Document Type : Research Paper


Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland


The paper introduces a new approach to preference structure, where from a weak preference relation derive the following relations:
strict preference, indifference and incomparability, which by aggregations and negations are created and examined. We decomposing a preference relation into a strict preference, an
indifference, and an incomparability relation.
This approach allows one to quantify different 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
defined 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.


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