The arithmetic of triangular Z-numbers with reduced calculation complexity using an extension of triangular distribution
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AuthorLi, Yangxue; Herrera Viedma, Enrique; Pérez Gálvez, Ignacio Javier; Xing, Wen; Morente Molinera, Juan Antonio
Z-numbersTriangular Z-numbersTriangular distributionProbability measure
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]
SponsorshipMCIN/AEI PID2019-103880RB-I00; FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades/Proyecto B-TIC-590-UGR20; China Scholarship Council; Andalusian government P2000673; 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.