An overview of Z numbers and its applications

In today's world, we are faced with a huge amount of growing information and uncertainty. Uncertainty in information has different types of ambiguity, possibility, probability, inaccuracy, etc., which make the use of information a challenge. Fuzzy logic, as a solution to deal with uncertainty, only deals with a certain part of these uncertainties and does not consider other aspects. In 2011, Zadeh proposed the concept of Z numbers, which consist of two components, the limit and the reliability of the limit, to cover possible and probable uncertainties.In this review article, the study of the background of Z numbers and its mathematical foundations will be discussed first. Then, the most important researches conducted in the applied fields of Z numbers include decision making, ranking, word calculations, machine learning, medical diagnosis, risk assessment, regression analysis, and review control. Examining the results of the articles indicates that the use of Z numbers can significantly improve the amount of error and accuracy. But the complexity of the calculations and the learning process in these structures are among the upcoming challenges in this field. Also, the use of Z numbers in some areas such as forecasting and optimization is among the future horizons.​