@misc{10481/85225,
year = {2023},
month = {11},
url = {https://hdl.handle.net/10481/85225},
abstract = {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.},
organization = {MCIN/AEI
	PID2019-103880RB-I00},
organization = {FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades/Proyecto
	B-TIC-590-UGR20},
organization = {China Scholarship Council},
organization = {Andalusian government
	P2000673},
organization = {Universidad de Granada/CBUA},
publisher = {Elsevier},
keywords = {Z-numbers},
keywords = {Triangular Z-numbers},
keywords = {Triangular distribution},
keywords = {Probability measure},
title = {The arithmetic of triangular Z-numbers with reduced calculation complexity using an extension of triangular distribution},
doi = {10.1016/j.ins.2023.119477},
author = {Li, Yangxue and Herrera Viedma, Enrique and Pérez Gálvez, Ignacio Javier and Xing, Wen and Morente Molinera, Juan Antonio},
}