nk-bags

Abstract

We generalize the concept of bags by introducing the notion of n k -bags with membership functions ranging in P~N !, the power set of positive integers. Consequently, a number of operations on n k -bags are defined and some characterizations are done.

Relations and functions in multiset context

“…Peterson [13] and Yager [17] made further contributions to it. Many conclusive results were established by these authors and further study was carried on by Jena et al [6] and many others [2,[4][5][6][7]9,14]. Blizard [16] gave a new dimension to MST, extending the theory to be known as MSTZ in which elements may belong to either a positive or a negative number of times (i.e.…”

On B-groups

“…In this section, the author presents a brief overview of the notions of bags [16], [14], [11], [9], [10] that is necessary for the proper understanding of the paper. A brief overview of the notion of groups is also presented [1], [18].…”

“…Shadows, as defined by Blizard in [21], also allow the repeated occurrence of objects. A bag, as introduced by Yager [16] is one kind of object collection where redundancy of objects is allowed [14], [11], [5], [10], [6], [13], [3], [16], [17]. The bags are frequently used for developing relational data models with multiset semantics and they can act as type constructors while defining objects.…”

Attributive indiscernibility and the notion of BM-spaces

“…Grefen and Deby proposed the notion of an extended relational algebra with multi-set semantics which includes constructs for extending the algebra to a complete sequential data manipulation language which can be used as a formal basis for multi set languages like SQL, or a data manipulation language on its own [10). Hence, with the multi set [1] semantics and bag-based theories [3]- [8], [12] in mind, bag projection and selection [12] are very useful in relational databases. Particularly, for relational database modelling and implementation, tions have been discussed.…”