Four-Fold Formal Concept Analysis Based on Complete Idempotent Semifields

Formal Concept Analysis (FCA) is a well-known supervised boolean data-mining technique rooted in Lattice and Order Theory, that has several extensions to, e.g., fuzzy idempotent semirings. At the heart of FCA lies Galois connection between two powersets. In this paper we extend formalism to include all four connections different semivectors spaces over semifields, at same time. The result K¯-four-fold (K¯-4FCA) where K¯ semifield biasing analysis. Since complete semifields come dually-ordered pairs—e.g., max-plus min-plus semirings—the basic construction shows dual-order-, row–column- Galois-connection-induced dualities appear simultaneously number times provide full spectrum variability. Our results lead fundamental theorem properly defines quadrilattices as 4-tuples (order-dually) isomorphic lattices vectors discuss its relevance vis-à-vis previous formal conceptual analyses some affordances their results.