Generalization of Dempster–Shafer theory: A complex mass function

ML-DSTnet: A Novel Hybrid Model for Breast Cancer Diagnosis Improvement Based on Image Processing Using Machine Learning and Dempster-Shafer Theory

Medical intelligence detection systems have changed with the help of artificial intelligence and have also faced challenges. Breast cancer diagnosis and classification are part of this medical intelligence system. Early detection can lead to an increase in treatment options. On the other hand, uncertainty is a case that has always been with the decision-maker. The system's parameters cannot be accurately estimated, and the wrong decision is made. To solve this problem, we have proposed a method in this article that reduces the ignorance of the problem with the help of Dempster-Shafer theory so that we can make a better decision. This research on the MIAS dataset, based on image processing machine learning and Dempster-Shafer mathematical theory, tries to improve the diagnosis and classification of benign, malignant masses. We first determine the results of the diagnosis of mass type with MLP by using the texture feature and CNN. We combine the results of the two classifications with Dempster-Shafer theory and improve its accuracy. The obtained results show that the proposed approach has better performance than others based on evaluation criteria such as accuracy of 99.10%, sensitivity of 98.4%, and specificity of 100%.

Negation of the Quantum Mass Function for Multisource Quantum Information Fusion With its Application to Pattern Classification

In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, we study quantum decisions from the negation perspective. Specifically, complex evidence theory (CET) is considered to be effective to express and handle uncertain information in a complex plane. Therefore, we first express CET in the quantum framework of Hilbert space. On this basis, a generalized negation method is proposed for quantum basic belief assignment (QBBA), called QBBA negation. In addition, a QBBA entropy is revisited to study the QBBA negation process to reveal the variation tendency of negation iteration. Meanwhile, the properties of the QBBA negation function are analyzed and discussed along with special cases. Then, several multisource quantum information fusion (MSQIF) algorithms are designed to support decision making. Finally, these MSQIF algorithms are applied in pattern classification to demonstrate their effectiveness. This is the first work to design MSQIF algorithms to support quantum decision making from a new perspective of "negation", which provides promising solutions to knowledge representation, uncertainty measure, and fusion of quantum information.

Bearing fault diagnosis method based on attention mechanism and multilayer fusion network

The methods with multi-sensor data fusion have been a remarkable way to improve the accuracy and robustness of bearing fault diagnosis under complicated conditions. However, most of the existing fusion models or methods belong to single fusion level and simple fusion structure is usually utilized, and the correlation and complementarity of information between multi-sensor data might be easily ignored. In order to improve the performance of fault diagnosis with multi-sensor data fusion, this paper proposes a novel model of multi-layer deep fusion network with attention mechanism (AMMFN). The proposed model consists of a central network and multiple branch networks stacking by Inception networks, and the deep features of each single-sensor data are extracted automatically by the branch networks, and the extracted features of multi-sensor data at different levels are fused with the central network, and then the information interaction between multi-sensor data can be significantly enhanced and the adaptive hierarchical fusion of information can be achieved. Moreover, a fusion strategy based on attention mechanism is designed to extract more correlation information during the fusion of features extracted from multi-sensor data. Extensive experiments are also performed to evaluate the performance of proposed approach, and the comparison results with other methods indicate that the presented method takes higher accuracy and stronger generalization ability.

CEQD: A Complex Mass Function to Predict Interference Effects

Uncertainty is inevitable in the decision-making process of real applications. Quantum mechanics has become an interesting and popular topic in predicting and explaining human decision-making behaviors, especially regarding interference effects caused by uncertainty in the process of decision making, due to the limitations of Bayesian reasoning. In addition, complex evidence theory (CET), as a generalized Dempster-Shafer evidence theory, has been proposed to represent and handle uncertainty in the framework of the complex plane, and it is an effective tool in uncertainty reasoning. Particularly, the complex mass function, also known as a complex basic belief assignment in CET, is complex-value modeled, which is superior to the classical mass function in expressing uncertain information. CET is considered to have certain inherent connections with quantum mechanics since both are complex-value modeled and can be applied in handling uncertainty in decision-making problems. In this article, therefore, by bridging CET and quantum mechanics, we propose a new complex evidential quantum dynamical (CEQD) model to predict interference effects on human decision-making behaviors. In addition, uniform and weighted complex Pignistic belief transformation functions are proposed, which can be used effectively in the CEQD model to help explain interference effects. The experimental results and comparisons demonstrate the effectiveness of the proposed method. In summary, the proposed CEQD method provides a new perspective to study and explain the interference effects involved in human decision-making behaviors, which is significant for decision theory.

Non-rigid Multi-Modal Medical Image Registration Based on Improved Maximum Mutual Information PV Image Interpolation Method

With the continuous improvement of medical imaging equipment, CT, MRI and PET images can obtain accurate anatomical information of the same patient site. However, due to the fuzziness of medical image physiological evaluation and the unhealthy understanding of objects, the registration effect of many methods is not ideal. Therefore, based on the medical image registration model of Partial Volume (PV) image interpolation method and rigid medical image registration method, this paper established the non-rigid registration model of maximum mutual information Novel Partial Volume (NPV) image interpolation method. The proposed NPV interpolation method uses the Davidon-Fletcher-Powell algorithm (DFP) algorithm optimization method to solve the transformation parameter matrix and realize the accurate transformation of the floating image. In addition, the cubic B-spline is used as the kernel function to improve the image interpolation, which effectively improves the accuracy of the registration image. Finally, the proposed NPV method is compared with the PV interpolation method through the human brain CT-MRI-PET image to obtain a clear CT-MRI-PET image. The results show that the proposed NPV method has higher accuracy, better robustness, and easier realization. The model should also have guiding significance in face recognition and fingerprint recognition.

Maximum Entropy (MaxEnt) Based DEMATEL and Its Application in Emergency Management

Since DEMATEL can visualize the structure of complex causal relationships, it is widely used in decision making. One of the important steps in DEMATEL is normalization, and it has received a lot of attention in recent years. Maximum entropy is a universal principle, and it is an effective tool for determining the amount of information existed in evidence. In this paper, maximum entropy based DEMATEL, named as MaxEnt-DEMETEL is proposed, the greatest contribution in this paper is the use of maximum entropy principle to determine the normalized direct influence matrix, which makes it possible to obtain the normalized matrix with minimal information loss. Emergency management is illustrated to show the superiority of the proposed method.

Weighted assignment fusion algorithm of evidence conflict based on Euclidean distance and weighting strategy, and application in the wind turbine system

In the process of intelligent system operation fault diagnosis and decision making, the multi-source, heterogeneous, complex, and fuzzy characteristics of information make the conflict, uncertainty, and validity problems appear in the process of information fusion, which has not been solved. In this study, we analyze the credibility and variation of conflict among evidence from the perspective of conflict credibility weight and propose an improved model of multi-source information fusion based on Dempster-Shafer theory (DST). From the perspectives of the weighting strategy and Euclidean distance strategy, we process the basic probability assignment (BPA) of evidence and assign the credible weight of conflict between evidence to achieve the extraction of credible conflicts and the adoption of credible conflicts in the process of evidence fusion. The improved algorithm weakens the problem of uncertainty and ambiguity caused by conflicts in the information fusion process, and reduces the impact of information complexity on analysis results. And it carries a practical application out with the fault diagnosis of wind turbine system to analyze the operation status of wind turbines in a wind farm to verify the effectiveness of the proposed algorithm. The result shows that under the conditions of improved distance metric evidence discrepancy and credible conflict quantification, the algorithm better shows the conflict and correlation among the evidence. It improves the accuracy of system operation reliability analysis, improves the utilization rate of wind energy resources, and has practical implication value.

A Unified Hierarchical XGBoost model for classifying priorities for COVID-19 vaccination campaign

The current ML approaches do not fully focus to answer a still unresolved and topical challenge, namely the prediction of priorities of COVID-19 vaccine administration. Thus, our task includes some additional methodological challenges mainly related to avoiding unwanted bias while handling categorical and ordinal data with a highly imbalanced nature. Hence, the main contribution of this study is to propose a machine learning algorithm, namely Hierarchical Priority Classification eXtreme Gradient Boosting for priority classification for COVID-19 vaccine administration using the Italian Federation of General Practitioners dataset that contains Electronic Health Record data of 17k patients. We measured the effectiveness of the proposed methodology for classifying all the priority classes while demonstrating a significant improvement with respect to the state of the art. The proposed ML approach, which is integrated into a clinical decision support system, is currently supporting General Pracitioners in assigning COVID-19 vaccine administration priorities to their assistants.

ER rule classifier with an optimization operator recommendation

It is difficult for many classic classification methods to consider expert experience and classify small-sample datasets well. The evidential reasoning rule (ER rule) classifier can solve these problems. The ER rule has strong processing and comprehensive analysis abilities for diversified mixed information and can solve problems with expert experience effectively. Moreover, the initial parameters of the classifier constructed based on the ER rule can be set according to empirical knowledge instead of being trained by a large number of samples, which can help the classifier classify small-sample datasets well. However, the initial parameters of the ER rule classifier need to be optimized, and choosing the best optimization algorithm is still a challenge. Considering these problems, the ER rule classifier with an optimization operator recommendation is proposed in this paper. First, the initial ER rule classifier is constructed based on training samples and expert experience. Second, the adjustable parameters are optimized, in which the optimization operator recommendation strategy is applied to select the best algorithm by partial samples, and then experiments with full samples are carried out. Finally, a case study on a turbofan engine degradation simulation dataset is carried out, and the results indicate that the ER rule classifier has a higher classification accuracy than other classic classifiers, which demonstrates the capability and effectiveness of the proposed ER rule classifier with an optimization operator recommendation.

MADA problem: A new scheme based on D numbers and aggregation functions

Describing and processing complex as well as ambiguous and uncertain information has always been an inescapable and challenging topic in multi-attribute decision analysis (MADA) problems. As an extension of Dempster-Shafer (D-S) evidence theory, D numbers breaks through the constraints of the constraint framework and is a new way of expressing uncertainty. The soft likelihood function based on POWA operator is one of the most useful tools recently developed for dealing with uncertain information, since it provides a more excellent performance for the aggregation of multiple compatible evidence. Recently, a new MADA model based on D numbers has been proposed, called DMADA. In this paper, inspired by the above mentioned theories, based on soft likelihood functions, POWA aggregation and D numbers we design a novel model to improve the performance of representing and processing uncertain information in MADA problems as an improvement of the DMADA approach. In contrast, our advantages include mainly the following. Firstly, the proposed method considers the reliability characteristics of each initial D number information. Secondly, the proposed method empowers decision makers with the possibility to express their perceptions through attitudinal features. In addition, an interesting finding is that the preference parameter in the proposed method can clearly distinguish the variability between candidates by adjusting the space values between adjacent alternatives, making the decision results clearer. Finally, the effectiveness and superiority of this model are proved through analysis and testing.

CED: A Distance for Complex Mass Functions

Evidence theory is an effective methodology for modeling and processing uncertainty that has been widely applied in various fields. In evidence theory, a number of distance measures have been presented, which play an important role in representing the degree of difference between pieces of evidence. However, the existing evidential distances focus on traditional basic belief assignments (BBAs) modeled in terms of real numbers and are not compatible with complex BBAs (CBBAs) extended to the complex plane. Therefore, in this article, a generalized evidential distance measure called the complex evidential distance (CED) is proposed, which can measure the difference or dissimilarity between CBBAs in complex evidence theory. This is the first work to consider distance measures for CBBAs, and it provides a promising way to measure the differences between pieces of evidence in a more general framework of complex plane space. Furthermore, the CED is a strict distance metric with the properties of nonnegativity, nondegeneracy, symmetry, and triangle inequality that satisfies the axioms of a distance. In particular, when the CBBAs degenerate into classical BBAs, the CED will degenerate into Jousselme et al.'s distance. Therefore, the proposed CED is a generalization of the traditional evidential distance, but it has a greater ability to measure the difference or dissimilarity between pieces of evidence. Finally, a decision-making algorithm for pattern recognition is devised based on the CED and is applied to a medical diagnosis problem to illustrate its practicability.

Age and Gender as Cyber Attribution Features in Keystroke Dynamic-Based User Classification Processes

Keystroke dynamics are used to authenticate users, to reveal some of their inherent or acquired characteristics and to assess their mental and physical states. The most common features utilized are the time intervals that the keys remain pressed and the time intervals that are required to use two consecutive keys. This paper examines which of these features are the most important and how utilization of these features can lead to better classification results. To achieve this, an existing dataset consisting of 387 logfiles is used, five classifiers are exploited and users are classified by gender and age. The results, while demonstrating the application of these two characteristics jointly on classifiers with high accuracy, answer the question of which keystroke dynamics features are more appropriate for classification with common classifiers.

Complex Entropy and Its Application in Decision-Making for Medical Diagnosis

In decision-making systems, how to measure uncertain information remains an open issue, especially for information processing modeled on complex planes. In this paper, a new complex entropy is proposed to measure the uncertainty of a complex-valued distribution (CvD). The proposed complex entropy is a generalization of Gini entropy that has a powerful capability to measure uncertainty. In particular, when a CvD reduces to a probability distribution, the complex entropy will degrade into Gini entropy. In addition, the properties of complex entropy, including the nonnegativity, maximum and minimum entropies, and boundedness, are analyzed and discussed. Several numerical examples illuminate the superiority of the newly defined complex entropy. Based on the newly defined complex entropy, a multisource information fusion algorithm for decision-making is developed. Finally, we apply the decision-making algorithm in a medical diagnosis problem to validate its practicability.

Evidence approach imprecise intervals: extensions and evaluation measures

In a number of applications the data will be represented in an interval format. We consider here a nested representation of uncertain information in intervals using Dempster-Shafer evidence approaches. These representations can be used in variety of applications including spatial and temporal reasoning and economic cost valuations. Two representations of nested intervals, RP1 and RP2, are defined and used in the paper. Basically an inner interval represents the more certain data and is nested in the outer less certain interval. We illustrate how the specificity measure could be used to evaluate such nested Dempster-Shafer intervals. We then consider Gini information measures applicable to the RP1 representation. We describe an example using our interval approach to COVID contact tracing in epidemiology. Finally examples of aggregation of intervals are provided. It is seen that an aggregated result can be evaluated and shown to increase the specificity of the result. Additionally, it is not always the case that aggregation increases specificity. An example is given illustrating such a case.

Complex Pignistic Transformation-Based Evidential Distance for Multisource Information Fusion of Medical Diagnosis in the IoT

Multisource information fusion has received much attention in the past few decades, especially for the smart Internet of Things (IoT). Because of the impacts of devices, the external environment, and communication problems, the collected information may be uncertain, imprecise, or even conflicting. How to handle such kinds of uncertainty is still an open issue. Complex evidence theory (CET) is effective at disposing of uncertainty problems in the multisource information fusion of the IoT. In CET, however, how to measure the distance among complex basis belief assignments (CBBAs) to manage conflict is still an open issue, which is a benefit for improving the performance in the fusion process of the IoT. In this paper, therefore, a complex Pignistic transformation function is first proposed to transform the complex mass function; then, a generalized betting commitment-based distance (BCD) is proposed to measure the difference among CBBAs in CET. The proposed BCD is a generalized model to offer more capacity for measuring the difference among CBBAs. Additionally, other properties of the BCD are analyzed, including the non-negativeness, nondegeneracy, symmetry, and triangle inequality. Besides, a basis algorithm and its weighted extension for multi-attribute decision-making are designed based on the newly defined BCD. Finally, these decision-making algorithms are applied to cope with the medical diagnosis problem under the smart IoT environment to reveal their effectiveness.

A Novel Hybrid Approach for Risk Evaluation of Vehicle Failure Modes

This paper addresses the problem of evaluating vehicle failure modes efficiently during the driving process. Generally, the most critical factors for preventing risk in potential failure modes are identified by the experience of experts through the widely used failure mode and effect analysis (FMEA). However, it has previously been difficult to evaluate the vehicle failure mode with crisp values. In this paper, we propose a novel hybrid scheme based on a cost-based FMEA, fuzzy analytic hierarchy process (FAHP), and extended fuzzy multi-objective optimization by ratio analysis plus full multiplicative form (EFMULTIMOORA) to evaluate vehicle failure modes efficiently. Specifically, vehicle failure modes are first screened out by cost-based FMEA according to maintenance information, and then the weights of the three criteria of maintenance time (T), maintenance cost (C), and maintenance benefit (B) are calculated using FAHP and the rankings of failure modes are determined by EFMULTIMOORA. Different from existing schemes, the EFMULTIMOORA in our proposed hybrid scheme calculates the ranking of vehicle failure modes based on three new risk factors (T, C, and B) through fuzzy linguistic terms for order preference. Furthermore, the applicability of the proposed hybrid scheme is presented by conducting a case study involving vehicle failure modes of one common vehicle type (Hyundai), and a sensitivity analysis and comparisons are conducted to validate the effectiveness of the obtained results. In summary, our numerical analyses indicate that the proposed method can effectively help enterprises and researchers in the risk evaluation and the identification of critical vehicle failure modes.

A GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral considering risk preference

Group multi-criteria decision-making (GMCDM) is an important part of decision theory, which is aimed to assess alternatives according to multiple criteria by collecting the wisdom of experts. However, in the process of evaluating, because of the limitation of human knowledge and the complexity of problems, an efficient GMCDM approach under uncertain environment still need to be further explored. Thus, in this paper, a novel GMCDM approach with linguistic Z-numbers based on TOPSIS and Choquet integral is proposed. Firstly, since linguistic Z-numbers performs better in coping with uncertain information, it is used to express the evaluation information. Secondly, TOPSIS, one of the most useful and systematic multi-criteria decision-making (MCDM) method, is adopted as the framework of the proposed approach. Thirdly, frequently it exists interaction between criteria, so Choquet integral is introduced to capture this kind of influence. What’s more, viewing that decision makers (DMs) show different preferences for uncertainty, the risk preference is regarded as a vital parameter when calculating the score of linguistic Z-numbers. An application in supplier selection is illustrated to demonstrate the effectiveness of the proposed approach. Finally, a further comparison and discussion of the proposed GMCDM method is given.

A New Evaluation Methodology for Quality Goals Extended by D Number Theory and FAHP

Evaluation of quality goals is an important issue in process management, which essentially is a multi-attribute decision-making (MADM) problem. The process of assessment inevitably involves uncertain information. The two crucial points in an MADM problem are to obtain weight of attributes and to handle uncertain information. D number theory is a new mathematical tool to deal with uncertain information, which is an extension of evidence theory. The fuzzy analytic hierarchy process (FAHP) provides a hierarchical way to model MADM problems, and the comparison analysis among attributes is applied to obtain the weight of attributes. FAHP uses a triangle fuzzy number rather than a crisp number to represent the evaluation information, which fully considers the hesitation to give a evaluation. Inspired by the features of D number theory and FAHP, a D-FAHP method is proposed to evaluate quality goals in this paper. Within the proposed method, FAHP is used to obtain the weight of each attribute, and the integration property of D number theory is carried out to fuse information. A numerical example is presented to demonstrate the effectiveness of the proposed method. Some necessary discussions are provided to illustrate the advantages of the proposed method.

Refined Expected Value Decision Rules under Orthopair Fuzzy Environment

Refined expected value decision rules can refine the calculation of the expected value and make decisions by estimating the expected values of different alternatives, which use many theories, such as Choquet integral, PM function, measure and so on. However, the refined expected value decision rules have not been applied to the orthopair fuzzy environment yet. To address this issue, in this paper we propose the refined expected value decision rules under the orthopair fuzzy environment, which can apply the refined expected value decision rules on the issues of decision making that is described in the orthopair fuzzy environment. Numerical examples were applied to verify the availability and flexibility of the new refined expected value decision rules model. The experimental results demonstrate that the proposed model can apply refined expected value decision rules in the orthopair fuzzy environment and solve the decision making issues with the orthopair fuzzy environment successfully.