On comparability relations in the class of interval-valued fuzzy relations

Abstract

In this paper a new relation for the set of interval-valued fuzzy relations is introduced.
This relation is an interval order
for the family of intervals and for the family of interval-valued fuzzy relations in a given set it has the reflexivity property.
Consequences of considering such relation are studied in the context of operations on interval-valued fuzzy relations.
A new transitivity property, namely possible $T$-transitivity is studied (pos-$T$-transitivity for short). This transitivity property is connected with
the new relation proposed here. Preservation of this type of transitivity by some operations is also discussed.