  In this paper, we present a generalization of the relational data model based
on paraconsistent intuitionistic fuzzy sets. Our data model is capable of
manipulating incomplete as well as inconsistent information. Fuzzy relation or
intuitionistic fuzzy relation can only handle incomplete information.
Associated with each relation are two membership functions one is called
truth-membership function $T$ which keeps track of the extent to which we
believe the tuple is in the relation, another is called false-membership
function which keeps track of the extent to which we believe that it is not in
the relation. A paraconsistent intuitionistic fuzzy relation is inconsistent if
there exists one tuple $a$ such that $T(a) + F(a) > 1$. In order to handle
inconsistent situation, we propose an operator called split to transform
inconsistent paraconsistent intuitionistic fuzzy relations into
pseudo-consistent paraconsistent intuitionistic fuzzy relations and do the
set-theoretic and relation-theoretic operations on them and finally use another
operator called combine to transform the result back to paraconsistent
intuitionistic fuzzy relation. For this model, we define algebraic operators
that are generalisations of the usual operators such as union, selection, join
on fuzzy relations. Our data model can underlie any database and knowledge-base
management system that deals with incomplete and inconsistent information.
