On the relation between fuzzy closing morphological operators, fuzzy consequence operators induced by fuzzy preorders and fuzzy closure and co-closure systems

Authors:
Jorge Elorza;RamóN Fuentes-GonzáLez;Jean Bragard;Pedro Burillo
Affiliations:
Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, P.O. Box 31008 Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, P.O. Box 31006 Pamplona, Spain;Departamento de Física y Matemática Aplicada, Facultad de Ciencias, Universidad de Navarra, P.O. Box 31008 Pamplona, Spain;Departamento de Automática y Computación, Universidad Pública de Navarra, Campus de Arrosadía, P.O. Box 31006 Pamplona, Spain
Venue:
Fuzzy Sets and Systems
Year:
2013

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Abstract

In a previous paper, Elorza and Burillo explored the coherence property in fuzzy consequence operators. In this paper we show that fuzzy closing operators of mathematical morphology are always coherent operators. We also show that the coherence property is the key to link the four following families: fuzzy closing morphological operators, fuzzy consequence operators, fuzzy preorders and fuzzy closure and co-closure systems. This will allow to translate important well-known properties from the field of approximate reasoning to the field of image processing.