Extending Relational Database Model for Uncertain Information

Abstract

In this paper, we propose a new probabilistic relational database model, denote by PRDB, as an extension of the classical relational database model where the uncertainty of relational attribute values and tuples are respectively represented by finite sets and probability intervals. A probabilistic interpretation of binary relations on finite sets is proposed for the computation of their probability measures. The combination strategies on probability intervals are employed to combine attribute values and compute uncertain membership degrees of tuples in a relation. The fundamental concepts of the classical relational database model are extended and generalized for PRDB. Then, the probabilistic relational algebraic operations are formally defined accordingly in PRDB. In addition, a set of the properties of the algebraic operations in this new model also are formulated and proven.

Fuzzy Relational Database Model and Managemant System for Imprecise Information

“…So far, there have been many fuzzy relational database models studied and built (e.g. [4][5][6][7][8][9][10][11][12][13][14][15], [18][19][20][21][22][23][24][25][26]) based on the fuzzy set theory [2,3] to overcome the limitations of the classical relational database model in representing and handling uncertain and imprecise information of objects in practice.…”

“…[4][5] or [6][7][8][9][10][11], respectively), whereby the membership degree of tuples for the relation is hidden in that of their attribute values; (2) representing each fuzzy relation as a fuzzy set of tuples whose each attribute only takes a single and precise value (e.g. [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]), whereby the membership degree of tuples for the relation also is the membership degree of elements for the fuzzy set expressing that fuzzy relation.…”

“…For the second approach, as the models in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], the attribute of relations only takes a single and precise value, each relation was represented as a fuzzy set of tuples (i.e. a fuzzy extension of CRDB relations), the fuzzy relational algebraic operations were defined by extending directly classical relational algebraic operations based on fuzzy set operations.…”

“…The models based on the second approach are capable of querying and manipulating data more effective than the models based on the first approach due to the low complexity in computing and handling classical relations well as well fuzzy set operations but the capability of expressing imprecise information is not as good as those models, because the imprecision of the information is not explicitly represented by attribute values of relations but only inferred from the membership degree of tuples for the relation including those attributes. There was a large number of models as in [12][13][14][15][16][17][18][19][20][21] and [23][24] that the membership degree of tuples is a number in [0, 1]. These models were restricted in representing the associated imprecise degree of attribute values.…”

A Hybrid Relational Database Model for Uncertain and Imprecise Information

“…Some models (e.g. [7], [8], [10], [12], [16], [19], [20], [22], [27], [28]) using only the probability theory could represent and handle uncertain information but not imprecise information of objects. Some other models (e.g.…”