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.

We are considering a two-stage optimal scheduling problem, which involves two similar projects with the same starting times for workers and the same deadlines for tasks. It is required that the starting times for workers and deadlines for tasks should be optimal for the first-stage project and, under this condition, also for the second-stage project. Optimality is measured with respect to the maximal lateness (or maximal delay) of tasks, which has to be minimized. We represent this problem as a...

A tropical version of Stickel's key exchange protocol was suggested by Grigoriev and Shpilrain (2014) and successfully attacked by Kotov and Ushakov (2018). We suggest some modifications of this scheme that use commuting matrices in tropical algebra and discuss some possibilities of attacks on these new modifications. We suggest some simple heuristic attacks on one of our new protocols, and then we generalize the Kotov and Ushakov attack on tropical Stickel's protocol and discuss the application...

The interval eigenproblem in max-min algebra is studied. A classification of interval eigenvectors is introduced and six types of interval eigenvectors are described. Characterization of all six types is given for the case of strictly increasing eigenvectors and Hasse diagram of relations between the types is presented.