کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
397712 | 1438470 | 2013 | 18 صفحه PDF | دانلود رایگان |
This paper is concerned with the relationship between contexts, closure spaces, and complete lattices. It is shown that, for a unital quantale L, both formal concept lattices and property oriented concept lattices are functorial from the category L-Ctx of L-contexts and infomorphisms to the category L-Sup of complete L-lattices and suprema-preserving maps. Moreover, the formal concept lattice functor can be written as the composition of a right adjoint functor from L-Ctx to the category L-Cls of L-closure spaces and continuous functions and a left adjoint functor from L-Cls to L-Sup.
► An adjunction is presented between categories of closure spaces and complete lattices.
► An adjunction is presented between categories of formal contexts and closure spaces.
► A decomposition is obtained for the formal concept lattice functor.
Journal: International Journal of Approximate Reasoning - Volume 54, Issue 1, January 2013, Pages 166–183