Eigensolutions of Partially Reliable Decision Preferences Described by Matrices of Z-Numbers Ra¯k A. Aliev Georgia State University, USA Azerbaijan State Oil and Industry University 20 Azadlig Ave., AZ1010, Baku, Azerbaijan Department of Information Systems Engineering Near East University, Lefkosa, North Cyprus raliev@asoa.edu.az Witold Pedrycz Department of Electrical & Computer Engineering University of Alberta, Edmonton, Canada, AB T6R 2G7 System Research Institute, Polish Academy of Sciences Warsaw, Poland Department of Electrical and Computer Engineering Faculty of Engineering, King Abdulaziz University Jeddah 21589, Saudi Arabia wpedrycz@ualberta.ca Oleg H. Huseynov * and Ra¯g 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 * oleg _ huseynov@yahoo.com † rafig.aliyev@hotmail.com Published 9 October 2020 Eigenvalues and eigenvectors are widely used in various applications. Particularly, these con- cepts 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 reliabil- ity. 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. Keywords: Z -number; fuzzy matrix; random matrix; eigenvalue; eigenvector; decision making. International Journal of Information Technology & Decision Making Vol. 19, No. 6 (2020) 1429–1450 ° c World Scienti¯c Publishing Company DOI: 10.1142/S0219622020500340 1429 Int. J. Info. Tech. Dec. Mak. 2020.19:1429-1450. Downloaded from www.worldscientific.com by 3.88.3.122 on 01/06/21. Re-use and distribution is strictly not permitted, except for Open Access articles.