Uncertainty Measure Based on Evidence Theory

2013 ◽  
Vol 329 ◽  
pp. 344-348
Author(s):  
Shao Pu Zhang ◽  
Tao Feng
Keyword(s):  
Information System ◽  
Information Fusion ◽  
Rough Set Theory ◽  
Evidence Theory ◽  
Belief Function ◽  
Mass Function ◽  
Uncertainty Measure ◽  
Rough Approximation ◽  
Uncertainty Information ◽  
Uncertainty Method

Evidence theory is an effective method to deal with uncertainty information. And uncertainty measure is to reflect the uncertainty of an information system. Thus we want to merge evidence theory with uncertainty method in order to measure the roughness of a rough approximation space. This paper discusses the information fusion and uncertainty measure based on rough set theory. First, we propose a new method of information fusion based on the Bayse function, and define a pair of belief function and plausibility function using the fused mass function in an information system. Then we construct entropy for every decision class to measure the roughness of every decision class, and entropy for decision information system to measure the consistence of decision table.

scholarly journals An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2137
Author(s):  
Dingyi Gan ◽  
Bin Yang ◽  
Yongchuan Tang
Keyword(s):  
Data Fusion ◽  
Data Management ◽  
Information Fusion ◽  
Evidence Theory ◽  
Belief Function ◽  
Mass Function ◽  
Combination Rule ◽  
Basic Probability ◽  
Belief Entropy ◽  
Management Method

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in the non-exhaustive FOD, the mass function value of the empty set is nonzero, which makes the base belief function no longer applicable.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 influence of the size of the FOD and the mass function value of the empty set, a new belief function named the extended base belief function (EBBF) is proposed. This method can modify the BPA in the non-exhaustive FOD and obtain intuitive fusion results by taking into account the characteristics of the non-exhaustive FOD. In addition, the EBBF can degenerate into the base belief function in the exhaustive FOD. At the same time, by calculating the belief entropy of the modified BPA, we find that the value of belief entropy is higher than before. Belief entropy is used to measure the uncertainty of information, which can show the conflict more intuitively. The increase of the value of entropy belief is the consequence of conflict. This paper also designs an improved conflict data management method based on the EBBF to verify the rationality and effectiveness of the proposed method.

Similarity measure for multi-granularity rough approximations of vague sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1609-1621
Author(s):  
Jie Yang ◽  
Wei Zhou ◽  
Shuai Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Target Concept ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Vague Sets ◽  
Rough Approximation ◽  
Vague Concept

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

Reduction Algorithms for Multi-Covering Information System

2012 ◽  
Vol 160 ◽  
pp. 159-164
Author(s):  
Shao Pu Zhang ◽  
Tao Feng
Keyword(s):  
Information System ◽  
Information Fusion ◽  
Conditional Entropy ◽  
Mass Function ◽  
Decision System ◽  
Belief Structure ◽  
Decision Systems ◽  
Covering System

This paper discusses the reduction algorithms of a multi-covering decision system. Firstly, we give the belief structure in a covering system and give a rule of information fusion of multi-covering information. Then, we introduce special conditional entropy of a covering decision system with multi-coverings by the fused mass function and study the reduction of multi-covering information by means of limited conditional entropy and consistent multi-covering decision systems by means of conditional entropy. Two algorithms are designed to compute reductions of a multi-covering system and a consistent covering decision system, respectively.

scholarly journals Relative Reduction of Neighborhood-Covering Pessimistic Multigranulation Rough Set Based on Evidence Theory

Information ◽  
2019 ◽  
Vol 10 (11) ◽  
pp. 334 ◽  
Author(s):  
Xiaoying You ◽  
Jinjin Li ◽  
Hongkun Wang
Keyword(s):  
Information System ◽  
Rough Set ◽  
Evidence Theory ◽  
Belief Function ◽  
Relative Reduction ◽  
Reduction Theory ◽  
Research Topics ◽  
Knowledge Reduction ◽  
Multigranulation Rough Set ◽  
Lower And Upper Approximations

Relative reduction of multiple neighborhood-covering with multigranulation rough set has been one of the hot research topics in knowledge reduction theory. In this paper, we explore the relative reduction of covering information system by combining the neighborhood-covering pessimistic multigranulation rough set with evidence theory. First, the lower and upper approximations of multigranulation rough set in neighborhood-covering information systems are introduced based on the concept of neighborhood of objects. Second, the belief and plausibility functions from evidence theory are employed to characterize the approximations of neighborhood-covering multigranulation rough set. Then the relative reduction of neighborhood-covering information system is investigated by using the belief and plausibility functions. Finally, an algorithm for computing a relative reduction of neighborhood-covering pessimistic multigranulation rough set is proposed according to the significance of coverings defined by the belief function, and its validity is examined by a practical example.

scholarly journals Temporal and Causal Relations on Evidence Theory: an Application on Adverse Drug Reactions

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Luiz Alberto Pereira Afonso Ribeiro ◽  
Ana Cristina Bicharra Garcia ◽  
Paulo Sérgio Medeiros Dos Santos
Keyword(s):  
Information Fusion ◽  
Evidence Theory ◽  
Mass Function ◽  
Data Sources ◽  
Drug Reactions ◽  
Clinical Notes ◽  
Dempster Shafer Theory ◽  
Multisensor Information Fusion ◽  
Shafer Theory ◽  
Theory Of Evidence

The use of big data and information fusion in electronichealth records (EHR) allowed the identification of adversedrug reactions(ADR) through the integration of heteroge-neous sources such as clinical notes (CN), medication pre-scriptions, and pathological examinations. This heterogene-ity of data sources entails the need to address redundancy,conflict, and uncertainty caused by the high dimensionalitypresent in EHR. The use of multisensor information fusion(MSIF) presents an ideal scenario to deal with uncertainty,especially when adding resources of the theory of evidence,also called Dempster–Shafer Theory (DST). In that scenariothere is a challenge which is to specify the attribution of be-lief through the mass function, from the datasets, named basicprobability assignment (BPA). The objective of the presentwork is to create a form of BPA generation using analy-sis of data regarding causal and time relationships betweensources, entities and sensors, not only through correlation, butby causal inference.

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

Sensors ◽  
2021 ◽  
Vol 21 (3) ◽  
pp. 840
Author(s):  
Fuyuan Xiao
Keyword(s):  
Decision Making ◽  
Information Fusion ◽  
Medical Diagnosis ◽  
Evidence Theory ◽  
Mass Function ◽  
Communication Problems ◽  
Multi Attribute Decision Making ◽  
Open Issue ◽  
The Difference ◽  
Complex Basis

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.

scholarly journals CBD: A New Divergence Measure for Complex Mass Function and its Application in Pattern Recognition

2021 ◽  
Author(s):  
Lan Luo ◽  
Fuyuan Xiao
Keyword(s):  
Pattern Recognition ◽  
Function Theory ◽  
Evidence Theory ◽  
Mass Function ◽  
Recognition Algorithm ◽  
Divergence Measure ◽  
Pattern Recognition Algorithm ◽  
Complex Mass ◽  
Open Issue ◽  
Uncertainty Information

Abstract The theory of complex mass function is an effective method to deal with uncertainty information, and it is a generalized of Dempster-Shafer evidence theory. However, divergence measure is still an open issue in the realm of complex mass function theory. The main contribution of our paper is to propose a generalized divergence measure for complex mass function that is called complex belief divergence (CBD),which has the properties of symmetry, nonnegativity, nondegeneracy. When complex mass function degenerates into classical mass function, the CBD will degenerate into classical belief divergence, which has a better ability to measure uncertainty of information. Finally, a pattern recognition algorithm based on CBD is designed and applied to a medical diagnosis problem, which proves its practical prospect.

Neural Network and D-S Evidence Theory Based Condition Monitoring and Fault Diagnosis of Drilling

2012 ◽  
Vol 249-250 ◽  
pp. 481-486
Author(s):  
Jiang Ping Wang ◽  
Shun De Lin ◽  
Ze Fu Bao
Keyword(s):  
Neural Network ◽  
Fault Diagnosis ◽  
Information Fusion ◽  
Evidence Theory ◽  
Mass Function ◽  
Primary Diagnosis ◽  
A Value ◽  
Engineering Data ◽  
The Neural Network ◽  
Basic Probability

This paper focuses on drilling fault diagnosis with the technology of information fusion based on neural network and Dempster-Shafer evidence theory. Neural network is used to process the drilling engineering data monitored from drilling on-site. The primary diagnosis results of drilling faults can be obtained by comparing the outputs of the neural network. And also the outputs of neural network are utilized to construct a basic probability assignment function (mass function) to assign a value of mass function for each type of drilling faults. The final fault diagnosis results will be achieved by using Dempster-Shafer evidence theory on decision level through further reasoning primary diagnosis results of neural network. The proposed method can in time discover the engineering data whether abnormal so that can diagnose and classify them, and will improve the accuracy of the drilling fault diagnosis.

Fault Classification of Hydroelectric Generating Unit Based on Improved Evidence Theory

2014 ◽  
Vol 7 (1) ◽  
pp. 78-83 ◽  
Author(s):  
Jiatang Cheng ◽  
Li Ai ◽  
Zhimei Duan ◽  
Yan Xiong
Keyword(s):  
Fault Diagnosis ◽  
Information Fusion ◽  
Evidence Theory ◽  
Fault Classification ◽  
Fusion Method ◽  
Inconsistent Result ◽  
High Conflict

Aiming at the problem of the conventional vibration fault diagnosis technology with inconsistent result of a hydroelectric generating unit, an information fusion method was proposed based on the improved evidence theory. In this algorithm, the original evidence was amended by the credibility factor, and then the synthesis rule of standard evidence theory was utilized to carry out information fusion. The results show that the proposed method can obtain any definitive conclusion even if there is high conflict evidence in the synthesis evidence process, and may avoid the divergent phenomenon when the consistent evidence is fused, and is suitable for the fault classification of hydroelectric generating unit.

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