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Título
Conditional extensions of fuzzy preorders
Autor(es)
Materia
Fuzzy relation
Transitivity
Acyclicity
Consistency
(Indifference) generator
Extension
Relación borrosa
Transitividad
Aciclicidad
Consistencia
Generador (indiferencia)
Extensión
Clasificación UNESCO
5307.15 Teoría microeconómica
Fecha de publicación
2015-11
Citación
Alcantud, J. C. R., Díaz, S. (2015). Conditional extensions of fuzzy preorders. Fuzzy Sets and Systems, 278, 3–19
Resumen
[EN]The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations and their applications. Several variations of the acclaimed Szpilrajn's theorem have been provided, inclusive of the case when some order conditions between elements are imposed on the extension. We extend the analysis of that topic by Alcantud to the fuzzy case. By appealing to generators to decompose (fuzzy) preference relations into strict preference and indifference relations, we give general extension results for the corresponding concept of compatible extension of a fuzzy reflexive relation. Then we investigate the conditions under which compatible order extensions exist such that certain elements are connected by the asymmetric part, resp., and certain other elements by the symmetric part, to respective elements with degree 1.
URI
ISSN
0165-0114
DOI
10.1016/j.fss.2014.09.009
Colecciones
- BORDA. Artículos [32]