Solvability and unique solvability of max-min fuzzy equations

摘要

The problem of solvability and the problem of unique solvability of a fuzzy relation equation in an arbitrary max-min algebra are considered and corresponding necessary and sufficient conditions are presented. The results allow to solve both problems by an O(mnp) algorithms, where m, n, p are the dimensions of the corresponding relations in the equation. The existence of the greatest and of the least solution is also considered.