Fuzzy Extension Conceptual Model of Temporal Databases: Algebra Calculus

This paper present a fuzzy temporal data model for uncertainty/implicit events more precisely, and introduce fuzzy temporal complex event value relations, which combine the concept of fuzzy temporal relations with the idea of fuzzy temporal values in a uniform framework. We elaborate a model theoretic definition of fuzzy temporal information combination strategies, which has a rigorous foundation on fuzzy temporal theory. And then define an algebra for querying database instances, which comprises the operations of selection, projection, join, Cartesian product, union, intersection, and difference. We prove that our data model and algebra for fuzzy temporal values generalizes the classical relational data model and algebra. Moreover, we show that under certain assumptions, all our algebraic operations are tractable. We finally introduce the syntax/semantic of fuzzy temporal relations and describe the calculus of the fuzzy temporal algebra.