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.
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Aliev, R.A., Alizadeh, A.V. (2019). Algebraic Properties of \( Z \)-Numbers Under Multiplicative Arithmetic Operations. In: Aliev, R., Kacprzyk, J., Pedrycz, W., Jamshidi, M., Sadikoglu, F. (eds) 13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018. ICAFS 2018. Advances in Intelligent Systems and Computing, vol 896. Springer, Cham. https://doi.org/10.1007/978-3-030-04164-9_9
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DOI: https://doi.org/10.1007/978-3-030-04164-9_9
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