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.

Domain Adaptation with Data Uncertainty Measure Based on Evidence Theory.

Domain adaptation aims to learn a classifier for a target domain task by using related labeled data from the source domain. Because source domain data and target domain task may be mismatched, there is an uncertainty of source domain data with respect to the target domain task. Ignoring the uncertainty may lead to models with unreliable and suboptimal classification results for the target domain task. However, most previous works focus on reducing the gap in data distribution between the source and target domains. They do not consider the uncertainty of source domain data about the target domain task and cannot apply the uncertainty to learn an adaptive classifier. Aimed at this problem, we revisit the domain adaptation from source domain data uncertainty based on evidence theory and thereby devise an adaptive classifier with the uncertainty measure. Based on evidence theory, we first design an evidence net to estimate the uncertainty of source domain data about the target domain task. Second, we design a general loss function with the uncertainty measure for the adaptive classifier and extend the loss function to support vector machine. Finally, numerical experiments on simulation datasets and real-world applications are given to comprehensively demonstrate the effectiveness of the adaptive classifier with the uncertainty measure.

Measuring Uncertainty in the Negation Evidence for Multi-Source Information Fusion.

Dempster-Shafer evidence theory is widely used in modeling and reasoning uncertain information in real applications. Recently, a new perspective of modeling uncertain information with the negation of evidence was proposed and has attracted a lot of attention. Both the basic probability assignment (BPA) and the negation of BPA in the evidence theory framework can model and reason uncertain information. However, how to address the uncertainty in the negation information modeled as the negation of BPA is still an open issue. Inspired by the uncertainty measures in Dempster-Shafer evidence theory, a method of measuring the uncertainty in the negation evidence is proposed. The belief entropy named Deng entropy, which has attracted a lot of attention among researchers, is adopted and improved for measuring the uncertainty of negation evidence. The proposed measure is defined based on the negation function of BPA and can quantify the uncertainty of the negation evidence. In addition, an improved method of multi-source information fusion considering uncertainty quantification in the negation evidence with the new measure is proposed. Experimental results on a numerical example and a fault diagnosis problem verify the rationality and effectiveness of the proposed method in measuring and fusing uncertain information.

Evaluating High-Variance Leaves as Uncertainty Measure for Random Forest Regression.

Uncertainty measures estimate the reliability of a predictive model. Especially in the field of molecular property prediction as part of drug design, model reliability is crucial. Besides other techniques, Random Forests have a long tradition in machine learning related to chemoinformatics and are widely used. Random Forests consist of an ensemble of individual regression models, namely, decision trees and, therefore, provide an uncertainty measure already by construction. Regarding the disagreement of single-model predictions, a narrower distribution of predictions is interpreted as a higher reliability. The standard deviation of the decision tree ensemble predictions is the default uncertainty measure for Random Forests. Due to the increasing application of machine learning in drug design, there is a constant search for novel uncertainty measures that, ideally, outperform classical uncertainty criteria. When analyzing Random Forests, it appears obvious to consider the variance of the dependent variables within each terminal decision tree leaf to obtain predictive uncertainties. Hereby, predictions that arise from more leaves of high variance are considered less reliable. Expectedly, the number of such high-variance leaves yields a reasonable uncertainty measure. Depending on the dataset, it can also outperform ensemble uncertainties. However, small-scale comparisons, i.e., considering only a few datasets, are insufficient, since they are more prone to chance correlations. Therefore, large-scale estimations are required to make general claims about the performance of uncertainty measures. On several chemoinformatic regression datasets, high-variance leaves are compared to the standard deviation of ensemble predictions. It turns out that high-variance leaf uncertainty is meaningful, not superior to the default ensemble standard deviation. A brief possible explanation is offered.

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.

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making.

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov's intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

Uncertainty of Interval Type-2 Fuzzy Sets Based on Fuzzy Belief Entropy.

Interval type-2 fuzzy sets (IT2 FS) play an important part in dealing with uncertain applications. However, how to measure the uncertainty of IT2 FS is still an open issue. The specific objective of this study is to present a new entropy named fuzzy belief entropy to solve the problem based on the relation among IT2 FS, belief structure, and Z-valuations. The interval of membership function can be transformed to interval BPA [Bel,Pl]. Then, Bel and Pl are put into the proposed entropy to calculate the uncertainty from the three aspects of fuzziness, discord, and nonspecificity, respectively, which makes the result more reasonable. Compared with other methods, fuzzy belief entropy is more reasonable because it can measure the uncertainty caused by multielement fuzzy subsets. Furthermore, when the membership function belongs to type-1 fuzzy sets, fuzzy belief entropy degenerates to Shannon entropy. Compared with other methods, several numerical examples are demonstrated that the proposed entropy is feasible and persuasive.

Accuracy, uncertainty, and adaptability of automatic myocardial ASL segmentation using deep CNN.

PURPOSE: To apply deep convolution neural network to the segmentation task in myocardial arterial spin labeled perfusion imaging and to develop methods that measure uncertainty and that adapt the convolution neural network model to a specific false-positive versus false-negative tradeoff. METHODS: The Monte Carlo dropout U-Net was trained on data from 22 subjects and tested on data from 6 heart transplant recipients. Manual segmentation and regional myocardial blood flow were available for comparison. We consider 2 global uncertainty measures, named "Dice uncertainty" and "Monte Carlo dropout uncertainty," which were calculated with and without the use of manual segmentation, respectively. Tversky loss function with a hyperparameter ß was used to adapt the model to a specific false-positive versus false-negative tradeoff. RESULTS: The Monte Carlo dropout U-Net achieved a Dice coefficient of 0.91 ± 0.04 on the test set. Myocardial blood flow measured using automatic segmentations was highly correlated to that measured using the manual segmentation (R2 = 0.96). Dice uncertainty and Monte Carlo dropout uncertainty were in good agreement (R2 = 0.64). As ß increased, the false-positive rate systematically decreased and false-negative rate systematically increased. CONCLUSION: We demonstrate the feasibility of deep convolution neural network for automatic segmentation of myocardial arterial spin labeling, with good accuracy. We also introduce 2 simple methods for assessing model uncertainty. Finally, we demonstrate the ability to adapt the convolution neural network model to a specific false-positive versus false-negative tradeoff. These findings are directly relevant to automatic segmentation in quantitative cardiac MRI and are broadly applicable to automatic segmentation problems in diagnostic imaging.

Explainable classifier for improving the accountability in decision-making for colorectal cancer diagnosis from histopathological images.

Pathologists are responsible for cancer type diagnoses from histopathological cancer tissues. However, it is known that microscopic examination is tedious and time-consuming. In recent years, a long list of machine learning approaches to image classification and whole-slide segmentation has been developed to support pathologists. Although many showed exceptional performances, the majority of them are not able to rationalize their decisions. In this study, we developed an explainable classifier to support decision making for medical diagnoses. The proposed model does not provide an explanation about the causality between the input and the decisions, but offers a human-friendly explanation about the plausibility of the decision. Cumulative Fuzzy Class Membership Criterion (CFCMC) explains its decisions in three ways: through a semantical explanation about the possibilities of misclassification, showing the training sample responsible for a certain prediction and showing training samples from conflicting classes. In this paper, we explain about the mathematical structure of the classifier, which is not designed to be used as a fully automated diagnosis tool but as a support system for medical experts. We also report on the accuracy of the classifier against real world histopathological data for colorectal cancer. We also tested the acceptability of the system through clinical trials by 14 pathologists. We show that the proposed classifier is comparable to state of the art neural networks in accuracy, but more importantly it is more acceptable to be used by human experts as a diagnosis tool in the medical domain.

An Improved Total Uncertainty Measure in the Evidence Theory and Its Application in Decision Making.

Dempster-Shafer evidence theory (DS theory) has some superiorities in uncertain information processing for a large variety of applications. However, the problem of how to quantify the uncertainty of basic probability assignment (BPA) in DS theory framework remain unresolved. The goal of this paper is to define a new belief entropy for measuring uncertainty of BPA with desirable properties. The new entropy can be helpful for uncertainty management in practical applications such as decision making. The proposed uncertainty measure has two components. The first component is an improved version of Dubois-Prade entropy, which aims to capture the non-specificity portion of uncertainty with a consideration of the element number in frame of discernment (FOD). The second component is adopted from Nguyen entropy, which captures conflict in BPA. We prove that the proposed entropy satisfies some desired properties proposed in the literature. In addition, the proposed entropy can be reduced to Shannon entropy if the BPA is a probability distribution. Numerical examples are presented to show the efficiency and superiority of the proposed measure as well as an application in decision making.

Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System.

The Pythagorean fuzzy number (PFN) consists of membership and non-membership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multi-criteria decision-making (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and high-quality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.

A New Belief Entropy in Dempster-Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment.

Dempster-Shafer theory has been widely used in many applications, especially in the measurement of information uncertainty. However, under the D-S theory, how to use the belief entropy to measure the uncertainty is still an open issue. In this paper, we list some significant properties. The main contribution of this paper is to propose a new entropy, for which some properties are discussed. Our new model has two components. The first is Nguyen entropy. The second component is the product of the cardinality of the frame of discernment (FOD) and Dubois entropy. In addition, under certain conditions, the new belief entropy can be transformed into Shannon entropy. Compared with the others, the new entropy considers the impact of FOD. Through some numerical examples and simulation, the proposed belief entropy is proven to be able to measure uncertainty accurately.

Paradox Elimination in Dempster-Shafer Combination Rule with Novel Entropy Function: Application in Decision-Level Multi-Sensor Fusion.

Multi-sensor data fusion technology in an important tool in building decision-making applications. Modified Dempster-Shafer (DS) evidence theory can handle conflicting sensor inputs and can be applied without any prior information. As a result, DS-based information fusion is very popular in decision-making applications, but original DS theory produces counterintuitive results when combining highly conflicting evidences from multiple sensors. An effective algorithm offering fusion of highly conflicting information in spatial domain is not widely reported in the literature. In this paper, a successful fusion algorithm is proposed which addresses these limitations of the original Dempster-Shafer (DS) framework. A novel entropy function is proposed based on Shannon entropy, which is better at capturing uncertainties compared to Shannon and Deng entropy. An 8-step algorithm has been developed which can eliminate the inherent paradoxes of classical DS theory. Multiple examples are presented to show that the proposed method is effective in handling conflicting information in spatial domain. Simulation results showed that the proposed algorithm has competitive convergence rate and accuracy compared to other methods presented in the literature.

Negation of Belief Function Based on the Total Uncertainty Measure.

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

A Novel Uncertainty Management Approach for Air Combat Situation Assessment Based on Improved Belief Entropy.

Uncertain information exists in each procedure of an air combat situation assessment. To address this issue, this paper proposes an improved method to address the uncertain information fusion of air combat situation assessment in the Dempster-Shafer evidence theory (DST) framework. A better fusion result regarding the prediction of military intention can be helpful for decision-making in an air combat situation. To obtain a more accurate fusion result of situation assessment, an improved belief entropy (IBE) is applied to preprocess the uncertainty of situation assessment information. Data fusion of assessment information after preprocessing will be based on the classical Dempster's rule of combination. The illustrative example result validates the rationality and the effectiveness of the proposed method.

An Extension to Deng's Entropy in the Open World Assumption with an Application in Sensor Data Fusion.

Quantification of uncertain degree in the Dempster-Shafer evidence theory (DST) framework with belief entropy is still an open issue, even a blank field for the open world assumption. Currently, the existed uncertainty measures in the DST framework are limited to the closed world where the frame of discernment (FOD) is assumed to be complete. To address this issue, this paper focuses on extending a belief entropy to the open world by considering the uncertain information represented as the FOD and the nonzero mass function of the empty set simultaneously. An extension to Deng’s entropy in the open world assumption (EDEOW) is proposed as a generalization of the Deng’s entropy and it can be degenerated to the Deng entropy in the closed world wherever necessary. In order to test the reasonability and effectiveness of the extended belief entropy, an EDEOW-based information fusion approach is proposed and applied to sensor data fusion under uncertainty circumstance. The experimental results verify the usefulness and applicability of the extended measure as well as the modified sensor data fusion method. In addition, a few open issues still exist in the current work: the necessary properties for a belief entropy in the open world assumption, whether there exists a belief entropy that satisfies all the existed properties, and what is the most proper fusion frame for sensor data fusion under uncertainty.

Modeling and Fusing the Uncertainty of FMEA Experts Using an Entropy-Like Measure with an Application in Fault Evaluation of Aircraft Turbine Rotor Blades.

As a typical tool of risk analysis in practical engineering, failure mode and effects analysis (FMEA) theory is a well known method for risk prediction and prevention. However, how to quantify the uncertainty of the subjective assessments from FMEA experts and aggregate the corresponding uncertainty to the classical FMEA approach still needs further study. In this paper, we argue that the subjective assessments of FMEA experts can be adopted to model the weight of each FMEA expert, which can be regarded as a data-driven method for ambiguity information modeling in FMEA method. Based on this new perspective, a modified FMEA approach is proposed, where the subjective uncertainty of FMEA experts is handled in the framework of Dempster-Shafer evidence theory (DST). In the improved FMEA approach, the ambiguity measure (AM) which is an entropy-like uncertainty measure in DST framework is applied to quantify the uncertainty degree of each FMEA expert. Then, the classical risk priority number (RPN) model is improved by aggregating an AM-based weight factor into the RPN function. A case study based on the new RPN model in aircraft turbine rotor blades verifies the applicable and useful of the proposed FMEA approach.

A Weighted Belief Entropy-Based Uncertainty Measure for Multi-Sensor Data Fusion.

In real applications, how to measure the uncertain degree of sensor reports before applying sensor data fusion is a big challenge. In this paper, in the frame of Dempster-Shafer evidence theory, a weighted belief entropy based on Deng entropy is proposed to quantify the uncertainty of uncertain information. The weight of the proposed belief entropy is based on the relative scale of a proposition with regard to the frame of discernment (FOD). Compared with some other uncertainty measures in Dempster-Shafer framework, the new measure focuses on the uncertain information represented by not only the mass function, but also the scale of the FOD, which means less information loss in information processing. After that, a new multi-sensor data fusion approach based on the weighted belief entropy is proposed. The rationality and superiority of the new multi-sensor data fusion method is verified according to an experiment on artificial data and an application on fault diagnosis of a motor rotor.

Turkish adaptation of the Mishel uncertainty in illness scale-community form.

PURPOSE: The study aims to conduct the Turkish validity and reliability study of the Mishel uncertainty in illness scale-community form. DESIGN AND METHODS: This is a study with a methodological design. It was carried out in a family health center in a province in the Black Sea Region between May and October 2019. The sample of the study consisted of 479 individuals with chronic diseases. The data were analyzed with exploratory and confirmatory factor analysis. FINDINGS: The Cronbach's alpha was found to be 0.79. The fit indices of the 20-item scale with three-factor structure are at an acceptable level (root mean square error of approximation: 0.056; comparative fit index: 0.926; incremental fix index: 0.927; goodness of fit index: 0.918; Tucker-Lewis index: 0.915; adjusted goodness of fit index: 0.896; χ2 /SD: 2.481, p < 0.001). PRACTICE IMPLICATIONS: The level of uncertainty revealed by the scale gives information about the chronic disease management of individuals.

An improved measure for belief structure in the evidence theory.

Dempster-Shafer evidence theory (D-S theory) is suitable for processing uncertain information under complex circumstances. However, how to measure the uncertainty of basic probability distribution (BPA) in D-S theory is still an open question. In this paper, a method of measuring total uncertainty based on belief interval distance is proposed. This method is directly defined in the D-S theoretical framework, without the need of converting BPA into probability distribution by Pignistic probability transformation. Thus, it avoids the loss of information. This paper analyzes the advantages and disadvantages of the previous total uncertainty of measurement, and the uncertainty measurement examples show the effectiveness of the new uncertainty measure. Finally, an information fusion method based on the new uncertainty measure is proposed. The validity and rationality of the proposed method are verified by two classification experiments from UCI data sets.