Further Galois Connections between Semimodules over Idempotent Semirings.
Francisco J. Valverde-Albacete, Carmen Peláez-Moreno · 2007
Abstract. In [14] a generalisation of Formal Concept Analysis was introduced with data mining applications in mind, K-Formal Concept Analysis, where incidences take values in certain kinds of semirings, instead of the standard Boolean carrier set. The construction leading to the pair of dually (order) isomorphic lattices can be further manipulated to obtain the three other types of Galois Connections providing a fuller set of tools to interpret any relations between data. We relate this result to previous descriptions of certain instances of such Galois Connections in qualitative data analysis and provide concrete examples of them related to Rmax,+-semimodules in quantitative data analysis. 1 Motivation: Lattices