Title :
The Category RSC of I-Rough Sets
Author :
Li, Xiao-shen ; Yuan, Xue-hai
Author_Institution :
Dept. of Appl. Math., Dalian Univ. of Technol., Dalian
Abstract :
This paper shall study theory of rough sets from the view of the category theory and topos theory. A category RSC of I-rough sets is presented. Topos properties of the category RSC are studied. It is proved that the category RSC satisfies all properties of a topos except one, for it has no subobject classifier. It is pointed that although the category RSC is not a topos, RSC has a middle object and consequently RSC is a weak topos. By the use of weak topos RSC, the operations of I-rough sets are naturally described.
Keywords :
category theory; rough set theory; I-rough set theory; category theory; middle object classifier; topos theory; Boolean algebra; Fuzzy set theory; Fuzzy sets; Fuzzy systems; Information systems; Knowledge engineering; Logic; Mathematics; Rough sets; Set theory; category; middle object; rough set; topos; weak topos;
Conference_Titel :
Fuzzy Systems and Knowledge Discovery, 2008. FSKD '08. Fifth International Conference on
Conference_Location :
Shandong
Print_ISBN :
978-0-7695-3305-6
DOI :
10.1109/FSKD.2008.106
