Representing expansions of bounded distributive lattices with Galois connections in terms of rough sets



: Dzik W, Jarvinen J, Kondo M

Publisher: ELSEVIER SCIENCE INC

: 2014

: International Journal of Approximate Reasoning

: INTERNATIONAL JOURNAL OF APPROXIMATE REASONING

: INT J APPROX REASON

: 55

: 1

: 427

: 435

: 9

: 0888-613X

DOI: https://doi.org/10.1016/j.ijar.13.07.005


This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set approximation operators. We prove that each bounded distributive lattice with a Galois connection can be embedded into the complex algebra of its canonical frame. We show that for every spatial Heyting algebra L equipped with a Galois connection, there exists a GC-frame such that L is isomorphic to the complex algebra of this frame, and an analogous result holds for weakly atomic Heyting-Brouwer algebras with a Galois connection. In each case of representation, given Galois connections are represented by rough set upper and lower approximations. (C) 2013 Elsevier Inc. All rights reserved.



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