scholarly journals Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference

2020 ◽  
Vol 15 (4) ◽  
Author(s):  
Lipeng Pan ◽  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Evidence Theory ◽  
Mass Function ◽  
New Method ◽  
Weighted Averaging ◽  
Minimum Entropy ◽  
Transform Method ◽  
Numerical Examples ◽  
Ordered Weighted Averaging ◽  
Open Issue

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.

scholarly journals Information Volume of Mass Function

2020 ◽  
Vol 15 (6) ◽  
Author(s):  
Yong Deng
Keyword(s):  
Probability Distribution ◽  
Shannon Entropy ◽  
Mass Function ◽  
Total Uncertainty ◽  
Numerical Examples ◽  
Distribution Of The Maximum ◽  
Open Issue ◽  
Deng Entropy

Given a probability distribution, its corresponding information volume is Shannon entropy. However, how to determine the information volume of a given mass function is still an open issue. Based on Deng entropy, the information volume of mass function is presented in this paper. Given a mass function, the corresponding information volume is larger than its uncertainty measured by Deng entropy. In addition, when the cardinal of the frame of discernment is identical, both the total uncertainty case and the BPA distribution of the maximum Deng entropy have the same information volume. Some numerical examples are illustrated to show the efficiency of the proposed information volume of mass function.

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

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 163 ◽  
Author(s):  
Qian Pan ◽  
Deyun Zhou ◽  
Yongchuan Tang ◽  
Xiaoyang Li ◽  
Jichuan Huang
Keyword(s):  
Evidence Theory ◽  
Mass Function ◽  
Probability Mass Function ◽  
Main Work ◽  
Basic Probability ◽  
Open Issue ◽  
Belief Entropy ◽  
Probability Mass ◽  
Hartley Entropy ◽  
Theory Framework

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.

scholarly journals An Uncertainty Measure for Interval-valued Evidences

2017 ◽  
Vol 12 (5) ◽  
pp. 631 ◽  
Author(s):  
Wen Jiang ◽  
Shiyu Wang
Keyword(s):  
Evidence Theory ◽  
Uncertain Information ◽  
Uncertainty Measure ◽  
Interval Numbers ◽  
Numerical Examples ◽  
Belief Structure ◽  
Belief Structures ◽  
Open Issue ◽  
Deng Entropy ◽  
Interval Valued

Interval-valued belief structure (IBS), as an extension of single-valued belief structures in Dempster-Shafer evidence theory, is gradually applied in many fields. An IBS assigns belief degrees to interval numbers rather than precise numbers, thereby it can handle more complex uncertain information. However, how to measure the uncertainty of an IBS is still an open issue. In this paper, a new method based on Deng entropy denoted as UIV is proposed to measure the uncertainty of the IBS. Moreover, it is proved that UIV meets some desirable axiomatic requirements. Numerical examples are shown in the paper to demonstrate the efficiency of UIV by comparing the proposed UIV with existing approaches. 

scholarly journals A New Conflict Management in Evidence Theory Based on DEMATEL Method

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Wentao Fan ◽  
Fuyuan Xiao
Keyword(s):  
Decision Making ◽  
Data Fusion ◽  
Conflict Management ◽  
Correlation Coefficient ◽  
Averaging Method ◽  
Target Recognition ◽  
Evidence Theory ◽  
New Method ◽  
Weighted Averaging ◽  
Combination Rule

D-S evidence theory is widely used in data fusion. However, the result of Dempster’s combination rule is not efficient and in highly conflicting situation. Though the existing methods have been proved efficient to deal with conflict in some applications, the indirect conflict among evidence is neglected to some degree. To solve this problem, a new method is proposed based on decision-making trial and evaluation laboratory (DEMATEL) and the belief correlation coefficient in this paper. The application in target recognition illustrates the efficiency of the proposed method. Compared with Dempster’s rule, averaging method and weighted averaging method, etc., the results obtained by the proposed method have better performance. The main reason is that the indirect conflict is well addressed in the proposed method.

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 A modification of the reduced differential transform method for fractional calculus

2018 ◽  
Vol 22 (4) ◽  
pp. 1871-1875 ◽  
Author(s):  
Kang-Le Wang ◽  
Kang-Jia Wang
Keyword(s):  
Heat Transfer ◽  
Fractional Calculus ◽  
Differential Transform Method ◽  
New Method ◽  
Transform Method ◽  
Numerical Examples ◽  
Differential Transform ◽  
Transfer Equations ◽  
Reduced Differential Transform Method

In this paper, the reduced differential transform method is modified and successfully used to solve the fractional heat transfer equations. The numerical examples show that the new method is efficient, simple, and accurate.

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.

The research and application of intuitionistic fuzzy decision making

2021 ◽  
pp. 1-15
Author(s):  
Leina Zheng ◽  
Junwei Wang ◽  
Meiling Liu ◽  
Jun Liu ◽  
Tiejun Pan ◽  
...  
Keyword(s):  
Decision Making ◽  
Average Distance ◽  
Integrated Approach ◽  
New Method ◽  
Weighted Averaging ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Ordered Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Decision Making Problem

This paper studies intuitionistic fuzzy (IF) decision making problems using an integrated approach. Firstly, an IF induced generalized ordered weighted averaging distance (IFIGOWAD) operator is introduced, that covers numerous IF aggregations distance operators. Then, two more generalized operators named IF quasi induced OWAD (Quasi-IFIOWAD) and IF induced generalized hybrid average distance (IFIGHAD) operator are presented. Furthermore, a new method using above operators is introduced to IF decision making problem and online trade systems. Finally, two real cases are present to show the effect of the method.

scholarly journals Barycentric prolate interpolation and pseudospectral differentiation

2021 ◽  
Author(s):  
Yan Tian
Keyword(s):  
Boundary Value Problem ◽  
Convergence Rates ◽  
Boundary Value ◽  
High Accuracy ◽  
Second Order ◽  
New Method ◽  
Numerical Examples ◽  
Helmholtz Problem ◽  
Collocation Scheme

AbstractIn this paper, we provide further illustrations of prolate interpolation and pseudospectral differentiation based on the barycentric perspectives. The convergence rates of the barycentric prolate interpolation and pseudospectral differentiation are derived. Furthermore, we propose the new preconditioner, which leads to the well-conditioned prolate collocation scheme. Numerical examples are included to show the high accuracy of the new method. We apply this approach to solve the second-order boundary value problem and Helmholtz problem.

Sign in / Sign up

Export Citation Format

Share Document