Discrete z-numbers

In this thesis, we discuss algebraic properties of Z-numbers under the four arithmetic operations, namely addition, subtraction, multiplication and divison which are defined by the extension principle. The concept of a Z-number relates to the issue of reliability of information. Firstly, we give definition of the Z-numbers. A Z-number, Z=(A,B) has two components, the first component A is restriction (constraint) on the values which a real valued uncertain variable, X, is allowed to take. The second component of a Z-number measure of reliability (certainty) of the first component. The concept of a Z-number has a potential for many applications, especially decision analysis, risk assesment and economics. The concept of a restriction but is not a constraint. A restriction may be viewed as a generalized constraint. Secondly, we give generalization level of uncertain numbers and operations on random variables. Key Words: Z-numbers, fuzzy numbers, uncertain numbers.