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Journal articles on the topic 'Basic Belief Assignments'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Dezert, Jean, and Albena Tchamova. "Involutory Negator of Basic Belief Assignments." Cybernetics and Information Technologies 23, no. 3 (2023): 3–22. http://dx.doi.org/10.2478/cait-2023-0021.

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Abstract This paper analyzes the different definitions of a negator of a probability mass function (pmf) and a Basic Belief Assignment (BBA) available in the literature. To overcome their limitations we propose an involutory negator of BBA, and we present a new indirect information fusion method based on this negator which can simplify the conflict management problem. The direct and indirect information fusion strategies are analyzed for three interesting examples of fusion of two BBAs. We also propose two methods for using the whole available information (the original BBAs and their negators)

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2

Li, Meizhu, Xi Lu, Qi Zhang, and Yong Deng. "Multiscale Probability Transformation of Basic Probability Assignment." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/319264.

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Decision making is still an open issue in the application of Dempster-Shafer evidence theory. A lot of works have been presented for it. In the transferable belief model (TBM), pignistic probabilities based on the basic probability assignments are used for decision making. In this paper, multiscale probability transformation of basic probability assignment based on the belief function and the plausibility function is proposed, which is a generalization of the pignistic probability transformation. In the multiscale probability function, a factorqbased on the Tsallis entropy is used to make the

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Zhao, Yonggang, Duofa Ji, Xiaodong Yang, Liguo Fei, and Changhai Zhai. "An Improved Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Deng Entropy and Belief Interval." Entropy 21, no. 11 (2019): 1122. http://dx.doi.org/10.3390/e21111122.

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It is still an open issue to measure uncertainty of the basic probability assignment function under Dempster-Shafer theory framework, which is the foundation and preliminary work for conflict degree measurement and combination of evidences. This paper proposes an improved belief entropy to measure uncertainty of the basic probability assignment based on Deng entropy and the belief interval, which takes the belief function and the plausibility function as the lower bound and the upper bound, respectively. Specifically, the center and the span of the belief interval are employed to define the to

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Broniatowski, Michel, and Wolfgang Stummer. "Some Theoretical Foundations of Bare-Simulation Optimization of Some Directed Distances between Fuzzy Sets Respective Basic Belief Assignments." Entropy 26, no. 4 (2024): 312. http://dx.doi.org/10.3390/e26040312.

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It is well known that in information theory—as well as in the adjacent fields of statistics, machine learning and artificial intelligence—it is essential to quantify the dissimilarity between objects of uncertain/imprecise/inexact/vague information; correspondingly, constrained optimization is of great importance, too. In view of this, we define the dissimilarity-measure-natured generalized φ–divergences between fuzzy sets, ν–rung orthopair fuzzy sets, extended representation type ν–rung orthopair fuzzy sets as well as between those fuzzy set types and vectors. For those, we present how to tac

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Ennaceur, Amel, Zied Elouedi, and Eric Lefevre. "Belief AHP Method — AHP Method with the Belief Function Framework." International Journal of Information Technology & Decision Making 15, no. 03 (2016): 553–73. http://dx.doi.org/10.1142/s0219622016500139.

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In this paper, the analytic hierarchy process (AHP) method is extended to an uncertain environment where the uncertainty is represented by belief functions as interpreted in the transferable belief model (TBM). Our proposed approach, called belief AHP, is developed to help the decision maker to determine what the best alternatives are, considering multiple conflicting criteria where both alternatives and criteria may be soiled with imperfection. The Belief AHP method aims at comparing subsets of criteria and groups of alternatives in order to reduce the pair-wise comparisons number. Furthermor

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6

Pan, Lipeng, and Yong Deng. "A New Belief Entropy to Measure Uncertainty of Basic Probability Assignments Based on Belief Function and Plausibility Function." Entropy 20, no. 11 (2018): 842. http://dx.doi.org/10.3390/e20110842.

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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.

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SMARANDACHE, FLORENTIN, and JEAN DEZERT. "UNIFORM AND PARTIALLY UNIFORM REDISTRIBUTION RULES." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 19, no. 06 (2011): 921–37. http://dx.doi.org/10.1142/s0218488511007404.

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This paper introduces two new fusion rules for combining quantitative basic belief assignments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.

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Wang, Zhi Song, Li Wei Tang, Wen Wen Yu, and Jin Hua Cao. "Antiaircraft Gun Automatic Fusion Diagnosis Based on D-S Evidence Theory." Applied Mechanics and Materials 241-244 (December 2012): 288–92. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.288.

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Antiaircraft gun automatic is irrotational machine, its motion presents characteristic of stage, so we proposed a fault diagnosis fusion model based on Dempster-Shafer (D-S) evidence theory. At first, feature parameters are extracted from test data of multi-sensor, then, we propose a revised Minkowski distance to create evidences. Finally, we fuse basic belief assignments according to Dempster combination rule, and the analysis result verifies the effectiveness and feasibility of proposed fault diagnosis method.

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9

Ma, Mengmeng, and Jiyao An. "Combination of Evidence with Different Weighting Factors: A Novel Probabilistic-Based Dissimilarity Measure Approach." Journal of Sensors 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/509385.

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To solve the invalidation problem of Dempster-Shafer theory of evidence (DS) with high conflict in multisensor data fusion, this paper presents a novel combination approach of conflict evidence with different weighting factors using a new probabilistic dissimilarity measure. Firstly, an improved probabilistic transformation function is proposed to map basic belief assignments (BBAs) to probabilities. Then, a new dissimilarity measure integrating fuzzy nearness and introduced correlation coefficient is proposed to characterize not only the difference between basic belief functions (BBAs) but al

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Chen, Yujie, Zexi Hua, Yongchuan Tang, and Baoxin Li. "Multi-Source Information Fusion Based on Negation of Reconstructed Basic Probability Assignment with Padded Gaussian Distribution and Belief Entropy." Entropy 24, no. 8 (2022): 1164. http://dx.doi.org/10.3390/e24081164.

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Multi-source information fusion is widely used because of its similarity to practical engineering situations. With the development of science and technology, the sources of information collected under engineering projects and scientific research are more diverse. To extract helpful information from multi-source information, in this paper, we propose a multi-source information fusion method based on the Dempster-Shafer (DS) evidence theory with the negation of reconstructed basic probability assignments (nrBPA). To determine the initial basic probability assignment (BPA), the Gaussian distribut

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11

Dong, Yilin, Lei Cao, and Kezhu Zuo. "Genetic Algorithm Based on a New Similarity for Probabilistic Transformation of Belief Functions." Entropy 24, no. 11 (2022): 1680. http://dx.doi.org/10.3390/e24111680.

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Recent studies of alternative probabilistic transformation (PT) in Dempster–Shafer (DS) theory have mainly focused on investigating various schemes for assigning the mass of compound focal elements to each singleton in order to obtain a Bayesian belief function for decision-making problems. In the process of such a transformation, how to precisely evaluate the closeness between the original basic belief assignments (BBAs) and transformed BBAs is important. In this paper, a new aggregation measure is proposed by comprehensively considering the interval distance between BBAs and also the sequenc

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Uzhga-Rebrov, Oleg, Ekaterina Karaseva, and Vasily V. Karasev. "Computational procedures of the evidence theory for interval and fuzzy assignments of the basic probability masses for focal elements." Information Technology and Management Science 22 (December 23, 2019): 47–51. http://dx.doi.org/10.7250/itms-2019-0007.

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The evidence theory is ascribed to a specific kind of uncertainty. In this theory, uncertainty refers to the fact that the element of our interest (the true world) may be included in subsets of other similar elements (possible worlds). In the original evidence theory, the estimates of the basic probability masses for the focal elements are given in an unambiguous form. In practice, to obtain such estimates is often difficult or even impossible. In such a situation, the relevant estimates are given in the interval or fuzzy form. The goal of the paper is to present and analyse the calculation pr

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Wu, Lei, Yongchuan Tang, Liuyuan Zhang, and Yubo Huang. "Uncertainty Management in Assessment of FMEA Expert Based on Negation Information and Belief Entropy." Entropy 25, no. 5 (2023): 800. http://dx.doi.org/10.3390/e25050800.

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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 c

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N, Arthi, and Mohana K. "A new divergence measure of interval-valued pythagorean fuzzy sets and its application." Journal of Computational Mathematica 5, no. 2 (2021): 9–24. http://dx.doi.org/10.26524/cm103.

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As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertain

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Su, Xiaoyan, Shuwen Shang, Leihui Xiong, Ziying Hong, and Jian Zhong. "Research on dependent evidence combination based on principal component analysis." Mathematical Biosciences and Engineering 21, no. 4 (2024): 4853–73. http://dx.doi.org/10.3934/mbe.2024214.

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<abstract><p>Dempster-Shafer evidence theory, as a generalization of probability theory, is a powerful tool for dealing with a variety of uncertainties, such as incompleteness, ambiguity, and conflict. Because of its advantages in information fusion compared with traditional probability theory, it is widely used in various fields. However, the classic Dempster's combination rule assumes that evidences are independent of each other, which is difficult to satisfy in real life. Ignoring the dependence among the evidences will lead to unreasonable fusion results, and even wrong conclus

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16

Gao, Zhen, Guoliang Lu, and Peng Yan. "Recognizing Human Actions in Low-Resolution Videos: An Approach Based on the Dempster–Shafer Theory." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 04 (2019): 1956002. http://dx.doi.org/10.1142/s0218001419560020.

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To address the problem that many existing approaches are not appropriate for action recognition in low-resolution (LR) videos, this paper presents a framework based on the Dempster–Shafer (DS) theory for this purpose. In the framework, artificial neural networks (ANNs) are firstly trained for every class with training samples, and then basic belief assignments (BBAs) for underlying classes are computed with the trained ANNs. The resulted BBAs are fused from all frames in the whole video sequentially by frame-by-frame based on DS’s rule of fusion. Action recognition is last performed with a thr

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17

Zhang, Yang, Jianhua Yang, and Hong Hou. "The Underwater Acoustic Target Recognition Algorithm Based on Evidence Clustering." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 1 (2018): 96–102. http://dx.doi.org/10.1051/jnwpu/20183610096.

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In underwater acoustic target recognition, the target signal is usually complex and the samples which are difficult to obtain also have some uncertain information. In order to effectively solve these problems, the evidence clustering recognition algorithm (TECRA) is presented. In this new method, the k-nearest neighbor are first determined by using the feature distance between the object and its neighbors in each class of the training set, and a reasonable initial basic belief assignments (bba's) for each target data are constructed by the improved k-nearest neighbor classification algorithm.

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18

Alpert, Sofiia. "Analysis of “mixing” combination rules and Smet’s combination rule." Ukrainian journal of remote sensing, no. 23 (December 28, 2019): 4–8. http://dx.doi.org/10.36023/ujrs.2019.23.158.

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The process of solution of different practical and ecological problems, using hyperspectral satellite images usually includes a procedure of classification. Classification is one of the most difficult and important procedures. Some image classification methods were considered and analyzed in this work. These methods are based on the theory of evidence. Evidence theory can simulate uncertainty and process imprecise and incomplete information. It were considered such combination rules in this paper: “mixing” combination rule (or averaging), convolutive x-averaging (or c-averaging) and Smet’s com

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19

Zhou, Qianli, Hongming Mo, and Yong Deng. "A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis." Mathematics 8, no. 1 (2020): 142. http://dx.doi.org/10.3390/math8010142.

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As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical app

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20

Rossi, Silvia Luisa. "Moving the Spotlight from Plagiarism to Academic Integrity in Paraphrasing Instruction." Canadian Perspectives on Academic Integrity 4, no. 2 (2021): 42. http://dx.doi.org/10.55016/ojs/cpai.v4i2.74170.

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For higher education students completing research-based assignments, paraphrasing is an essential skill. While instructors often expect students to be reasonably proficient in paraphrasing by the time they finish high school, the reality is that many students arrive at college or university never having experienced explicit instruction in paraphrasing. They have certainly used paraphrasing in their previous academic work, but their understanding of this critical skill rarely goes beyond the basic notion that paraphrasing means “saying it in your own words,” and many believe that synonym substi

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Li, Jingchao, Yulong Ying, Yuan Ren, et al. "Research on rolling bearing fault diagnosis based on multi-dimensional feature extraction and evidence fusion theory." Royal Society Open Science 6, no. 2 (2019): 181488. http://dx.doi.org/10.1098/rsos.181488.

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Rolling bearing failure is the main cause of failure of rotating machinery, and leads to huge economic losses. The demand of the technique on rolling bearing fault diagnosis in industrial applications is increasing. With the development of artificial intelligence, the procedure of rolling bearing fault diagnosis is more and more treated as a procedure of pattern recognition, and its effectiveness and reliability mainly depend on the selection of dominant characteristic vector of the fault features. In this paper, a novel diagnostic framework for rolling bearing faults based on multi-dimensiona

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22

Dezert, Jean, and Florentin Smarandache. "Canonical decomposition of dichotomous basic belief assignment." International Journal of Intelligent Systems 35, no. 7 (2020): 1105–25. http://dx.doi.org/10.1002/int.22236.

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Xu, Xing, Xingzhi Wang, and Guangzhong Sun. "Coal-Mine Water-Hazard Risk Evaluation Based on the Combination of Extension Theory, Game Theory, and Dempster–Shafer Evidence Theory." Water 16, no. 20 (2024): 2881. http://dx.doi.org/10.3390/w16202881.

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Due to the complex hydrogeological conditions and water hazards in coal mines, there are multiple indexes, complexities, incompatibilities, and uncertainty issues in the risk evaluation process of coal-mine water hazards. To accurately evaluate the risk of coal-mine water hazards, a comprehensive evaluation method based on extension theory, game theory, and Dempster–Shafer (DS) evidence theory is proposed. Firstly, a hierarchical water-hazard risk-evaluation index system is established, and then matter-element theory in extension theory is used to establish a matter-element model for coal-mine

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24

Azhari, Ahmad, Muhammad Riyadhi, and Dimas Chaerul Ekty Saputra. "Convolutional Neural Network on Brain Concentration and Art of Reading the Qur'an." Mobile and Forensics 4, no. 2 (2023): 89–101. http://dx.doi.org/10.12928/mf.v4i2.5836.

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In Islam there is a belief that reading the Qur'an can increase one's concentration power in doing something. Concentration can be influenced by several factors, to be able to identify or characterize individuals, it is necessary to measure brain wave activity. Brain waves are one of the biometric properties that can be used to identify individuals based on their physical. An electroencephalogram (EEG) can be used to measure and capture brain wave activity. To be able to naturally record brain wave activity requires constant and emergent brain activity. The activities needed are in the form of

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Jiang, Wen, Miaoyan Zhuang, Chunhe Xie, and Jun Wu. "Sensing Attribute Weights: A Novel Basic Belief Assignment Method." Sensors 17, no. 4 (2017): 721. http://dx.doi.org/10.3390/s17040721.

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Li, Wei, Deqiang Han, Jean Dezert, and Yi Yang. "Basic Belief Assignment Determination Based on Radial Basis Function Network." Chinese Journal of Information Fusion 1, no. 3 (2024): 175–82. https://doi.org/10.62762/cjif.2024.841250.

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In Dempster-Shafer evidence theory (DST), the determination of basic belief assignment (BBA) is an important yet challenging issue. The rational mass determination of compound focal elements is crucial for fully taking advantage of DST, i.e., the ability to represent the ambiguity. In this paper, for the compound focal elements, we select and construct the \enquote{compound-class samples} with ambiguous class membership. Then, we use these samples to construct an end-to-end model called Evidential Radial Basis Function Network (E-RBFN), with the input as the sample and the output as the corres

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Yang, Yi, and Yuanli Liu. "Iterative Approximation of Basic Belief Assignment Based on Distance of Evidence." PLOS ONE 11, no. 2 (2016): e0147799. http://dx.doi.org/10.1371/journal.pone.0147799.

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28

Limboo, Bulendra, and Palash Dutta. "A q-rung orthopair basic probability assignment and its application in medical diagnosis." Decision Making: Applications in Management and Engineering 5, no. 1 (2022): 290–308. http://dx.doi.org/10.31181/dmame191221060l.

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Dempster-Shafer theory is widely used in decision-making and considered as one of the potential mathematical tools in order to fuse the evidence. However, existing studies in this theory show disadvantage due to conflicting nature of standard evidence set and the combination rule of evidence. In this paper, we have constructed the framework of q-rung evidence set to address the issue of conflicts based on the q-rung fuzzy number due to its more comprehensive range of advantage compared to the other fuzzy or discrete numbers. The proposed q-rung evidence set has the flexibility in assessing a p

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Luo, Ziyuan, and Yong Deng. "A Matrix Method of Basic Belief Assignment's Negation in Dempster–Shafer Theory." IEEE Transactions on Fuzzy Systems 28, no. 9 (2020): 2270–76. http://dx.doi.org/10.1109/tfuzz.2019.2930027.

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YANG, Yi, Deqiang HAN, and Jean DEZERT. "Basic belief assignment approximations using degree of non-redundancy for focal element." Chinese Journal of Aeronautics 32, no. 11 (2019): 2503–15. http://dx.doi.org/10.1016/j.cja.2019.05.003.

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Fan, Xinnan, Pengfei Shi, Jianjun Ni, and Min Li. "A Thermal Infrared and Visible Images Fusion Based Approach for Multitarget Detection under Complex Environment." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/750708.

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Multitarget detection under complex environment is a challenging task, where the measured signal will be submerged by noise. D-S belief theory is an effective approach in dealing with Multitarget detection. However, there are some limitations of the general D-S belief theory under complex environment. For example, the basic belief assignment is difficult to establish, and the subjective factors will influence the update process of evidence. In this paper, a new Multitarget detection approach based on thermal infrared and visible images fusion is proposed. To easily characterize the defected he

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Xie, Kangyang, and Fuyuan Xiao. "Negation of Belief Function Based on the Total Uncertainty Measure." Entropy 21, no. 1 (2019): 73. http://dx.doi.org/10.3390/e21010073.

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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

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Yang, Yi, X. Rong Li та Deqiang Han. "An improved α-cut approach to transforming fuzzy membership function into basic belief assignment". Chinese Journal of Aeronautics 29, № 4 (2016): 1042–51. http://dx.doi.org/10.1016/j.cja.2016.03.007.

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Gao, Kangkai, Yong Wang, and Liyao Ma. "Belief Entropy Tree and Random Forest: Learning from Data with Continuous Attributes and Evidential Labels." Entropy 24, no. 5 (2022): 605. http://dx.doi.org/10.3390/e24050605.

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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

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Gao, Kangkai, Yong Wang, and Liyao Ma. "Belief Entropy Tree and Random Forest: Learning from Data with Continuous Attributes and Evidential Labels." Entropy 24, no. 5 (2022): 605. http://dx.doi.org/10.3390/e24050605.

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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

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Li, Jiapeng, and Qian Pan. "A New Belief Entropy in Dempster–Shafer Theory Based on Basic Probability Assignment and the Frame of Discernment." Entropy 22, no. 6 (2020): 691. http://dx.doi.org/10.3390/e22060691.

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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 conditi

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Zhang, Hepeng, and Yong Deng. "Engine fault diagnosis based on sensor data fusion considering information quality and evidence theory." Advances in Mechanical Engineering 10, no. 11 (2018): 168781401880918. http://dx.doi.org/10.1177/1687814018809184.

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Fault diagnosis is a problem processing variable information obtained from different sources in nature. Evidence theory, efficient to deal with information viewed as evidence, is widely used in fault diagnosis. However, a shortcoming of the existing fault diagnosis methods only gets probability distribution rather than the basic probability assignment. A novel method of generating basic probability assignment that takes information quality into account is proposed. The probability distribution is determined by the preliminary matrix and sampling matrix that are constructed by sensor data. And

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Ma, Tianshuo, and Fuyuan Xiao. "An Improved Method to Transform Triangular Fuzzy Number Into Basic Belief Assignment in Evidence Theory." IEEE Access 7 (2019): 25308–22. http://dx.doi.org/10.1109/access.2019.2900362.

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Xu, Shijun, Yi Hou, Xinpu Deng, Peibo Chen, and Shilin Zhou. "Logarithmic Negation of Basic Probability Assignment and Its Application in Target Recognition." Information 13, no. 8 (2022): 387. http://dx.doi.org/10.3390/info13080387.

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The negation of probability distribution is a new perspective from which to obtain information. Dempster–Shafer (D–S) evidence theory, as an extension of possibility theory, is widely used in decision-making-level fusion. However, how to reasonably construct the negation of basic probability assignment (BPA) in D–S evidence theory is an open issue. This paper proposes a new negation of BPA, logarithmic negation. It solves the shortcoming of Yin’s negation that maximal entropy cannot be obtained when there are only two focal elements in the BPA. At the same time, the logarithmic negation of BPA

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Chen, Yong, Yongchuan Tang, and Yan Lei. "An Improved Data Fusion Method Based on Weighted Belief Entropy considering the Negation of Basic Probability Assignment." Journal of Mathematics 2020 (November 1, 2020): 1–11. http://dx.doi.org/10.1155/2020/1594967.

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Uncertainty in data fusion applications has received great attention. Due to the effectiveness and flexibility in handling uncertainty, Dempster–Shafer evidence theory is widely used in numerous fields of data fusion. However, Dempster–Shafer evidence theory cannot be used directly for conflicting sensor data fusion since counterintuitive results may be attained. In order to handle this issue, a new method for data fusion based on weighted belief entropy and the negation of basic probability assignment (BPA) is proposed. First, the negation of BPA is applied to represent the information in a n

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Pietkiewicz, Tadeusz. "Fusion of Identification Information from ESM Sensors and Radars Using Dezert–Smarandache Theory Rules." Remote Sensing 15, no. 16 (2023): 3977. http://dx.doi.org/10.3390/rs15163977.

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This paper presents a method of fusion of identification (attribute) information provided by two types of sensors: combined primary and secondary (IFF) surveillance radars and ESMs (electronic support measures). In the first section, the basic taxonomy of attribute identification is adopted in accordance with the standards of STANAG 1241 ed. 5 and STANAG 1241 ed. 6 (draft). These standards provide the following basic values of the attribute identifications: FRIEND; HOSTILE; NEUTRAL; UNKNOWN; and additional values, namely ASSUMED FRIEND and SUSPECT. The basis of theoretical considerations is De

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Li, Mujin, Honghui Xu, and Yong Deng. "Evidential Decision Tree Based on Belief Entropy." Entropy 21, no. 9 (2019): 897. http://dx.doi.org/10.3390/e21090897.

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Decision Tree is widely applied in many areas, such as classification and recognition. Traditional information entropy and Pearson’s correlation coefficient are often applied as measures of splitting rules to find the best splitting attribute. However, these methods can not handle uncertainty, since the relation between attributes and the degree of disorder of attributes can not be measured by them. Motivated by the idea of Deng Entropy, it can measure the uncertain degree of Basic Belief Assignment (BBA) in terms of uncertain problems. In this paper, Deng entropy is used as a measure of split

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Wang, Dan, Jiale Gao, and Daijun Wei. "A New Belief Entropy Based on Deng Entropy." Entropy 21, no. 10 (2019): 987. http://dx.doi.org/10.3390/e21100987.

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For Dempster–Shafer evidence theory, how to measure the uncertainty of basic probability assignment (BPA) is still an open question. Deng entropy is one of the methods for measuring the uncertainty of Dempster–Shafer evidence. Recently, some limitations of Deng entropy theory are found. For overcoming these limitations, some modified theories are given based on Deng entropy. However, only one special situation is considered in each theory method. In this paper, a unified form of the belief entropy is proposed on the basis of Deng entropy. In the new proposed method, the scale of the frame of d

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HERNANDEZ, ENRIC, and JORDI RECASENS. "ON POSSIBILISTIC AND PROBABILISTIC APPROXIMATIONS OF UNRESTRICTED BELIEF FUNCTIONS BASED ON THE CONCEPT OF FUZZY T-PREORDER." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10, no. 02 (2002): 185–200. http://dx.doi.org/10.1142/s0218488502001417.

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This paper presents a new method for approximating an unrestricted belief measure assuring that the "order" defined by the compatibility degree between evidence and the singletons set is preserved. Our approach, based on the concept of fuzzy T-preorder, also allows us to define several equivalence criteria over the set of all basic probability assignment functions on a given domain. Some others related aspects as uniqueness of the approximations are also addressed.

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Zhang, Yang, Yun Liu, Qing-An Zeng, and Qing Liu. "An Integrated Data Combination Method in Wireless Sensor Networks." International Journal of Interdisciplinary Telecommunications and Networking 10, no. 4 (2018): 61–76. http://dx.doi.org/10.4018/ijitn.2018100104.

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This article proposes an integrated information fusion approach in wireless sensor networks (WSNs) based on the Dempster-Shafer evidence theory, which includes four main aspects: the construction of basic probability assignment; a novel reliability coefficient function converting similarity to initial weight factors; an improved fusion approach by reassigning reliability coefficients; and the “Discount Rule.” Utilizing the integrated approach, conflicting data are fused more accurately and effectively than using the traditional fusion method. Experimental results show that the combined belief

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Pan, Qian, Deyun Zhou, Yongchuan Tang, Xiaoyang Li, and Jichuan Huang. "A Novel Belief Entropy for Measuring Uncertainty in Dempster-Shafer Evidence Theory Framework Based on Plausibility Transformation and Weighted Hartley Entropy." Entropy 21, no. 2 (2019): 163. http://dx.doi.org/10.3390/e21020163.

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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 transform

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Zhao, Yu-xin, Xin-an Wu, and Yan Ma. "A New Real-Time Path Planning Method Based on the Belief Space." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/260578.

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A new approach of real-time path planning based on belief space is proposed, which solves the problems of modeling the real-time detecting environment and optimizing in local path planning with the fusing factors. Initially, a double-safe-edges free space is defined for describing the sensor detecting characters, so as to transform the complex environment into some free areas, which can help the robots to reach any positions effectively and safely. Then, based on the uncertainty functions and the transferable belief model (TBM), the basic belief assignment (BBA) spaces of each factor are prese

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Gan, Dingyi, Bin Yang, and Yongchuan Tang. "An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion." Mathematics 8, no. 12 (2020): 2137. http://dx.doi.org/10.3390/math8122137.

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The Dempster–Shafer evidence theory has been widely applied in the field of information fusion. However, when the collected evidence data are highly conflicting, the Dempster combination rule (DCR) fails to produce intuitive results most of the time. In order to solve this problem, the base belief function is proposed to modify the basic probability assignment (BPA) in the exhaustive frame of discernment (FOD). However, in the non-exhaustive FOD, the mass function value of the empty set is nonzero, which makes the base belief function no longer applicable. In this paper, considering the influe

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Dezert, Jean, and Albena Tchamova. "On the Effectiveness of Measures of Uncertainty of Basic Belief Assignments." Information & Security: An International Journal, 2022. http://dx.doi.org/10.11610/isij.5201.

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Florentin, Smarandache, Martin Arnaud, and Osswald Christophe. "Contradiction Measures and Specificity Degrees of Basic Belief Assignments." May 2, 2014. https://doi.org/10.5281/zenodo.30148.

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In the theory of belief functions, many measures of uncertainty have been introduced. However, it is not always easy to understand what these measures really try to represent. In this paper, we re-interpret some measures of uncertainty in the theory of belief functions. We present some interests and drawbacks of the existing measures. On these observations, we introduce a measure of contradiction.

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