Conditions for the existence of the least solution and minimal solutions to fuzzy relation equations over complete Brouwerian lattices

This paper discusses properties and existence conditions of minimal solutions to sup-inf fuzzy relation equations over complete Brouwerian lattices. The relationship between minimal solutions to a system of fuzzy relation equations and minimal solutions to a fuzzy relation equation in the system is illustrated by two examples. Necessary and sufficient conditions for the existence of the least solution and minimal solutions to a system of fuzzy relation equations are given.