Incomplete Information in Relational Databases
Journal of the ACM (JACM)
Interval valued fuzzy sets based on normal forms
Fuzzy Sets and Systems
Database queries with fuzzy linguistic quantifiers
IEEE Transactions on Systems, Man and Cybernetics
Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems
ACM Transactions on Database Systems (TODS)
A foundation of CODD's relational maybe-operations
ACM Transactions on Database Systems (TODS)
Extending the database relational model to capture more meaning
ACM Transactions on Database Systems (TODS)
A relational model of data for large shared data banks
Communications of the ACM
A Logical Framework for Integrating Inconsistent Information in Multiple Databases
FoIKS '02 Proceedings of the Second International Symposium on Foundations of Information and Knowledge Systems
Fuzzy Sets and Systems
SQLf: a relational database language for fuzzy querying
IEEE Transactions on Fuzzy Systems
Reasoning about actions with imprecise and incomplete state descriptions
Fuzzy Sets and Systems
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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.