Decomposition of Fuzzy Relations: An Application to the Definition, Construction and Analysis of Fuzzy Preferences
María Jesús Campión,
Esteban Induráin,
Armajac Raventós-Pujol
Affiliations
María Jesús Campión
Inarbe (Institute for Advanced Research in Business and Economics) and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
Esteban Induráin
InaMat2 (Institute for Advanced Materials and Mathematics) and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
Armajac Raventós-Pujol
Inarbe (Institute for Advanced Research in Business and Economics) and Departamento de Estadística, Informática y Matemáticas, Universidad Pública de Navarra, 31006 Pamplona, Spain
In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences.
