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| Titel: |
Complete Orders, Categories and Lattices of Approximations |
| Auteur: |
Wolski, Marcin |
| Verschenen in: |
Fundamenta informaticae |
| Paginering: | Jaargang 72 (2006) nr. 1-3 pagina's 421-435 |
| Jaar: |
2006-08-08 |
| Inhoud: |
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. |
| Uitgever: |
IOS Press |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 11 van 31 gevonden artikelen
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