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The binomial decomposition of OWA functions, the 2‐additive and 3‐additive cases in n dimensions
Author(s) -
Bortot Silvia,
Marques Pereira Ricardo Alberto,
Nguyen Thuy Hong
Publication year - 2018
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21947
Subject(s) - binomial (polynomial) , decomposition , mathematics , binomial coefficient , additive model , statistics , discrete mathematics , chemistry , organic chemistry
In the context of the binomial decomposition of ordered weighted averaging (OWA) functions, we investigate the constraints associated with the 2‐additive and 3‐additive cases in n dimensions. The 2‐additive case depends on one coefficient whose feasible region does not depend on the dimension n . On the other hand, the feasible region of the 3‐additive case depends on two coefficients and is explicitly dependent on the dimension n . This feasible region is a convex polygon with n vertices and n edges, which is strictly expanding in the dimension n . The orness of the OWA functions within the feasible region is linear in the two coefficients, and the vertices associated with maximum and minimum orness are identified. Finally, we discuss the 3‐additive binomial decomposition in the asymptotic infinite dimensional limit.