Toward eigenvalues and eigenvectors of matrices of z-numbers

Abstract

Eigenvalues and eigenvectors are widely used in various practical applications in decision making, planning, control and other fields. Particularly, these concepts underlie analysis of consistency of a decision maker’s (DM) knowledge. In real-world problems, DM’s knowledge is naturally characterized by 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 paper we initiate study of Z-number valued eigenvalue and eigenvector of matrices, components of which are Z-numbers. A statement of problem and a solution approach for computation of Z-number valued eigensolutions are proposed. An example is provided to prove validity of the proposed approach.