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Eigensolutions of Partially Reliable Decision Preferences Described by Matrices of Z-Numbers

Author

Listed:
  • Rafik A. Aliev

    (Georgia State University, USA2Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan3Department of Information Systems Engineering, Near East University, Lefkosa, North Cyprus)

  • Witold Pedrycz

    (Department of Electrical & Computer Engineering, University of Alberta, Edmonton, Canada, AB T6R 2G7, Canada5System Research Institute, Polish Academy of Sciences Warsaw, Poland6Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Oleg H. Huseynov

    (Research Laboratory of Intelligent Control and Decision Making, Systems in Industry and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan)

  • Rafig R. Aliyev

    (Research Laboratory of Intelligent Control and Decision Making, Systems in Industry and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan)

Abstract

Eigenvalues and eigenvectors are widely used in various applications. Particularly, these concepts underlie analysis of consistency of a decision maker’s (DMs) preference knowledge. In real-world problems, DMs knowledge is inherently associated with imprecision and partial reliability. This involves combination of fuzzy and probabilistic information. The concept of a Z-number is a formal construct to describe such kind of information. In this study, we formulate the concepts of Z-number valued eigenvalue and eigenvector for matrices components of which are Z-numbers. A formal statement of the problem and a solution method for computation of Z-number valued eigensolutions are proposed. Numerical examples and an application devoted to foreign market selection problem are provided to show the usefulness of the proposed approach.

Suggested Citation

  • Rafik A. Aliev & Witold Pedrycz & Oleg H. Huseynov & Rafig R. Aliyev, 2020. "Eigensolutions of Partially Reliable Decision Preferences Described by Matrices of Z-Numbers," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1429-1450, November.
    • Handle: RePEc:wsi:ijitdm:v:19:y:2020:i:06:n:s0219622020500340
    DOI: 10.1142/S0219622020500340
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