In decision making problems preferences of decision maker (DM) as usual is expressed in matrix form. Main problem in DM preference formalization is testing of consistency of DM preference knowledge expressed in matrix form. This problem is related with eigensolution of a given matrix. Investigation of eigensolution of numerical and fuzzy matrix is well known. Unfortunately, up today there are works in existing scientific literature on investigation eigenvalues and eigenvectors of Z-number valued matrices. In this paper for the first time we investigate 2 by 2 decision matrix, elements of which are Z-numbers, expressing fuzzy and probabilistic uncertainty of DM preference.


Z-number Z matrix Eigensolution Fuzzy numbers Fuzzy and probabilistic uncertainty 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Azerbaijan State Oil and Industry UniversityBakuAzerbaijan

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