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

Abstract

Max-plus algebra is the set Rmax or Rϵ=Re {ϵ} where R 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 Rmin or Rϵ'=R {ϵ} 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 IRϵ={x=[x-,x̄|x-,x̄ϵR,x≤x̄