Abstract :
The paper introduces a new approach to preference structure,
where from a weak preference relation derive the following relations: strict preference,
indierence and incomparability, which by aggregations and negations
are created and examined. We decomposing a preference relation into a strict
preference, an indierence, and an incomparability relation. This approach
allows one to quantify dierent types of uncertainty in selecting alternatives.
In presented preference structure we use interval-valued fuzzy relations, which
can be interpreted as a tool that may help to model in a better way imperfect
information, especially under imperfectly dened facts and imprecise knowledge.
Preference structures are of great interest nowadays because of their
applications, so we propose at the end the algorithm of decision making by use
new preference structure.
