AUTHOR'S PROOF JrnlID 10472 ArtID 9397 Proof#1 - 08/01/2014 UNCORRECTED PROOF Ann Math Artif Intell DOI 10.1007/s10472-014-9397-7 Application of the L-fuzzy concept analysis in the morphological image and signal processing 1 2 Cristina Alcalde · Ana Burusco · Ram´ on Fuentes-Gonz´ alez 3 4 © Springer Science+Business Media Dordrecht 2014 5 Abstract In this work we are going to set up a new relationship between the L-fuzzy 6 Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the 7 problem of finding fuzzy images or signals that remain invariant under a fuzzy morpholog- 8 ical opening or under a fuzzy morphological closing, is equal to the problem of finding the 9 L-fuzzy concepts of some L-fuzzy context. Moreover, since the Formal Concept Analysis 10 and the Mathematical Morphology are the particular cases of the fuzzy ones, the showed 11 result has also an interpretation for binary images or signals. 12 Keywords L-fuzzy concept analysis · Fuzzy mathematical morphology · Morphological 13 image processing 14 Mathematics Subject Classifications (2010) Q1 15 1 Introduction 16 The L-fuzzy Concept Analysis [15, 16], as an extension of the Formal Concept Analy- Q2 17 sis [36], and the Fuzzy Mathematical Morphology [5, 10, 11] were developed in different 18 contexts but both use the lattice theory as algebraic framework. 19 C. Alcalde () Departamento Matem´ atica Aplicada, Universidad del Pa´ ıs Vasco UPV/EHU, Plaza de Europa 1, 20018 San Sebasti´ an, Spain e-mail: c.alcalde@ehu.es A. Burusco · R. Fuentes-Gonz´ alez Departamento de Autom´ atica y Computaci´ on, Universidad P´ ublica de Navarra, Campus de Arrosad´ ıa, 31006 Pamplona, Spain A. Burusco e-mail: burusco@unavarra.es R. Fuentes-Gonz´ alez e-mail: rfuentes@unavarra.es