|
| << previous | next >> |
Journal description
All volumes of the corresponding journal
All issues of the corresponding volume
All articles of the corresponding issues
Details for article 11 of 31 found articles
| Title: |
Complete Orders, Categories and Lattices of Approximations |
| Author: |
Wolski, Marcin |
| Appeared in: |
Fundamenta informaticae |
| Paging: | Volume 72 (2006) nr. 1-3 pages 421-435 |
| Year: |
2006-08-08 |
| Contents: |
The present article deals with the problem whether and how the bilattice orderings of knowledge ⩽_k and truth ⩽_t might enrich the theory of rough sets. Passing to the chief idea of the paper, we develop a bilattice-theoretic generalisation of the concept of rough set to be called A-approximation. It is proved that A-approximations (induced by a topological approximation space) together with the knowledge ordering ⩽_k constitute a complete partial order (CPO) and that the meet and join operations induced by the truth ordering ⩽_t are continuous functions with respect to ⩽_k. Crisp sets are then obtained as maximal elements of this CPO. The second part of this article deals with the categorical and algebraic properties of A-approximations induced by an Alexandroff topological space. We build a *-autonomous category of A-approximations by means of the Chu construction applied to the Heyting algebra of open sets of Alexandroff topological space. From the algebraic point of view A-approximations under ⩽_t ordering constitute a special Nelson lattice and, as a result, provide a semantics for constructive logic with strong negation. Such lattice may be obtained by means of the twist construction over a Heyting algebra which resembles very much the Chu construction. Thus A-approximations may be retrived from very elementary structures in elegant and intuitive ways. |
| Publisher: |
IOS Press |
| Source file: |
Elektronische Wetenschappelijke Tijdschriften |
Details for article 11 of 31 found articles
| << previous | next >> |