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Algebraic Properties of Z-Numbers Under Additive Arithmetic Operations

  • Akif V. Alizadeh
  • Rashad R. Aliyev
  • Oleg H. HuseynovEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 896)

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 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.

Keywords

Fuzzy arithmetic Probabilistic arithmetic Associativity law Commutativity law Z-number 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Akif V. Alizadeh
    • 1
  • Rashad R. Aliyev
    • 2
  • Oleg H. Huseynov
    • 3
    Email author
  1. 1.Department of Control and Systems EngineeringAzerbaijan State Oil and Industry UniversityBakuAzerbaijan
  2. 2.Department of MathematicsEastern Mediterranean UniversityFamagustaTurkey
  3. 3.Research Laboratory of Intelligent Control and Decision Making Systems in Industry and EconomicsAzerbaijan State Oil and Industry UniversityBakuAzerbaijan

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