The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche [10, 11] introduced a max-algebraic approach to the single criterion… (More)

Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in R+. This theory is based on the observation that… (More)

We prove that the sequence of eigencones (i.e., cones of nonnegative eigenvectors) of matrix powers is periodic both in max algebra and in nonnegative linear algebra. Using an argument of Pullman, we… (More)

The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly… (More)

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold… (More)

The alternating method for solving A⊗x = B⊗y over max-algebra is generalized to the systems A1⊗x1 = . . . = Ak⊗xk. The known convergence results are extended in this general setting to the case when… (More)

A max-algebraic analogue of the Markov Chain Tree Theorem is presented, and its connections with the classical Markov Chain Tree Theorem and the max-algebraic spectral theory are investigated.

The results are presented on characterization of internal-tin Nb3Sn strands designed and fabricated for use in full scale ITER TF conductor sample. The microstructure of strands has been investigated… (More)

We consider a discrete classical integrable model on the 3-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of the different 3-dimensional spin… (More)

We give simple algebraic proofs of results on generators and bases of max cones, some of which are known. We show that every generating set S for a cone in max algebra can be partitioned into two… (More)