On B-Groups

Abstract

The notion of bags play an essential role in dealing with knowledge representation problems where object classes allow repeated occurrence of elements. Sometimes bags with some special conditions can be drawn from a given set. Under these situations, is possible to define some algebraic structures on the given set. The present paper considers the situation when some bags with special conditions are drawn from a set, which, under a given operation, forms a group. Consequently, it demonstrates how an existing group structure defined on a given set can induce special structures on some bags drawn from this set. Hence, the notions of induced B-groups, induced abelian B-groups, and induced semi B-groups are introduced and discussed. Further, some characteristics of B-groups, abelian B-groups, and semi B-Groups are studied.