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.