@INPROCEEDINGS { Rsds4840,
author = {Haruna, Taichi and Gunji, Yukio-Pegio}, 
title = {Double Approximation and Complete Lattices}, 
booktitle = {Rough Sets and Knowledge Technology}, 
conference = {Rough Sets and Knowledge Technology}, 
series =  = {Lecture Notes in Artificial Intelligence}, 
volume = 5589, 
pages = {52--59}, 
publisher = {Springer-Verlag}, 
address = {Heidelberg - Berlin, Germany}, 
month = {July}, 
year = 2009, 
editor = {Wen, Peng and Li, Yuefeng and Polkowski, Lech and Yao, Yiyu and Tsumoto, Shusaku and Wang, Guoying}, 
url = {http://www.springerlink.com/content/q0857121u072/?p=fc4581dabf904891bbe1f9cc3f4fdd0d&pi=313}, 
issn = {0302-9743}, 
isbn = {978-3-642-02961-5}, 
abstract = {A representation theorem for complete lattices by double approximation systems proved in [Gunji, Y.-P., Haruna, T., submitted] is analyzed in terms of category theory. A double approximation system consists of two equivalence relations on a set. One equivalence relation defines the lower approximation and the other defines the upper approximation. It is proved that the representation theorem can be extended to an equivalence of categories.}, 
keywords = {rough sets, complete lattices, representation theorem, equivalence of categories, }, 
}