The Pseudo-Pascal Triangle of Maximum Deng Entropy

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

Uncertainty measure of pythagorean fuzzy sets

Pythagorean fuzzy sets (PFS) can better express and handle the uncertainty information and has the more lager representation space. Hence, the reasonable and effective method to measure the uncertainty of PFS can better analyze information. From the view of Dempster-Shafer evidence theory, hesitancy degree can include the two focal elements (member-ship, non-membership). Hence, considering the number of focal elements for hesitancy degree to measure uncertainty is important. In addition, the difference between membership and non-membership degree plays an essential role in uncertainty measure. From the above views, the paper proposed the new uncertainty measure. Based on the new uncertainty measure, cross entropy and divergence of PFS can be presented. In addition, some numerical examples are used to explain the proposed methods by comparing other methods. Finally, the proposed divergence can be used in pattern recognition to verify its effectiveness.ISSN:0922-6389ISSN:1879-831