Properties of fuzzy relations and aggregation process in decision making

In this contribution connections between input fuzzy relations R1, . . . ,Rn on a set X and the output fuzzy relation RF = F(R1, . . . ,Rn) are studied. F is a function of the form F : [0, 1]n → [0, 1] and RF is called an aggregated fuzzy relation. In the literature the problem of preservation, by a function F, diverse types of properties of fuzzy relations R1, . . . ,Rn is examined. Here, it is considered the converse approach. Namely, fuzzy relation RF = F(R1, . . . ,Rn) is assumed to have a given property and then it is checked if fuzzy relations R1, . . . ,Rn have this property. Moreover, a discussion on the mentioned two approaches is provided. The properties, which are examined in this paper, depend on their notions on binary operations B : [0, 1]2 → [0, 1]. By incorporating operation B these properties are generalized versions of known properties of fuzzy relations.