# Eigensolution of 2 by 2 Z-Matrix

• Kamala Aliyeva
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1095)

## Abstract

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.

## Keywords

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

## References

1. 1.
Buckley, B.: Fuzzy eigenvalue problems and input output analysis. Fuzzy Sets Syst. 34, 187–195 (1998)
2. 2.
Chiao, C.: Generalized fuzzy eigenvalue problems. Tamsui Oxf. J. Math. Sci. 14, 31–37 (1998)
3. 3.
Theodoroua, Y., Drossosb, C., Alevizosb, P.: Correspondence analysis with fuzzy data: the fuzzy eigenvalue problem. Fuzzy Sets Syst. 158, 113–137 (2007)
4. 4.
Tian, Z.: Fuzzy eigenvectors of real matrix. J. Math. Res. 2(3), 103 (2010)
5. 5.
Allahviranloo, T., Salahshour, S., Khezerloo, M.: Maximal- and minimal symmetric solutions of fully fuzzy linear systems. J. Comput. Appl. Math. 235, 4652–4662 (2011)
6. 6.
Allahviranloo, T., Mikaelvand, N., Aftab Kiani, N., Mastani Shabestari, R.: Signed decomposition of fully fuzzy linear system. J. Comput. Appl. Math. 1, 77–88 (2008)
7. 7.
Allahviranloo, T., Afshar Kermani, M.: Solution of a fuzzy system of linear equation. Appl. Math. Comput. 175, 519–531 (2006)
8. 8.
Sevastjanov, P., Dymova, L.: A new method for solving interval and fuzzy equations: linear case. Inf. Sci. 179, 925–937 (2009)