A Data Model Based on Paraconsistent Intuitionistic Fuzzy Relations

Paraconsistent intuitionistic fuzzy set is an extension of intuitionistic fuzzy set or interval-valued fuzzy set. It relaxes the requirement that t + f ≤ 1, where t is grade of truth-membership and f is grade of false-membership. In paraconsistent intuitionistic fuzzy set, t, f ∈ [0, 1], 0 ≤ t + f ≤ 2. In this paper, we present a generalization of the relational model of data based on paraconsistent intuitionistic fuzzy set. Our data model is capable of manipulating incomplete as well as inconsistent information. Associated with each relation there are two membership functions which keep track of the extent to which we believe the tuple is in the relation and the extent to which we believe that it is not in the relation. In order to handle inconsistent situations, we propose an operator, called “split”, to transform inconsistent paraconsistent intuitionistic fuzzy relations into pseudo-consistent paraconsistent intuitionistic fuzzy relations. We may then manipulate these pseudo-consistent paraconsistent intuitionistic fuzzy relations by performing set-theoretic and relation-theoretic operations on them. Finally, we can use another operator, called “combine”, to transform the results back to paraconsistent intuitionistic fuzzy relations. For this model, we define algebraic operators that are generalization of the usual operators such as union, selection, join on fuzzy relations. Our data model can underlie any database management system that deals with incomplete or inconsistent information.