Szpilrajn-type extensions of fuzzy quasi-orderings
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The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations. After Szpilrajn’s result, several variations have been published. Alcantud studied in 2009 the case where the extension is asked to satisfy some order conditions between elements. He first studied and solved a particular formulation where conditions are imposed in terms of strict preference only, which helps to precisely identify which quasiorderings can be extended when we allow for additional conditions in terms of indifference too. In this contribution we generalize both results to the fuzzy case
The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations. After Szpilrajn’s result, several variations have been published. Alcantud studied in 2009 the case where the extension is asked to satisfy some order conditions between elements. He first studied and solved a particular formulation where conditions are imposed in terms of strict preference only, which helps to precisely identify which quasiorderings can be extended when we allow for additional conditions in terms of indifference too. In this contribution we generalize both results to the fuzzy case
Descripción:
EUROFUSE 2013: Workshop on Imprecision and Uncertainty in Preference Modeling and Decision Making, December 2013, Oviedo, Spain
Patrocinado por:
Project ECO2012-31933 (Spanish Ministerio de Econom´ıa y Competitividad) and partially supported by Project MTM2010-17844
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