Algebraic Properties of Z-Numbers Under Additive Arithmetic Operations
Prof. L.A. Zadeh introduced the concept of a Z-number for description of real-world information. A Z-number is an ordered pair \( Z = (A,B) \) of fuzzy numbers \( A \) and \( B \) used to describe a value of a random variable \( X \). \( A \) is an imprecise estimation of a value of \( X \) and \( B \) is an imprecise estimation of reliability of \( A \). A series of important works on computations with Z-numbers and applications were published. However, no study exists on properties of operation of Z-numbers. Such theoretical study is necessary to formulate the basics of the theory of Z-numbers. In this paper we prove that Z-numbers exhibit fundamental properties under additive arithmetic operations.
KeywordsFuzzy arithmetic Probabilistic arithmetic Associativity law Commutativity law Z-number
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