A Type-2 Fuzzy Relational Database Model
AbstractThis paper introduces a type-2 fuzzy relational database model (T-2FRDB) as an extension of type-1 fuzzy relational database models with a full set of basic fuzzy relational algebraic operations that can represent and query uncertain and imprecise information in real world applications. In this model, the membership degree of tuples in a fuzzy relation is represented by fuzzy numbers on [0,1], and fuzzy relational algebraic operations are defined by using the extension principle for computing minimum and maximum values of such fuzzy numbers. Some properties of the type-2 fuzzy relational algebraic operations in T-2FRDB are also formulated and proven as extensions of their counterpart in the type-1 fuzzy relational database models.
C. J. Date, An introduction to database systems, 8th ed. Addison Wesley, 2003.
E. F. Codd, “A relational model of data for large shared data banks,” Communications of the ACM, vol. 13, no. 6, pp. 377–387, 1970.
G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic: theory and applications. Prentice-Hall, Inc., 1994.
L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.
S. Chakraborty, “Codd’s relational data model and fuzzy logic: A practical approach to find the computer solution,” International Journal of Advanced Technology & Engineering Research (IJATER), vol. 2, no. 4, pp. 21–27, 2012.
J. C. Cubero, J. M. Medina, O. Pons, and M.-A. Vila, “Data summarization in relational databases through fuzzy dependencies,” Information Sciences, vol. 121, no. 3, pp. 233–270, 1999.
D. Dubois and H. Prade, “Using fuzzy sets in flexible querying: Why and how?” in Flexible query answering systems. Springer, 1997, pp. 45–60.
J. Mishra and S. Ghosh, “Uncertain query processing using vague set or fuzzy set: which one is better?” International Journal of Computers Communications & Control, vol. 9, no. 6, pp. 730–740, 2014.
F. E. Petry, “Fuzzy databases: Principles and applications,” International series in intelligent technologies, 1996.
K. Raju and A. K. Majumdar, “Fuzzy functional dependencies and lossless join decomposition of fuzzy relational database systems,” ACM Transactions on Database Systems (TODS), vol. 13, no. 2, pp. 129–166, 1988.
P. Saxena and D. K. Tayal, “Normalization in type-2 fuzzy relational data model based on fuzzy functional dependency using fuzzy functions,” International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, vol. 20, no. 01, pp. 99–138, 2012.
X. Meng, Z. Ma, and X. Zhu, “A knowledge-based fuzzy query and results ranking approach for relational databases,” Journal of Computational Information Systems, vol. 6, no. 6, pp. 2037–2044, 2010.
O. Pivert and H. Prade, “Dealing with aggregate queries in an uncertain database model based on possibilistic certainty,” in International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer, 2014, pp. 150–159.
A. A. Sabour, A. M. Gadallah, and H. A. Hefny, “Flexible Querying of Relational Databases: Fuzzy Set Based Approach,” in International Conference on Advanced Machine Learning Technologies and Applications. Springer, 2014, pp. 446–455.
S. M. Darwish, T. F. Mabrouk, and Y. F. Mokhtar, “Enriching
Vague Queries by Type-2 Fuzzy Orderings,” Lecture Notes
on Information Theory Vol, vol. 2, no. 2, 2014.
A. Niewiadomski, “A type-2 fuzzy approach to linguistic summarization of data,” IEEE Transactions on Fuzzy Systems, vol. 16, no. 1, pp. 198–212, 2008.
N. Ha, “A fuzzy relational database model,” Journal of Information and Communications Technology, vol. 5, no. 1, pp. 37–45, 2015.
S. Parsons, “Current approaches to handling imperfect information in data and knowledge bases,” IEEE Transactions on knowledge and data engineering, vol. 8, no. 3, pp. 353–372, 1996.
A. Konar, Computational intelligence: principles, techniques and applications. Springer, 2005.
T. J. Ross, Fuzzy logic with engineering applications, 3rd ed. John Wiley & Sons, 2010.
N. N. Karnik and J. M. Mendel, “Operations on type-2 fuzzy sets,” Fuzzy sets and systems, vol. 122, no. 2, pp. 327–348, 2001.