Interval min-plus algebraic structure and matrices over interval min-plus algebra

Abstract

Max-plus algebra is the set or where is the set of all real number and ε = −∞ which is equipped with maximum (⊕) and plus (⊗) operations. The structure of max-plus algebra is semifield. Another semifield that can be learned is min-plus algebra. Min-plus algebra is the set or where ε′ = ∞ which is equipped with minimum (⊕ ′) and plus (⊗) operations. Max-plus algebra has been generalized into interval max-plus algebra, so that min-plus algebra can be developed into an interval min-plus algebra. Interval min-plus algebra is defined as a set which have minimum and addition operations. A matrix in which its components are the element of is called matrix over max-plus algebra. Matrices over max-plus algebra has been generalized into interval matrices in which its components are the element of . This research will discusses the interval min-plus algebraic structure and matrices over interval min-plus algebra.