The max-plus algebra can be used to model and analyze a networks, like the project scheduling, production system, queueing networks, etc (Bacelli, et al. (2001), Rudhito, A. (2003), Krivulin, N.K. (2001)). The networks modelling with max-plus algebra approach is usually a max-plus linear system equations and it can be written as a matrix equation. The periodical properties of networks dynamics can be analyzed through the max-plus eigenvalues and eigenvectors of matrices in its modelling.

Recently, the fuzzy networks modelling has been developed. In this paper, the fuzzy network refers to networks whose their activity times are fuzzy number. The fuzzy scheduling can be read in Chanas, S., Zielinski, P. (2001), and Soltoni, A., Haji, R. (2007). The fuzzy queueing networks can read in Lüthi, J., Haring, G. (1997), and Pardoa & Fuente (2007).

When we follow the notions of modelling and analyzing of networks with max-plus algebra approach, we can use the analyzing of periodical properties of the dynamic can be do through eigenvalues and eigenvectors of matrices over max-plus fuzzy number in its modelling. For this reasons, this paper will discuss eigenvalues and eigenvectors of matrices over max-plus fuzzy number.

Before we proceed the essential considerations, we will reviewed the notions of eigenvalues and eigenvectors of matrices over max-plus algebra, and eigenvalues and eigenvectors of matrices over interval max-plus algebra.

Outline article (next sections/posting):2. Eigenvalues and Eigenvectors of Matrices over Max-plus algebra

3. Eigenvalues and Eigenvectors of Matrices over Interval Max-Plus Algebra

4. Eigenvalues and Eigenvectors of Matrices over Fuzzy Number Max-Plus Algebra

5. Conclusion

References:

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Chanas, S., Zielinski, P. 2001. Critical path analysis in the network with fuzzy activity times. Fuzzy Sets and Systems. Elsevier Science B.V.

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Lüthi, J., Haring, G. 1997. Fuzzy Queueing Network Models of Computing Systems. Proceedings of the 13th UK Performance Engineering Workshop, Ilkley, UK, Edinburgh University Press, July 1997.

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