Abstract: The characteristics of interval systems under the framework of extremum algebra is a meaningful research direction. In this paper we study the characterizations of various kinds of solvabilities of interval linear inequalities in the max-min algebra, including the weak solvability, strong solvability, tolerance solvability, strongly tolerance solvability, control solvability and strongly control solvability. Furthermore, we analyze the existence of solutions and the solvabilities, and show these two concepts are equivalent in certain situations. In addition, we find the maximum solutions corresponding to different kinds of solvabilities.

Key words: Interval linear system , Max-min algebra, Maximum solution