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

The arithmetic of triangular Z-numbers with reduced calculation complexity using an extension of triangular distribution

This work was supported by project PID2019-103880RB-I00 funded by MCIN/AEI/10.13039/501100011033, by FEDER/Junta de Andalucia-Consejeria de Transformacion Economica, Industria, Conocimiento y Universidades/Proyecto B-TIC-590-UGR20, by the China Scholarship Council (CSC) , and by the Andalusian government through project P2000673. Funding for open access charge: Universidad de Granada/CBUA.Information that people rely on is often uncertain and partially reliable. Zadeh introduced the concept of Z-numbers as a more adequate formal construct for describing uncertain and partially reliable information. Most existing applications of Z-numbers involve discrete ones due to the high complexity of calculating continuous ones. However, the continuous form is the most common form of information in the real world. Simplifying continuous Z-number calculations is significant for practical applications. There are two reasons for the complexity of continuous Z-number calculations: the use of normal distributions and the inconsistency between the meaning and definition of Z-numbers. In this paper, we extend the triangular distribution as the hidden probability density function of triangular Z-numbers. We add a new parameter to the triangular distribution to influence its convexity and concavity, and then expand the value's domain of the probability measure. Finally, we implement the basic operations of triangular Z-numbers based on the extended triangular distribution. The suggested method is illustrated with numerical examples, and we compare its computational complexity and the entropy (uncertainty) of the resulting Z-number to the traditional method. The comparison shows that our method has lower computational complexity, higher precision and lower uncertainty in the results.MCIN/AEI PID2019-103880RB-I00FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades/Proyecto B-TIC-590-UGR20China Scholarship CouncilAndalusian government P2000673Universidad de Granada/CBU