Linear independence in bottleneck algebras
The paper presents ten diverse generalizations of the definition of vector independence over a field to that over a lattice used in recent literature [cf. e.g. \textit{M. Gondran} and \textit{M. Minoux}, L'indépendance linéaire dans les dioides, Bull. Dir. Etudes Rech., Sér. C Math. Inform. 38-48 (1978); \textit{K. H. Kim} and \textit{F. W. Roush}, Fuzzy Sets Syst. 4, 293-315 (1980; Zbl 0451.20055); \textit{P. Butkovič}, \textit{K. Cechlárová} and \textit{P. Szabó}, Linear Algebra Appl. 94, 133-155 (1987; Zbl 0629.90093)]. Precisely, a max-min dependence of vectors over the semiring \(([0,1]\), max, min) is discussed. Many characterizations and interrelations of these definitions are proved.
scientific article; zbMATH DE number 1004752
scientific article