Browsing by Author "Ghanim, M. N."

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    On lower and upper intension order relations by different cover concepts
    (ELSEVIER SCIENCE INC., 2011) Ghanim, M. N.; Mustafa, H. I.; Abd El Aziz, S.
    In 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.