As an extension of probability theory, evidence theory is able to better handle unknown and imprecise information. Owing toits advantages, evidence theory has more flexibility and effectiveness for modeling and processing uncertain information.Uncertainty measure plays an essential role both in evidence theory and probability theory.In probability theory, Shannon entropy provides a novel perspective for measuring uncertainty. Various entropies exist for measuring the uncertainty of basic probability assignment (BPA) in evidence theory. However, from the standpoint of the requirements of uncertainty measurement and physics, these entropies are controversial. Therefore, the process for measuring BPA uncertainty currently remains an open issue in the literature.Firstly, this paper reviews the measures of uncertainty in evidence theory followed by an analysis of some related controversies. Secondly, we discuss the development of Deng entropy as an effective way to measure uncertainty, including introducing its definition, analyzing its properties, and comparing it to other measures. We also examine the concept of maximum Deng entropy, the pseudo-Pascal triangle of maximum Deng entropy, generalized belief entropy, and measures of divergence.In addition, we conduct an analysis of the application of Deng entropy and further examine the challenges for future studies on uncertainty measurement in evidence theory. Finally, a conclusion is provided to summarize this study.

Uncertainty measure in evidence theory

PPascal triangle (known as Yang Hui Triangle in Chinese) is an important model in mathematics while the entropy has been heavily studied in physics or as uncertainty measure in information science. How to construct the the connection between Pascal triangle and uncertainty measure is an interesting topic. One of the most used entropy, Tasllis entropy, has been modelled with Pascal triangle. But the relationship of the other entropy functions with Pascal triangle is still an open issue. Dempster-Shafer evidence theory takes the advantage to deal with uncertainty than probability theory since the probability distribution is generalized as basic probability assignment, which is more efficient to model and handle uncertain information. Given a basic probability assignment, its corresponding uncertainty measure can be determined by Deng entropy, which is the generalization of Shannon entropy. In this paper, a Pseudo-Pascal triangle based the maximum Deng entropy is constructed. Similar to the Pascal triangle modelling of Tasllis entropy, this work provides the a possible way of Deng entropy in physics and information theory.

http://univagora.ro/jour/index.php/ijccc/article/download/1006/1371

The Pseudo-Pascal Triangle of Maximum Deng Entropy

In this paper, uncertainty has been measured in the form of fuzziness which arises due to imprecise boundaries of fuzzy sets. Uncertainty caused due to human's cognition can be decreased by the use of fuzzy soft sets. There are different approaches to deal with the measurement of uncertainty. The method we proposed uses fuzzified evidence theory to calculate total degree of fuzziness of the parameters. It consists of mainly four parts. The first part is to measure uncertainties of parameters using fuzzy soft sets and then to modulate the uncertainties calculated. Afterward, the appropriate basic probability assignments with respect to each parameter are produced. In the last, we use Dempster's rule of combination to fuse independent parameters into integrated one. To validate the proposed method, we perform an experiment and compare our outputs with grey relational analysis method. Also, a medical diagnosis application in reference to COVID-19 has been given to show the effectiveness of advanced method by comparing with other method.

/pdf/an-advanced-uncertainty-measure-using-fuzzy-soft-sets-2gfb7pfuuu.pdf

An advanced uncertainty measure using fuzzy soft sets: Application to decision-making problems

Information volume fractal dimension

The extropy has recently been introduced as the dual concept of entropy. Moreover, in the context of the Dempster–Shafer evidence theory, Deng studied a new measure of discrimination, named the Deng entropy. In this paper, we define the Deng extropy and study its relation with Deng entropy, and examples are proposed in order to compare them. The behaviour of Deng extropy is studied under changes of focal elements. A characterization result is given for the maximum Deng extropy and, finally, a numerical example in pattern recognition is discussed in order to highlight the relevance of the new measure.

https://www.mdpi.com/1099-4300/22/5/582/pdf

A Dual Measure of Uncertainty: The Deng Extropy.

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 discernment (FOD) and the relative scale of a focal element with reference to FOD are considered. Meanwhile, for an example, some properties of the belief entropy are obtained based on a special situation of a unified form. Some numerical examples are illustrated to show the efficiency and accuracy of the proposed belief entropy.

https://www.mdpi.com/1099-4300/21/10/987/pdf

A New Belief Entropy Based on Deng Entropy

One of the major challenges in the design of flexible microwave absorbers is to achieve flexibility, particularly the stretchability of the overall structure while ensuring broadband absorption. In general, the comprehensive properties of flexible dielectric materials are good enough, whereas those of flexible conductive materials are relatively poor. Materials with both good conductivity and stretchability are rarely reported. In this letter, a stretchable absorber was designed with the conductive material made into the hauberk structure, utilizing the relative movement of the rings of the hauberk to realize the stretchability. At the same time, this structure can achieve extra-broad-band absorption at large incident angles. Approximately 80% absorption under vertically incident TE and TM waves was measured in (10–40) GHz, showing good agreement with the simulation results. When the overall structure was stretched uniaxially by 10%, experiment results showed that the absorption decreased slightly but was still broadband, which agreed well with the simulation results. What is more, the structure maintained broadband absorption under 0°, 45°, and 75° incident angles.

Stretchable Broadband Absorbers Based on the Hauberk Structure

Abstract In this work, we proposed a method of extracting feature parameters for deep neural network prediction based on the vectorgraph storage format, which can be applied to the design of electromagnetic metamaterials with sandwich structures. Compared to current methods of manually extracting feature parameters, this method can automatically and precisely extract the feature parameters of arbitrary two-dimensional surface patterns of the sandwich structure. The position and size of surface patterns can be freely defined, and the surface patterns can be easily scaled, rotated, translated, or transformed in other ways. Compared to the pixel graph feature extraction method, this method can adapt to very complex surface pattern design in a more efficient way. And the response band can be easily shifted by scaling the designed surface pattern. To illustrate and verify the method, a 7-layer deep neural network was built to design a metamaterial broadband polarization converter. Prototype samples were fabricated and tested to verify the accuracy of the prediction results. In general, the method is potentially applicable to the design of different kinds of sandwich-structure metamaterials, with different functions and in different frequency bands. 

/pdf/deep-neural-network-training-method-based-on-vectorgraphs-15hy8b9w.pdf

Deep neural network training method based on vectorgraphs for designing of metamaterial broadband polarization converters

Some new characterizations of the generalized Bott–Duffin inverse are proposed by using range, nullspace and matrix equations. We extend the famous fact that the rank equation characterizes the inverse of matrices to the generalized Bott–Duffin inverse, and give its several representations. Additionally, we show the relationships between the generalized Bott–Duffin inverse and two classes of nonsingular bordered matrices and apply them to the Cramer's rules of two classes of restricted linear equations.

New characterizations and representations of the generalized Bott–Duffin inverse and its applications

In recent years, advances in wearable medical devices have been driven by the development of flexible sensors and wireless IoT technologies, with research and applications in this field rapidly increasing. Plantar pressure analysis is a gait method that can be used to analyze foot pressure during human movement to identify potential health problems, but most of the devices based on this method are currently single-functional, poorly portable, and expensive. This work proposes a smart insole using meshless conductive rubber sensors, as well as a multi-channel data acquisition and transmission system based on these sensors, deep learning networks, and Bluetooth technology. The smart insole sensing unit and circuit board were made of flexible materials and powered by rechargeable lithium batteries. The system can be used to collect plantar pressure data from the sensors in real time, analyze the pressure in different regions of the foot through a neural network, and infer the gait cycle and abnormal gait of the user. The effective communication range can be up to 70 meters under barrier-free conditions. This smart insole has a bright future thanks to the pressure detection range, fast response time, and good durability.

/pdf/smart-insoles-for-gait-analysis-based-on-meshless-conductive-2lf5fk9r.pdf

Smart Insoles for Gait Analysis Based on Meshless Conductive Rubber Sensors and Neural Networks

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