The research entitled “Optimalisasi Norma Jangkauan Vektor Eigen Atas Aljabar Maks-Plus Interval” was conducted by Siswanto under the guidance of Dr.rer.nat. Ari Suparwanto, M.Si. and Dr. M. Andy Rudhito, S.Pd., M.Si. in 2018.
The following is the abstract of this research.
Let R be the set of real numbers and R epsilon: the set of real number union infinite negative. Max-plus algebra is algebraic structure formed from the set R epsilon equipped with maximum and addition operations. A matrix in the size of m times n, whose components belong to R epsilon, called matrix over max-plus algebra. The set of matrices over max-plus algebra is denoted by R epsilon power m times n. Algebraic structure formed from the set of all interval in R epsilon union [infinite negative, infinite negative] equipped with maximum and plus operations is called interval max-plus algebra. A matrix in the size of m times n, whose components belong to all interval in R epsilon union [infinite negative,infinite negative], called matrix over interval max-plus algebra. In this research discussed about optimizing range norm of eigenvector over interval max-plus algebra and optimizing range norm of eigenvector over interval max-plus algebra with prescribed components. This research based on expanssion of max-plus algebra into interval max-plus algebra, optimizing range norm of eigenvector over max-plus algebra and optimizing range norm of eigenvector over max-plus algebra with prescribed components. The discussing initiated how to find eigenvalue. eigenvector and eigenvector space over max-plus algebra the generally matrices included reducible and irreducible matrices. In the last part of this research given application examples of the problem of eigenvalue and eigenvector over interval max-plus algebra in the production system. The concepts related to the main discussion were also investigated in this research. The concepts related, namely how to indicate the existence and uniqueness of solution of linear equation system in interval max-plus algebra by the normalization of linear equation system. Included in the discussion of linear equation system are the concepts about image set of matrices over interval max-plus algebra, strongly reguler matrices and simple image set.
Keywords: Optimalisasi, Norma Jangkauan, Aljabar Maks-Plus Interval