Zero-Sum Matrix Game with Payoffs of Dempster-Shafer Belief Structures and Its Applications on Sensors

A new D numbers’ integration rule based on pessimistic criterion

For D numbers theory, there are some drawbacks in the D numbers’ integration rule. For example, the missing information is ignored in the final decision judgment for multi-attribute decision (MADM). For this problem, some researchers have improved the D numbers’ integration rules based on optimistic criterion for overcoming the shortcoming of D numbers’ integration rule. However, optimistic and pessimistic criterion are two sides of the coin for fuzzy environment. Therefore, in this article, a new D numbers’ integration rules based on pessimistic criterion is proposed. We improve the D numbers’ integration rules to redefine the missing information distribution rules based on pessimistic criterion. The missing information is distributed in inverse proportion to each D number according to the size of the original evidence credibility. Two examples of MADM is applied by the proposed method, the results show that the proposed method can be applied to MADM.

Game-Theoretic Learning for Sensor Reliability Evaluation Without Knowledge of the Ground Truth

Sensor fusion has attracted a lot of research attention during the few last years. Recently, a new research direction has emerged dealing with sensor fusion without knowledge of the ground truth. In this article, we present a novel solution to the latter pertinent problem. In contrast to the first reported solutions to this problem, we present a solution that does not involve any assumption on the group average reliability which makes our results more general than previous works. We devise a strategic game where we show that a perfect partitioning of the sensors into reliable and unreliable groups corresponds to a Nash equilibrium of the game. Furthermore, we give sound theoretical results that prove that those equilibria are indeed the unique Nash equilibria of the game. We then propose a solution involving a team of learning automata (LA) to unveil the identity of each sensor, whether it is reliable or unreliable, using game-theoretic learning. The experimental results show the accuracy of our solution and its ability to deal with settings that are unsolvable by legacy works.

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.

A Mission Reliability-Driven Manufacturing System Health State Evaluation Method Based on Fusion of Operational Data

The rapid development of complexity and intelligence in manufacturing systems leads to an increase in potential operational risks and therefore requires a more comprehensive system-level health diagnostics approach. Based on the massive multi-source operational data collected by smart sensors, this paper proposes a mission reliability-driven manufacturing system health state evaluation method. Characteristic attributes affecting the mission reliability are monitored and analyzed based on different sensor groups, including the performance state of the manufacturing equipment, the execution state of the production task and the quality state of the manufactured product. The Dempster-Shafer (D-S) evidence theory approach is used to diagnose the health state of the manufacturing system. Results of a case study show that the proposed evaluation method can dynamically and effectively characterize the actual health state of manufacturing systems.

A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function

How to measure the uncertainty of the basic probability assignment (BPA) function is an open issue in Dempster–Shafer (D–S) theory. The main work of this paper is to propose a new belief entropy, which is mainly used to measure the uncertainty of BPA. The proposed belief entropy is based on Deng entropy and probability interval consisting of lower and upper probabilities. In addition, under certain conditions, it can be transformed into Shannon entropy. Numerical examples are used to illustrate the efficiency of the new belief entropy in measurement uncertainty.

A Novel Evidence Theory and Fuzzy Preference Approach-Based Multi-Sensor Data Fusion Technique for Fault Diagnosis

The multi-sensor data fusion technique plays a significant role in fault diagnosis and in a variety of such applications, and the Dempster–Shafer evidence theory is employed to improve the system performance; whereas, it may generate a counter-intuitive result when the pieces of evidence highly conflict with each other. To handle this problem, a novel multi-sensor data fusion approach on the basis of the distance of evidence, belief entropy and fuzzy preference relation analysis is proposed. A function of evidence distance is first leveraged to measure the conflict degree among the pieces of evidence; thus, the support degree can be obtained to represent the reliability of the evidence. Next, the uncertainty of each piece of evidence is measured by means of the belief entropy. Based on the quantitative uncertainty measured above, the fuzzy preference relations are applied to represent the relative credibility preference of the evidence. Afterwards, the support degree of each piece of evidence is adjusted by taking advantage of the relative credibility preference of the evidence that can be utilized to generate an appropriate weight with respect to each piece of evidence. Finally, the modified weights of the evidence are adopted to adjust the bodies of the evidence in the advance of utilizing Dempster’s combination rule. A numerical example and a practical application in fault diagnosis are used as illustrations to demonstrate that the proposal is reasonable and efficient in the management of conflict and fault diagnosis.

Research on the Fusion of Dependent Evidence Based on Rank Correlation Coefficient

In order to meet the higher accuracy and system reliability requirements, the information fusion for multi-sensor systems is an increasing concern. Dempster–Shafer evidence theory (D–S theory) has been investigated for many applications in multi-sensor information fusion due to its flexibility in uncertainty modeling. However, classical evidence theory assumes that the evidence is independent of each other, which is often unrealistic. Ignoring the relationship between the evidence may lead to unreasonable fusion results, and even lead to wrong decisions. This assumption severely prevents D–S evidence theory from practical application and further development. In this paper, an innovative evidence fusion model to deal with dependent evidence based on rank correlation coefficient is proposed. The model first uses rank correlation coefficient to measure the dependence degree between different evidence. Then, total discount coefficient is obtained based on the dependence degree, which also considers the impact of the reliability of evidence. Finally, the discount evidence fusion model is presented. An example is illustrated to show the use and effectiveness of the proposed method.

Fuzzy Risk Evaluation in Failure Mode and Effects Analysis Using a D Numbers Based Multi-Sensor Information Fusion Method

Failure mode and effect analysis (FMEA) is a useful tool to define, identify, and eliminate potential failures or errors so as to improve the reliability of systems, designs, and products. Risk evaluation is an important issue in FMEA to determine the risk priorities of failure modes. There are some shortcomings in the traditional risk priority number (RPN) approach for risk evaluation in FMEA, and fuzzy risk evaluation has become an important research direction that attracts increasing attention. In this paper, the fuzzy risk evaluation in FMEA is studied from a perspective of multi-sensor information fusion. By considering the non-exclusiveness between the evaluations of fuzzy linguistic variables to failure modes, a novel model called D numbers is used to model the non-exclusive fuzzy evaluations. A D numbers based multi-sensor information fusion method is proposed to establish a new model for fuzzy risk evaluation in FMEA. An illustrative example is provided and examined using the proposed model and other existing method to show the effectiveness of the proposed model.

A Time-Space Domain Information Fusion Method for Specific Emitter Identification Based on Dempster-Shafer Evidence Theory

Specific emitter identification plays an important role in contemporary military affairs. However, most of the existing specific emitter identification methods haven’t taken into account the processing of uncertain information. Therefore, this paper proposes a time–space domain information fusion method based on Dempster–Shafer evidence theory, which has the ability to deal with uncertain information in the process of specific emitter identification. In this paper, radars will generate a group of evidence respectively based on the information they obtained, and our main task is to fuse the multiple groups of evidence to get a reasonable result. Within the framework of recursive centralized fusion model, the proposed method incorporates a correlation coefficient, which measures the relevance between evidence and a quantum mechanical approach, which is based on the parameters of radar itself. The simulation results of an illustrative example demonstrate that the proposed method can effectively deal with uncertain information and get a reasonable recognition result.

A Novel Single-Valued Neutrosophic Set Similarity Measure and Its Application in Multicriteria Decision-Making

The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems. The key to using neutrosophic sets in decision-making applications is to make a similarity measure between single-valued neutrosophic sets. In this paper, a new method to measure the similarity between single-valued neutrosophic sets using Dempster–Shafer evidence theory is proposed, and it is applied in multicriteria decision-making. Finally, some examples are given to show the reasonable and effective use of the proposed method.

A Reliability-Based Method to Sensor Data Fusion

Multi-sensor data fusion technology based on Dempster–Shafer evidence theory is widely applied in many fields. However, how to determine basic belief assignment (BBA) is still an open issue. The existing BBA methods pay more attention to the uncertainty of information, but do not simultaneously consider the reliability of information sources. Real-world information is not only uncertain, but also partially reliable. Thus, uncertainty and partial reliability are strongly associated with each other. To take into account this fact, a new method to represent BBAs along with their associated reliabilities is proposed in this paper, which is named reliability-based BBA. Several examples are carried out to show the validity of the proposed method.

Evidence conflict measure based on OWA operator in open world

Dempster-Shafer evidence theory has been extensively used in many information fusion systems since it was proposed by Dempster and extended by Shafer. Many scholars have been conducted on conflict management of Dempster-Shafer evidence theory in past decades. However, how to determine a potent parameter to measure evidence conflict, when the given environment is in an open world, namely the frame of discernment is incomplete, is still an open issue. In this paper, a new method which combines generalized conflict coefficient, generalized evidence distance, and generalized interval correlation coefficient based on ordered weighted averaging (OWA) operator, to measure the conflict of evidence is presented. Through ordered weighted average of these three parameters, the combinatorial coefficient can still measure the conflict effectively when one or two parameters are not valid. Several numerical examples demonstrate the effectiveness of the proposed method.