  In this paper, we present a generalization of the relational data model based
on interval neutrosophic set. 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 falsity-membership function F
which keeps track of the extent to which we believe that it is not in the
relation. A neutrosophic 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 neutrosophic
relations into pseudo-consistent neutrosophic 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 neutrosophic
relation. For this data model, we define algebraic operators that are
generalizations of the usual operators such as intersection, 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.
