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

Max-plus algebra is the set ℝmax or ℝε=ℝ∪{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 I ( ℝ ) ε ′ ={x=[ x _ , x ¯ ] | x _ , x ¯ ∈ℝ , x _ ≤ x ¯ < ε ′ } which have minimum (⊕¯′) and addition (⊗¯) operations. A matrix in which its components are the element of ℝε 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 I(ℝ)ε. This research will discusses the interval min-plus algebraic structure and matrices over interval min-plus algebra.