Similarity, probability and database organisation

Abstract

The question of storing imperfect data within a database framework has been discussed in the literature almost since the time when the first formal database structure was proposed. The matter received an additional impetus with the advent of fuzzy sets and its promise of formally capturing the notion of imprecision. If the imperfection is one of uncertainty as to whether a certain data item (or data structure) is actually present in the database, then the use of probability would be natural. However, when the imperfection relates to the relative proximity of the actual data to some idealised value, the use of a fuzzy-like model (possibility or similarity) seems warranted. In practice, the choice of model appears to be a matter of personal preference for a researcher. Characteristically, there has been no attempt to utilise both possibility and probability within the same data model. This might be due, in part, to the difficulty of capturing, in a reasonable way, various interactions between the simultaneously present possibility and probability weights. This paper describes work in progress, dealing with our research in modelling the interaction between similarity among the tuples (a binary function) and the probabilities of the tuples in the relational data model. The importance of such a study is underlined by the ubiquity of situations which involve, in a natural fashion, both probabilistic and possibilistic considerations. We illustrate it on two examples.