Continuing our categorical study of L-fuzzy extensions of formal concept analysis, we provide a representation theorem for the category of L-Chu correspondences between L-formal contexts and prove that it is equivalent to the category of completely lattice L-ordered sets.

In this paper, we propose a filter active-set algorithm for the minimization problem over a product of multiple ball/sphere constraints. By making effective use of the special structure of the ball/sphere constraints, a new limited memory BFGS (L-BFGS) scheme is presented. The new L-BFGS implementation takes advantage of the sparse structure of the Jacobian of the constraints, and generates cur...

We prove a Fundamental Theorem of Finite Semidistributive Lattices (FTFSDL), modelled on Birkhoff’s Distributive Lattices. Our FTFSDL is the form “A poset L finite semidistributive lattice if and only there exists set with some additional structure, such that isomorphic to admissible subsets ordered by inclusion; in this case, its structure are uniquely determined L.” The combinatorial abstract...