The arithmetic of triangular Z-numbers with reduced calculation complexity using an extension of triangular distribution Li, Yangxue Herrera Viedma, Enrique Pérez Gálvez, Ignacio Javier Xing, Wen Morente Molinera, Juan Antonio Z-numbers Triangular Z-numbers Triangular distribution Probability measure 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. 2023-10-25T07:20:52Z 2023-10-25T07:20:52Z 2023-11 journal article Y. Li, E. Herrera-Viedma, I.J. Pérez et al. The arithmetic of triangular Z-numbers with reduced calculation complexity using an extension of triangular distribution. Information Sciences 647 (2023) 119477. [https://doi.org/10.1016/j.ins.2023.119477] https://hdl.handle.net/10481/85225 10.1016/j.ins.2023.119477 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier