Ghanim, M. N.Mustafa, H. I.Abd El Aziz, S.2019-12-022019-12-022011Cited References in Web of Science Core Collection: 420020-0255https://doi.org/10.1016/j.ins.2011.04.041https://www.sciencedirect.com/science/article/pii/S0020025511002155Accession Number: WOS:000292123500012In this paper, the concept of intension is used to introduce two types of ordering relations based on information that generates a cover for the universal set. These types of ordering relations are distinct from the well-known ordering relation based on set inclusion. For these ordering relations, we consider the algebraic structures that arise in various types of covers. We show that in the case of a representative cover, the algebraic structure resulting from the lower intension inclusion is a double Stone algebra, while in the case of a reduced cover, it is a Boolean algebra. In addition, the algebraic structure resulting from the upper intension inclusion in the case of a representative cover is a Boolean algebra, and in the case of a reduced cover, the two Boolean algebraic structures from lower and upper intension inclusions are isomorphic. (C) 2011 Elsevier Inc. All rights reserved.enOctober University for University of ROUGH SET-THEORYFUZZY INFORMATION-SYSTEMSFORMAL CONCEPT ANALYSISDECISION SYSTEMSSIMILARITYRepresentative coverLower intension inclusionsUpper intension inclusionsArticlehttps://doi.org/10.1016/j.ins.2011.04.041