Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings

Abstract

Mainstream approaches to uncertainty modeling in relational databases are probabilistic. Still some researchers persist in proposing representations based on possibility theory. They are motivated by the ability of this latter setting for modeling epistemic uncertainty and by its qualitative nature. Interestingly enough, several possibilistic models have been proposed over time, and have been motivated by different application needs ranging from database querying, to database design and to data cleaning. Thus, one may distinguish between four different frameworks ordered here according to an increasing representation power: databases with (i) layered tuples; (ii) certainty-qualified attribute values; (iii) attribute values restricted by general possibility distributions; (iv) possibilistic c-tables. In each case, we discuss the role of the possibility-necessity duality, the limitations and the benefit of the representation settings, and their suitability with respect to different tasks.

Uncertainty representation in software models: a survey

“…Other uncertainty classifications have also been proposed for specific domains within software development and engineering, mainly in the areas of adaptive systems [73,135,144,180,199,201,223], complex event processing [125], databases [131,156,175,178,195,200,224], requirements engineering [207], and cyber-physical systems [120,121]. All of them try to harmonize the terminology of uncertainty and propose conceptual frameworks that classify different types of uncertainty according to several criteria.…”

“…Similarly, we did not consider the numerous works dealing with model-based performance or reliability engineering of software systems, which enrich software models with the information required for evaluation using different notations (e.g., UML Profiles such as SPT [190], MARTE [72] or DAM [129]), transform the enriched model to a formal and mathematical model supporting the evaluation (e.g., Queueing Networks [161,217], Probabilistic Process Algebras [157], Stochastic Petri Nets [182,183], Fault Trees [143] or Markov chains [214]) and evaluate the performance or reliability of the system using the tools available for the formal model [139,127]. The interested reader can consult already existing corresponding surveys about these topics, such as [131,156,175,195,200,224] in the context of databases, [125] in the context of complex event processing, or [127,128,168,160] on model-based performance or reliability engineering of software systems. Second, we excluded papers that only describe transformations between notations representing uncertainty that are semantically equivalent.…”

Possibilistic keys

“…Nevertheless, we will now comment on various possibilistic data models, their expressiveness, and their main target areas. From the least to the most expressive, we can at least distinguish four possibilistic models for uncertain data [55]: Layered tuples. This is the data model we use here.…”