Finitary solvability conditions for systems of fuzzy relation equations

In this paper, we consider the problem of solving systems of fuzzy relation equations. Two types of these systems with different compositions are considered and processed simultaneously. A new sufficient condition and new solvability criteria are proposed for systems of both types. All these conditions are finitary and thus can be easily verified. The sufficient condition and criteria of solvability characterize a relationship between a skeleton n × n matrix (n is a number of equations) and a vector of the right-hand side.