Z-numbers and arithmetic operations on Z-numbers

Many problems in real world require mathematical formulization. However, the uncertainty in these problems and the reliability of the information makes this formulation difficult. Although the concept of fuzzy numbers is used for this purpose, fuzzy numbers are deal with only for modeling uncertainties. Z-numbers, proposed by Zadeh, are more convenient for modeling real life problems. A Z-number consists of an ordered pair in the form Z = (A, B). Here, A is a fuzzy number expressing uncertainty and B is also a fuzzy number related to the reliability of A. In linguistic sentences, containing uncertainty, can be expressed mathematically by Z-numbers. For instance, (The incubation period of COVID-19 is around 5 days, Probably) is a Z-number. Here, the phrase "The incubation period of COVID-19 is around 5 days" corresponds to the fuzzy number A, and the expression "Probably" corresponds to the fuzzy number B, which indicates the reliability of A. Z-numbers are used in decision-making processes where precise and reliable information is not available. However, arithmetic operations with Z-numbers are not so easy. In this thesis, first, detailed information about Z-numbers is presented. Then, a comprehensive literature review on how to perform arithmetic operations on Z-numbers is given. Finally, this subject has been reinforced with various examples.