A characterization of PQI interval orders

Authors:
A. Tsoukiàs;Ph. Vincke
Affiliations:
LAMSADE - CNRS, Université Paris Dauphine, 75775 Paris Cedex 16, France;SMG/ISRO, Université Libre de Bruxelles, CP 210/01, Bld. du Triomphe, 1050 Bruxelles, Belgium
Venue:
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Year:
2003

Citing 0
Cited 7

Valued Tolerance and Decision Rules

RSCTC '00 Revised Papers from the Second International Conference on Rough Sets and Current Trends in Computing
Numerical representation of PQI interval orders

Discrete Applied Mathematics - Ordinal and symbolic data analysis (OSDA 2000)
Valued Hesitation in Intervals Comparison

SUM '07 Proceedings of the 1st international conference on Scalable Uncertainty Management
Numerical representation of PQI interval orders

Discrete Applied Mathematics - Ordinal and symbolic data analysis (OSDA 2000)
Representability of binary relations through fuzzy numbers

Fuzzy Sets and Systems
Representing preferences using intervals

Artificial Intelligence
Performance evaluation of competing forecasting models: A multidimensional framework based on MCDA

Expert Systems with Applications: An International Journal

Quantified Score

Hi-index	0.00

Visualization

Abstract

We provide an answer to an open problem concerning the representation of preferences by intervals. Given a finite set of elements and three relations on this set (indifference, weak preference and strict preference), necessary and sufficient conditions are provided for representing the elements of the set by intervals in such a way that (1) two elements are indifferent when the interval associated to one of them is included in the interval associated to the other; (2) an element is weakly preferred to another when the interval of the first is "more to the right" than the interval of the other, but the two intervals have a non-empty intersection; (3) an element is strictly preferred to another when the interval of the first is "more to the right" than the interval of the other and their intersection is empty.