Framework Of Dempster-Shafer Evidence Theory Research Articles

Measures of extended fractional Deng entropy and extropy with applications

Recently, Zhang and Shang introduced modifications to the concept of fractional entropy and proved some properties based on the inverse Mittag-Leffler function (MLF). The Deng entropy serves as a valuable measure in the Dempster-Shafer evidence theory (DST) to tackle uncertainty. In this study, we extend the fractional Deng entropy measure, introducing two distinct versions: E fd 1 α ( m ) and E fd 2 α ( m ) . We call this new measure the extended fractional Deng entropy, EFDEn. Additionally, we apply a similar approach to the fractional Deng extropy measure, resulting in E X fd 1 α ( m ) and E X fd 2 α ( m ) . We call this new measure the extended fractional Deng extropy, EFDEx. These two measures are complementary, leading to provide a deeper analysis of known and unknown information. Subsequently, we conduct a comparative analysis of these measures within the DST framework. We also propose the decomposable fractional Deng entropy, an extension of the decomposable entropy for Dempster–Shafer evidence theory, which effectively decomposes fractional Deng entropy. Finally, we delve into a pattern recognition classification problem to highlight the importance of these new measures.

Probabilistic Hesitant Fuzzy Evidence Theory and Its Application in Capability Evaluation of a Satellite Communication System.

Evaluating the capabilities of a satellite communication system (SCS) is challenging due to its complexity and ambiguity. It is difficult to accurately analyze uncertain situations, making it difficult for experts to determine appropriate evaluation values. To address this problem, this paper proposes an innovative approach by extending the Dempster-Shafer evidence theory (DST) to the probabilistic hesitant fuzzy evidence theory (PHFET). The proposed approach introduces the concept of probabilistic hesitant fuzzy basic probability assignment (PHFBPA) to measure the degree of support for propositions, along with a combination rule and decision approach. Two methods are developed to generate PHFBPA based on multi-classifier and distance techniques, respectively. In order to improve the consistency of evidence, discounting factors are proposed using an entropy measure and the Jousselme distance of PHFBPA. In addition, a model for evaluating the degree of satisfaction of SCS capability requirements based on PHFET is presented. Experimental classification and evaluation of SCS capability requirements are performed to demonstrate the effectiveness and stability of the PHFET method. By employing the DST framework and probabilistic hesitant fuzzy sets, PHFET provides a compelling solution for handling ambiguous data in multi-source information fusion, thereby improving the evaluation of SCS capabilities.

Uncertainty Management in Assessment of FMEA Expert Based on Negation Information and Belief Entropy.

The failure mode and effects analysis (FMEA) is a commonly adopted approach in engineering failure analysis, wherein the risk priority number (RPN) is utilized to rank failure modes. However, assessments made by FMEA experts are full of uncertainty. To deal with this issue, we propose a new uncertainty management approach for the assessments given by experts based on negation information and belief entropy in the Dempster-Shafer evidence theory framework. First, the assessments of FMEA experts are modeled as basic probability assignments (BPA) in evidence theory. Next, the negation of BPA is calculated to extract more valuable information from a new perspective of uncertain information. Then, by utilizing the belief entropy, the degree of uncertainty of the negation information is measured to represent the uncertainty of different risk factors in the RPN. Finally, the new RPN value of each failure mode is calculated for the ranking of each FMEA item in risk analysis. The rationality and effectiveness of the proposed method is verified through its application in a risk analysis conducted for an aircraft turbine rotor blade.

Solution-Space-Reduction-Based Evidence Theory Method for Stiffness Evaluation of Air Springs with Epistemic Uncertainty

In the Dempster–Shafer evidence theory framework, extremum analysis, which should be repeatedly executed for uncertainty quantification (UQ), produces a heavy computational burden, particularly for a high-dimensional uncertain system with multiple joint focal elements. Although the polynomial surrogate can be used to reduce computational expenses, the size of the solution space hampers the efficiency of extremum analysis. To address this, a solution-space-reduction-based evidence theory method (SSR-ETM) is proposed in this paper. The SSR-ETM invests minimal additional time for potentially high-efficiency returns in dealing with epistemic uncertainty. In the SSR-ETM, monotonicity analysis of the polynomial surrogate over the range of evidence variables is first performed. Thereafter, the solution space can be narrowed to a smaller size to accelerate extremum analysis if the surrogate model is at least monotonic in one dimension. Four simple functions and an air spring system with epistemic uncertainty demonstrated the efficacy of the SSR-ETM, indicating an apparent superiority over the conventional method.

A novel evidence combination rule based on compromise conflict indicator and conflict focal element

The Dempster–Shafer evidence theory (DSET) has been commonly used in the fusion of multisource information in various fields. Owing to the normalization process based on the conflict measurement, the conclusion when fusing high conflict evidence is counter-intuitive when using Dempster’s Combination Rule (DCR). To solve the DCR issue, several combination rules have been developed. However, each of them has unreasonable behaviors in certain cases. In this study, the set of mathematical properties that must be satisfied by all the combinatorial rules is further refined. Under the framework of DSET, a novel combination rule is proposed by comprehensively considering the conflict focal elements and metrics. The conflict measurement is achieved through the newly proposed compromise conflict indicator. The advantages of the proposed combination rule over the existing methods are demonstrated by experiments on a few numerical examples and applications.

Fractional Deng Entropy and Extropy and Some Applications.

Deng entropy and extropy are two measures useful in the Dempster–Shafer evidence theory (DST) to study uncertainty, following the idea that extropy is the dual concept of entropy. In this paper, we present their fractional versions named fractional Deng entropy and extropy and compare them to other measures in the framework of DST. Here, we study the maximum for both of them and give several examples. Finally, we analyze a problem of classification in pattern recognition in order to highlight the importance of these new measures.

A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy.

Dempster-Shafer evidence theory (DST) has shown its great advantages to tackle uncertainty in a wide variety of applications. However, how to quantify the information-based uncertainty of basic probability assignment (BPA) with belief entropy in DST framework is still an open issue. The main work of this study is to define a new belief entropy for measuring uncertainty of BPA. The proposed belief entropy has two components. The first component is based on the summation of the probability mass function (PMF) of single events contained in each BPA, which are obtained using plausibility transformation. The second component is the same as the weighted Hartley entropy. The two components could effectively measure the discord uncertainty and non-specificity uncertainty found in DST framework, respectively. The proposed belief entropy is proved to satisfy the majority of the desired properties for an uncertainty measure in DST framework. In addition, when BPA is probability distribution, the proposed method could degrade to Shannon entropy. The feasibility and superiority of the new belief entropy is verified according to the results of numerical experiments.

A Note on Incomplete Information Modeling in the Evidence Theory

Incomplete information exists widely in practical engineering. How to model the incomplete information in the Dempster-Shafer evidence theory (DST) framework is still an open issue. In this paper, we present a framework on incomplete information processing in DST. We extend the model of uncertain information from the closed world assumption to the open world assumption where the incomplete information is a new type of uncertain information excluded in the closed world assumption. After that, we give a framework of incomplete information modelling and fusion in the DST framework. Finally, an example of decision-making process in air combat situation assessment with incomplete situation is introduced to show the rationality of the proposed method.

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.

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.

Approach to Multi-Attributes Decision Making With Intuitionistic Linguistic Information Based on Dempster-Shafer Evidence Theory

Considering the limitations of the applications of a Dempster-Shafer evidence theory (DSET) in multiple attributes decision-making (MADM) and the defects of the existing MADM methods with intuitionistic linguistic numbers (ILNs), in this paper, we propose a new MADM approach. First, we provide a method to translate the evaluation values denoted by ILNs into the mass functions (MFs) under the framework of DSET. Second, we calculate the subjective weights of attributes based on the AHP method. Then, we propose a new definition of fuzzy entropy (FE) for ILNs and the objective weights of attributes are calculated by the defined FE. Moreover, we develop a linear objective programming model to obtain the comprehensive weights of attributes based on the obtained subjective and objective weights of attributes. Third, we introduce some procedures to modify the MFs of alternatives on each attribute. On these bases, a new DSET-based MADM approach with ILNs is presented. Furthermore, an application example of hotel selection is used to illustrate the presented approach. At last, some comparative analyses with other MADM methods are conducted to show the feasibility and superiority of the proposed approach.

AMWRPN: Ambiguity Measure Weighted Risk Priority Number Model for Failure Mode and Effects Analysis

The relative importance of each risk factor in failure mode and effects analysis (FMEA) should be addressed properly. Intuitively, in the assessments coming from the FEMA experts, there exists a potential judgement on which risk factor has a higher weight for the FMEA item. Based on this cognition and perspective, a new ambiguity measure weighted risk priority number (AMWRPN) for FMEA is proposed. AMWRPN takes into consideration of the relative weight of different risk factors by measuring the ambiguity degree of the experts’ assessments. If the assessment of an expert has a certain belief on the judgement, then the relative importance of the corresponding risk factor will be higher than the uncertain one; and vice versa. The ambiguity measure (AM) in the framework of the Dempster–Shafer evidence theory (DST) has been used to construct the exponential weight of each risk factor in AMWRPN. In comparison with the weight factor basing on fuzzy sets theory or other theories in the DST framework, the AM-based weight factor for uncertainty measure of the subjective assessment ensures the internal coordination of the proposed method. An application of the proposed method in aircraft turbine rotor blade verifies the effectiveness of the new risk priority number model.

A modified belief entropy in Dempster-Shafer framework.

How to quantify the uncertain information in the framework of Dempster-Shafer evidence theory is still an open issue. Quite a few uncertainty measures have been proposed in Dempster-Shafer framework, however, the existing studies mainly focus on the mass function itself, the available information represented by the scale of the frame of discernment (FOD) in the body of evidence is ignored. Without taking full advantage of the information in the body of evidence, the existing methods are somehow not that efficient. In this paper, a modified belief entropy is proposed by considering the scale of FOD and the relative scale of a focal element with respect to FOD. Inspired by Deng entropy, the new belief entropy is consistent with Shannon entropy in the sense of probability consistency. What’s more, with less information loss, the new measure can overcome the shortage of some other uncertainty measures. A few numerical examples and a case study are presented to show the efficiency and superiority of the proposed method.

An evidential view of similarity measure for Atanassov’s intuitionistic fuzzy sets

In this paper, the construction of similarity measures for Atanassov's intuitionistic fuzzy sets (AIFSs) is considered from the view of evidence theory. We define similarity measures for AIFSs in the framework of Dempster-Shafer evidence theory. The proposed similarity measures are applied to deal with pattern recognition and multiple criteria decision making problems. First, existing similarity measures for AIFSs are critically reviewed. Then we introduce the transformation from AIFSs to basic probability assignments (BPAs) in evidence theory. Based on Jousselme's distance measure and cosine similarity measure between BPAs, two similarity measures between AIFSs are proposed. A composite similarity measure is constructed following the proof of properties related to our proposed similarity measures. Then, we use some contrastive examples to illustrate that the proposed similarity measure between AIFSs can overcome the drawbacks of existing similarity measures. Finally, we apply the proposed similarity measures between AIFSs to deal with pattern recognition and multiple criteria decision making problems. It is demonstrated that our proposed similarity measures can provide compatible results compared to those results obtained based on previous measures.

High-Resolution Optical and SAR Image Fusion for Building Database Updating

This paper addresses the issue of cartographic database (DB) creation or updating using high-resolution synthetic aperture radar and optical images. In cartographic applications, objects of interest are mainly buildings and roads. This paper proposes a processing chain to create or update building DBs. The approach is composed of two steps. First, if a DB is available, the presence of each DB object is checked in the images. Then, we verify if objects coming from an image segmentation should be included in the DB. To do those two steps, relevant features are extracted from images in the neighborhood of the considered object. The object removal/inclusion in the DB is based on a score obtained by the fusion of features in the framework of Dempster-Shafer evidence theory.