Proceedings of: 10th International Conference on Concept Lattices and Their Applications. (CLA 2013). La Rochelle, France, October 15-18, 2013.Previous work has shown a relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. We investigate the spectra of reducible matrices over completed idempotent semifields in the framework of dioids, naturally-ordered semirings, that encompass several of those extensions. Considering special sets of eigenvectors also brings out complete lattices in the picture and we argue that such structure may be more important than standard eigenspace structure for matrices over completed idempotent semifields.FJVA is supported by EU FP7 project LiMoSINe (contract 288024). CPM has been partially supported by the Spanish Government-Comisión Interministerial de Ciencia y Tecnología project TEC2011-26807 for this paper.Publicad
