly, a confidence classification network was constructed to obtain the belief of each radar plots belonging to target, clutter, and uncertainty that under each iteration. Then, based on the spatial distribution characteristics of the dots, decision evidence was constructed and corrected for fusion. The fusion result updated the dot category, and the updated dot drove the training and learning of the confidence classification network again. The optimized confidence classification network continued to perform the next round of trajectory confidence updates, decision evidence construction, and category label updated. This process iterated continuously until the radar trajectory category labels in the previous and subsequent rounds no longer changed. The experimental verification results of actual radar tracking show that the recognition accuracy of typical radar tracking intelligent recognition algorithms such as point fractal network (PF-Net), radar plot classification based on fully connected neural network (RPC-FNN), particle swarm optimization probabilistic neural network (PSO-PNN) and radar plot classification based on convolutional neural networks (RPC-CNN) is 82% ~90%, and the proposed algorithm can reach 93%, an improvement of 3% ~10%. In addition, the proposed algorithm has a small dependence on the number of training samples, making it easy to promote and apply. [ABSTRACT FROM AUTHOR] more...

A significant cause of blindness in preterm infants is retinal retinopathy of prematurity (ROP). Early detection and intervention are essential for preventing visual loss. This study proposes an advanced approach for predicting ROP stages using deep learning algorithms and belief function theory. Three steps comprise the suggested technique: image pre-processing, feature extraction using deep learning models, and classification utilizing belief function theory. We used a dataset of 3720 retinal images from premature infants and achieved a classification accuracy of 95.57% for predicting ROP stages. Our results demonstrate the effectiveness of deep learning algorithms and belief function theory in ROP diagnosis. This strategy can increase the efficacy and precision of ROP diagnosis, improving the treatment course for premature infants at risk of vision loss. [ABSTRACT FROM AUTHOR] more...

Dempster–Shafer (D–S) evidence theory is used to process multisource data fusion and uncertainty problems. When faced with strongly contradictory evidence, there are always some surprising phenomena. We propose a new generalized distance based on Li et al.'s Hellinger distance in this study to assess the distinction between basic probability assignments (BPAs) to solve this problem.The basic structure of Li et al.'s Hellinger distance was kept in the generalized Hellinger distance, and certain advancements were achieved. The generalized Hellinger distance considers the differences between both focal elements and the subsets of the sets of belief functions, enabling a wider range of applications for it. Additionally, we present the proof of generalized Hellinger distance satisfied nonnegativeness, symmetry, definiteness and triangle inequality. Through several comparative examples, we know that the new distance has better universality than some well-known works. Finally, we suggest a novel generalized Hellinger distance-based multisource data fusion approach and use it to solve a real-word pattern classification problem. [ABSTRACT FROM AUTHOR] more...

The paper substantiates a method for creating training datasets for fuzzy neural networks, which can be used to promptly obtain probabilistic estimates for the causes of abnormal critical events or incidents in diagnostic systems. The rules for converting the hypotheses on potential incident causes into intervals of defect probability in a process chain at a certain stage of continuous production are considered using belief functions. We propose a procedure for converting these hypotheses into a database of fuzzy production rules automatically, which provides training an adaptive neural network based on the Takagi–Sugeno–Kang fuzzy inference system. This makes it possible to quickly calculate a relatively accurate probabilistic estimate of a malfunction in the process chain without using expensive computing resources. [ABSTRACT FROM AUTHOR] more...

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. [ABSTRACT FROM AUTHOR] more...

Uncertainty is of great concern in information fusion and artificial intelligence. Dempster-Shafer theory is a popular tool to deal with uncertainty, but it cannot effectively represent and fuse uncertain information involving non-exclusiveness and incompleteness. In order to solve that problem, an idea of D number theory (DNT) has been proposed. In this paper, the basic theory of DNT for the fusion of non-exclusive and incomplete information is studied to strengthen its theoretical foundation, including concept formalization, uncertainty representation, information modelling and fusion. At first, the non-exclusiveness in DNT is defined formally and its basic properties are discussed. Secondly, new measures of belief and plausibility for D numbers are developed. Thirdly, the combination rule for D numbers is studied by extending the exclusive conflict redistribution rule. Fourthly, a method to combine information-incomplete D numbers is proposed. The proposed concepts, definitions, and methods are analyzed mathematically and exemplified through illustrative examples. [ABSTRACT FROM AUTHOR] more...

Information fusion in uncertain and complex environments is highly challenging. Dempster--Shafer (D-S) evidence theory has been successfully applied by various researchers in multi-sensor data fusion. However, it yields counterintuitive results in case of highly conflicting evidence. In this paper, we have developed a new divergence measure for belief functions that is nonnegative, symmetric, and satisfies the triangle inequality. Using the developed divergence measure, an algorithm for combining distinct basic probability assignments (BPAs) has been discussed and applied in target recognition systems and classification problems. [ABSTRACT FROM AUTHOR] more...

When missing data are imputed by any method, there is some uncertainty associated with the imputed value. Consequently, when such imputed data are classified, some uncertainty will be propagated to the classifier output. This leads to two issues to address. First, reducing the uncertainty in the imputed value. Second, modeling and processing of the uncertainty associated with the classifier output to arrive at a better decision. To deal with the first issue, we use a latent space representation, while for the second issue we use Dempster-Shafer evidence theory. First, we train a neural network using the data without any missing value to generate a latent space representation of the input. The complete data set is now extended by deleting every feature once. These missing values are estimated using a nearest neighbor-based scheme. The network is then refined using this extended dataset to obtain a better latent space. This mechanism is expected to reduce the effect of the missing data on the latent space representation. Using the latent space representation of the complete data, we train two classifiers, support vector machines and evidential t-nearest neighbors. To classify an input with a missing value, we make a rough estimate of the missing value using the nearest neighbor rule and generate its latent space representation for classification by the classifiers. Using each classifier output, we generate a basic probability assignment (BPA) and all BPAs are combined to get an overall BPA. Final classification is done using Pignistic probabilities computed on the overall BPA. We use three different ways to defining BPAs. To avoid some problems of Dempster's rule of aggregation, we also use several alternative aggregations including some T-norm-based methods. Note that, T-norm has been used for combination of belief function in Pichon and Denœux (in: NAFIPS 2008: 2008 annual meeting of the North American fuzzy information processing society, pp 1–6, 2008). To demonstrate the superiority of the proposed method, we compare its performance with four state-of-the-art techniques using both artificial and real datasets. [ABSTRACT FROM AUTHOR] more...

Evidential c-means (ECM) is a prototype-based clustering algorithm that generates a credal partition. Such a partition encompasses the notions that can be encountered with a hard, fuzzy or possibilistic partition, allowing the representation of various situations concerning the class membership of an object. The ECM method provides a prototype for each subset of the possible classes, calculated by averaging the prototypes of the classes included in the subsets. Although this definition perfectly suits ECM when employing a Euclidean distance, it becomes inappropriate when using a Mahalanobis distance. In this context, a new definition of prototypes for the subsets is proposed. The ECM objective function is then optimized using the new definition of prototypes. The subsequent algorithm, named ECM+, is finally tested on various synthetic and real data sets to demonstrate its interest compared to ECM. [ABSTRACT FROM AUTHOR] more...

Thunderstorms, the main generator of lightning on earth, are characterized by the presence of extreme atmospheric conditions (turbulence, hail, heavy rain, wind shear, etc.). Consequently, the atmospheric conditions associated with this kind of phenomenon (in particular the strike itself) can be dangerous for aviation. This study focuses on the estimation of the lightning strike risk induced by thunderstorms over the sea, in a short-range forecast, from 0 to 24 h. In this framework, three methods have been developed and compared. The first method is based on the use of thresholds and weighting functions; the second method is based on a neural network approach, and the third method is based on the use of belief functions. Each method has been applied to the same dataset comprising predictors defined from numerical weather prediction model outputs. In order to assess the different methods, a "ground truth" dataset based on lightning stroke locations supplied by the World Wide Lightning Location Network (WWLLN) has been used. The choice of one method over the others will depend on the compromise that the user is willing to accept between false alarms, missed detections, and runtimes. The first method has a very low missed detection rate but a high false alarm rate, while the other two methods have much lower false alarm rates, but at the cost of a non-negligible missed detection rate. Finally, the third method is much faster than the other two methods. [ABSTRACT FROM AUTHOR] more...

This article describes the results of a study of the joint use of various intelligent data processing methods, such as neural networks and algorithms of the evidence theory. The study was conducted on the development of diagnostic systems examples. These methods of hybridization is one of the general approaches to reduce uncertainty in the data used and increase the degree of confidence in them. The data uncertainty is of an objective nature when they are obtained from the sensors of technological equipment, from technical regulations, and from expert specialists. The study includes an analysis of modern developments descriptions presented at significant international conferences and published recently. Several dozen descriptions of the systems composition, structure and main algorithms functioning developed for projects in various fields were reviewed. As a result, the joint application modes of neural networks and evidence theory algorithms including the features of architectures and their implementation have been determined. We also summarize information about the effectiveness of these methods' joint application in terms of the uncertainty level reducing and confidence level increasing in the decision-making data. The scope of this study results application is the architectural solutions design of a hybrid expert system for diagnosing the technology processes state and detecting anomalies in them. [ABSTRACT FROM AUTHOR] more...

Dempster–Shafer (D‐S) evidence theory is invaluable in the domain of multisource information fusion for handing uncertainty problems. However, there may be counter‐intuitive phenomenon when facing highly conflicting information. In this paper, a novel symmetric enhanced belief χ2 ${\chi }^{2}$ divergence measure, called SEBχ2 $SEB{\chi }^{2}$, is proposed to measure the discrepancy between basic probability assignments (BPAs). The SEBχ2 $SEB{\chi }^{2}$ divergence consider the features of BPAs as the influence of both single‐element subsets and multielement subsets is taken into account. Furthermore, the SEBχ2 $SEB{\chi }^{2}$ divergence is proven to be symmetric, nonnegative and nondegenerate, which are desirable properties for conflict management. Then, a new algorithm for multisource information fusion based on the SEBχ2 $SEB{\chi }^{2}$ divergence measure is derived. Finally, an application for pattern classification is used to illustrate the superiority of the proposed SEBχ2 $SEB{\chi }^{2}$ divergence measure‐based fusion method over other existing well‐known and recent related works with a better classification accuracy of 94.39%. [ABSTRACT FROM AUTHOR] more...

The article examines some algorithms for joint processing of raw data on the state of a complex multistage continuous production process to obtain probabilistic characteristics of abnormal critical events that can potentially lead to single failures or even emergencies. The article, thus, proposes and substantiates an approach to developing a technology to detect and predict malfunctions and determine their causes. The sequence of operations to process and convert diagnostic process data is considered essential. As a result, the article presents a general diagnostic model of a multistage production process. The model can formalize the main objects and processes in terms of the problem being solved. An incident is defined as an abnormal critical event described by non-normative values of diagnostic variables. Incidents are shown to be indicated by the corresponding membership functions. The hypotheses on potential incident causes are discussed to be built with belief functions being the basis of evidence theory or Dempster–Shafer theory. The hypotheses are characterized by an interval of malfunction probability in some process chain. The authors propose a procedure of converting these hypotheses into fuzzy production rules automatically. The automatical procedure is a prerequisite to using fuzzy neural networks to obtain a reliable estimate of the degree of belief in the incident cause. As a summary, the generated database of the production rules to train a neural network is substantiated to be used with the TSK architecture that makes possible to estimate a malfunction probability in the process chain quickly without resource-intensive computations. [ABSTRACT FROM AUTHOR] more...

The existing methods for information fusion and attribute selection typically require a computationally intensive grid search to determine the optimal parameter. This grid search can significantly impact the efficiency of these processes. To tackle this issue, this paper introduces the concept of neighborhood entropy, which incorporates both the neighborhood and decision classes, and delves into its applications in multi-source information fusion and attribute selection. First, the concept of a δ -neighborhood based on a predefined distance is introduced. Then the neighborhood entropy based on the δ -neighborhood is defined. The optimal parameters for information fusion and attribute selection are determined by minimizing the neighborhood entropy. Furthermore, an information fusion method and an attribute selection algorithm based on the neighborhood entropy, conditional information entropy (CIE), and belief functions are developed. Finally, we demonstrate the effectiveness of our approach through experiments and Wilcoxon tests on 12 datasets, including a large-scale gene dataset. The experimental results show that the optimal parameter determined by the neighborhood entropy aligns with that obtained through grid search and the neighborhood entropy reduces the computational burden of information fusion and attribute selection compared to grid search. When compared to other state-of-the-art algorithms, our approach based on the neighborhood entropy and CIE demonstrates superior classification performance and time efficiency. These findings demonstrate the efficiency and effectiveness of neighborhood entropy and pave the way for applying granular-computing-based information fusion methods to large-scale datasets. • Neighborhood entropy is defined based on the δ -neighborhood. • The optimal parameters of information fusion and attribute selection are determined by minimizing the neighborhood entropy. • An information fusion method and an attribute selection algorithm are proposed. • The results of experiments show that neighborhood entropy reduces the computational burden of information fusion and attribute selection. [ABSTRACT FROM AUTHOR] more...

Belief functions as a powerful model to represent and deal with uncertain information are widely used in information fusion. However, semantic association within a frame of discernment is not well defined in traditional framework of belief function theory. To solve the problem, in this work models and methods for evidence representation of uncertain information on a frame of discernment with semantic association are studied. These contributions are made in the study. At first, a formal definition for the concept of semantic association is proposed via an axiomatic manner. Second, new evidence representation models including belief, plausibility and commonality measures, are designed with the consideration of semantic association. Third, a novel evidence discounting operation, called associative discounting, is proposed to amend original evidence in terms of more refined meta-knowledge regarding the reliability of information sources. The effectiveness of proposed models and methods is verified through practical applications on UCI (University of California, Irvine) data sets for the combination of multiple classifiers. This work, on the one hand, has successfully imported the concept of semantic association into the framework of belief function theory; on the other hand, it provides a new scheme to correct original information in a more refined manner. • Models for evidence representation of uncertain information with the consideration of semantic association are proposed. • The concept of semantic association within a FOD is formalized mathematically in an axiomatic manner. • A new evidence discounting operation, called associative discounting, is proposed on the basis of the defined semantic association. [ABSTRACT FROM AUTHOR] more...

If the samples, features and information values in a real-valued information system are cells, genes and gene expression values, respectively, then for convenience, this system is said to be a single cell gene space. In the era of big data, people are faced with high dimensional gene expression data with redundancy and noise causing its strong uncertainty. D–S evidence theory excels at tackling the problem of uncertainty, and its conditions to be met are weaker than Bayesian probability theory. Therefore, this paper studies the gene selection in a single cell gene space to remove noise and redundancy with D–S evidence theory. The distance between two cells in each gene is first defined. Then, the tolerance relation is established according to the defined distance. In addition, the belief and plausibility functions to grasp the uncertainty of a single cell gene space are introduced on the basis of the tolerance classes. Statistical analysis shows that they can effectively measure the uncertainty of a single cell gene space. Furthermore, several gene selection algorithms in a single cell gene space are presented using the proposed belief and plausibility. Finally, the performance of the proposed algorithm is compared to other algorithms on some published single-cell data sets. Experimental results and statistical tests show that the classification and clustering performance of the presented algorithm not only exceeds the other three state-of-the-art algorithms, but also its gene reduction rate is very high. [ABSTRACT FROM AUTHOR] more...

Feature selection is one basic and critical technology for data mining, especially in current “big data era”. Rough set theory (RST) is sensitive to noise in feature selection due to the strict condition of equivalence relation. However, D-S evidence theory is flexible to measure uncertainty of information. This paper introduces robust feature evaluation metrics “belief function” and “plausibility function” into feature selection algorithm to avoid the defect that classification effect is affected by noise. First of all, similarity between information values in an interval-valued information system (IVIS) is given and a variable parameter to control the similarity of samples is introduced. Then, $\theta $ -lower approximation and $\theta $ -upper approximation in IVIS are put forward. Next, belief function and plausibility function based on $\theta $ -lower approximation and $\theta $ -upper approximation are put forward. Finally, four feature selection algorithms in an IVIS based on D-S evidence theory are proposed. The experimental results on four real interval-valued datasets show that the proposed metrics are robust to noise, and the proposed algorithms are more effective than the existing algorithms. more...

As well-known machine learning methods, decision trees are widely applied in classification and recognition areas. In this paper, with the uncertainty of labels handled by belief functions, a new decision tree method based on belief entropy is proposed and then extended to random forest. With the Gaussian mixture model, this tree method is able to deal with continuous attribute values directly, without pretreatment of discretization. Specifically, the tree method adopts belief entropy, a kind of uncertainty measurement based on the basic belief assignment, as a new attribute selection tool. To improve the classification performance, we constructed a random forest based on the basic trees and discuss different prediction combination strategies. Some numerical experiments on UCI machine learning data set were conducted, which indicate the good classification accuracy of the proposed method in different situations, especially on data with huge uncertainty. [ABSTRACT FROM AUTHOR] more...

Counter deception is one of the main content in data fusion. The existence of deceptive data may cause great hidden dangers to the generation of correct decisions. While among previous studies, whether evidence should aggregate is still virgin and may become a fascinating question. In this paper, a new counter deception model based on the Shapley value methodology is proposed, which provides a perspective for determining the weight of evidence. Then, we present that the distance of evidence is a kind of "marginal contribution" to the anomaly of the entire fusion system. Moreover, we also investigated the properties of the proposed method to judge whether there is deceptive data in the information fusion based on the cooperation benefits of all basic belief assignment (BBA) combinations. Several numerical examples and a classification application were used to illustrate the practicability and effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR] more...

Dempster–Shafer theory is invaluable for handing uncertain problems in multisource information fusion field. But how to fuse highly conflicting information remains a pending issue. To deal with the issue, we propose a novel reinforced belief χ 2 divergence measure (named as χ 2 divergence) to calculate the conflict degree between evidence. The proposed χ 2 divergence comprehensively considers the effects of the single‐element subset and the multielement subset. In addition, the χ 2 divergence has been proved to be a bounded, nondegenerate, and symmetrical divergence measure. Then, we design a new χ 2 divergence‐based multisource information fusion method. This method combines information volume weights and supports degree weights to modify the evidence before fusion. Finally, an application for fault diagnosis is provided to show that the proposed method is superior to other existing methods [ABSTRACT FROM AUTHOR] more...

In this paper, we investigate the role of trust in supply forecast signalling in a supply chain with a supplier and a manufacturer in a one-shot game. It is assumed that the supplier faces a random yield uncertainty that is multiplied by the manufacturer’s order quantity. The supplier has a private forecast of yield risk. Based on the information, the supplier decides whether to share its forecast truthfully, or not to share. On the other hand, the manufacturer is faced with two ordering strategies. If it trusts the supplier’s report, then it updates its belief on the yield risk providing a forecast signal by the supplier. Otherwise, it orders based on its prior belief. We analytically obtain the optimal order quantity where the random yield uncertainty follows uniform distribution. The intuitive result indicates that the supplier has a tendency to deviate from reporting true forecast information. The numerical results support the intuitive conclusion. [ABSTRACT FROM AUTHOR] more...

In a recent paper Ronald Meester and Timber Kerkvliet argue by example that infinite epistemic regresses have different solutions depending on whether they are analyzed with probability functions or with belief functions. Meester and Kerkvliet give two examples, each of which aims to show that an analysis based on belief functions yields a different numerical outcome for the agent's degree of rational belief than one based on probability functions. In the present paper we however show that the outcomes are the same. The only way in which probability functions and belief functions can yield different solutions for the agent's degree of belief is if they are applied to different examples, i.e. to different situations in which the agent finds himself. [ABSTRACT FROM AUTHOR] more...

To measure conflict between two basic probability assignment functions plays the key role of conflict management in Dempster-shafer evidence theory. In this paper, a new conflict measure is proposed. First, the classical pignistic probability transform (PPT) is generalized as pignistic belief transform (PBT). One of the advantages of PBT is that it can assign belief to multiple sets. When the belief is assigned to single element, the proposed PBT is degenerated as classical PPT. Then, the betting distance of two pignistic belief transforms is proposed, which can be used as a new conflict degree of BPAs. Finally, a numerical example is illustrated to show the use of the proposed method to combine conflicting evidence. more...

Transfer learning (TL) has grown popular in recent years. It is effective to improve the classification accuracy in the target domain by using the training knowledge in the related domain (called source domain). However, the classification of missing data (or incomplete data) is a challenging task for TL because different strategies of imputation may have strong impacts on learning models. To address this problem, we propose credal transfer learning (CTL) with multi-estimation for missing data based on belief function theory by introducing uncertainty and imprecision in data imputation procedure. CTL mainly consists of three steps: Firstly, the query patterns are reasonably mapped into multiple versions in source domain to characterize the uncertainty caused by missing values. Afterwards, the multiple mapping patterns are classified in the source domain to obtain the corresponding outputs with different discounting factors. Finally, the discounted outputs, represented by the basic belief assignments (BBAs), are submitted to a new belief-based fusion system to get the final classification result for the query patterns. Three comparative experiments are given to illustrate the interests and potentials of CTL method. more...