The relation of dominance between aggregation operators has recently been studied quite intensively
[9, 12, 10, 11, 13, 14].We propose to study its 'graded' generalization in the foundational framework
of higher-order fuzzy logic, also known as Fuzzy Class Theory (FCT) introduced in . FCT is
specially designed to allow a quick and sound development of graded, lattice-valued generalizations of
the notions of traditional 'fuzzy mathematics' and is a backbone of a broader program of logic-based
foundations for fuzzy mathematics, described in .
This short abstract is to be understood as just a 'teaser' of the broad and potentially very interesting
area of graded dominance. We sketch basic definitions and properties related to this notion and
present a few examples of results in the area of equivalence and order relations (in particular, we show
interesting graded generalization of basic results from [6, 12]). Also some of our theorems are, for
expository purposes, stated in a less general form here and can be further generalized substantively.
In this paper, we work in Fuzzy Class Theory over the logic MTLD of all left-continuous t-norms
. The apparatus of FCT and its standard notation is explained in detail in the primer , which is
freely available online. Furthermore we use X vY for D(X vY).