Max-min algebra and its various aspects have been intensively studied by many authors [1, 4] because of its applicability to various areas, such as fuzzy system, knowledge management and others. Binary operations of addition and multiplication of real numbers used in classical linear algebra are replaced in max-min algebra by operations of maximum and minimum. We consider two-sided systems of max-min linear equations $A\otimes x=B\otimes x$, with given coefficient matrices $A$ and $B$. We present a polynomial method for...

Max-min algebra is an algebraic structure in which classical addition and multiplication are replaced by $\oplus$ and $\otimes$, where $a\oplus b=max\{a,b\},a\otimes b=min\{a,b\}$. The notation $𝐀\otimes 𝐱=𝐛$ represents an interval system of linear equations, where $𝐀=[\underline{A},\overline{A}]$, $𝐛=[\underline{b},\overline{b}]$ are given interval matrix and interval vector, respectively, and a solution is from a given interval vector $𝐱=[\underline{x},\overline{x}]$. We define six types of solvability of max-min interval systems with bounded solution and give necessary and sufficient conditions for them.

This paper provides an extension of results connected with the problem of the optimization of a linear objective function subject to $max-*$ fuzzy relational equations and an inequality constraint, where $*$ is an operation. This research is important because the knowledge and the algorithms presented in the paper can be used in various optimization processes. Previous articles describe an important problem of minimizing a linear objective function under a fuzzy $max-*$ relational equation and an inequality constraint,...