Algebraic properties of Z-numbers under multiplicative arithmetic operations

Abstract

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 operations 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 multiplicative arithmetic operations.