24.2.2 Family of Criteria
The performance of alternatives in set Items is analyzed upon a set of criteria for
each user, in order to model all their characteristics, attributes, effects, or consequences [77, 97]. In recommender systems, the criteria may refer to the multiple
features of an item (often the case in content-based recommendations) or to the
multiple dimensions upon which the item is being evaluated/rated.
Any criterion c can be represented by function gc(i) that expresses the preferences
of one user (therefore is user-specific), in order for the user to be able to decide
between two alternatives i1 and i2, i.e., whether gc(i1) > gc(i2), in the case that
alternative i1 is preferred to alternative i2, or whether gc(i1) = gc(i2), in the case
that the two alternatives are considered equivalent (i.e., perfectly substitutable for
the particular user on this criterion). To be able to make rational decisions using
multiple criteria, it has to be ensured that the whole set of these functions creates a
consistent family of criteria [77]. A family of criteria is said to be consistent when
it has the following three properties: