Application of the L-fuzzy concept analysis in the morphological image and signal processing

Abstract

The final publication is available at Springer via http://dx.doi.org/10.1007/s10472-014-9397-7In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, since the Formal Concept Analysis and the Mathematical Morphology are the particular cases of the fuzzy ones, the showed result has also an interpretation for binary images or signals.This work has been partially supported by the Research Group “Intelligent Systems and Energy (SI+E)” of the Basque Government, under Grant IT519-10, and by the Research Group “Adquisición de conocimiento y minería de datos, funciones especiales y métodos numéricos avanzados” of the Public University of Navarra