In this talk the problem of connections between input fuzzy
relations R_1,...,R_n on a set X and the output fuzzy
relation R_F = F(R_1,...,R_n) is studied, where F is an
aggregation function. The problem of preservation of diverse
types of fuzzy relation properties by an aggregation function
F is examined. Moreover, the converse problem is also
discussed. Namely, fuzzy relation R_F is assumed to have a
given property and the properties of fuzzy relations
R_1,...,R_n are examined. Presented results are connected
with decision making problems.