An Extended Type-2 Fuzzy Relational Database Model for Aggregate and Grouping Operations
DOI:
https://doi.org/10.56532/mjsat.v3i3.169Keywords:
Fuzzy number, Type-2 fuzzy set, Type-2 fuzzy relation, Fuzzy aggregate function, ET-2FRDB modelAbstract
This paper introduces an extended type-2 fuzzy relational database model (ET-2FRDB) for aggregate and grouping operations that can represent and query uncertain and imprecise information in the real world applications. In ET-2FRDB, each fuzzy relation is represented by a type-2 fuzzy set whose membership degree of each tuple is a fuzzy number on [0, 1], the fuzzy aggregate functions, the fuzzy relational algebraic, aggregate and grouping operations are defined as extensions of those in the classical relational database model thereby the membership degree of tuples associated by using the minimum and maximum of fuzzy numbers. Also, some properties of the fuzzy relational algebraic, aggregate and grouping operations in ET-2FRDB are formulated and proven.
References
B.P. Buckles and F. Petry, “A fuzzy representation of data for relational databases,” Journal of Fuzzy sets and Systems, vol.7, pp. 213-226, 1982.
E. Doumard, O. Pivert, G. Smits and V. Thion, “Processing fuzzy relational queries using fuzzy views,” Proc. of the 2019 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), New Orleans, Louisiana, USA, 2019, pp. 332-337.
G. Nowakowski, “Fuzzy queries on relational databases,” Proc. of the 2018 International Interdisciplinary PhD Workshop, Swinoujscie, Poland, 2018, pp.293-299.
A.A. Sabour, A.M. Gadallah and H.A. Hefny, “Flexible querying of relational databases: fuzzy set based approach,” Advanced Machine Learning Technologies and Applications Communications in Computer and Information Science, vol.488, pp.446-455, 2014.
M. Umano and S. Fukami, “Fuzzy relational algebra for possibility-distribution-relational model of fuzzy data,” International Journal of Intelligent Systems, vol.3, pp.7-28, 1994.
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.
A. Silberschatz, H.F. Korth and S. Sudarshan, Database System Concepts, Seventh Edition, McGraw-Hill, 2019.
H. Prade and C. Testemale, “Generalizing database relational algebra for the treatment of incomplete/uncertain information and vague queries,” International Journal of Information Sciences, vol.34, no.2, pp.115-143, 1984.
X. Tang and G. Chen, “Equivalence and transformation of extended algebraic operators in fuzzy relational databases,” Journal of Fuzzy Sets and Systems, vol.157, no.12, pp.1581-1596, 2006.
O. Pivert and H. Prade, “Dealing with aggregate queries in an uncertain database model based on possibilistic certainty,” Proc. of the 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Montpellier, France, 2014, pp.150-159.
E.A. Rundensteiner and L. Bic, “Aggregates in possibilistic databases,” Proc. of the Fifteenth International Conference on Very Large Data Bases, Amsterdam, Netherlands, 1989, pp.287- 295.
A. Aguilera, R.M. Toledo, A. Subero, M. Monger and P. Gupta, “On an extension of fuzzy aggregate functions for databases,” Journal of Information Systems&Operations Management, vol.7, no.1, pp.1-8, 2013.
X.L. Ye, H. Wang and Y.F. Chen, “Fuzzy aggregation queries in relational databases,” Applied Mechanics and Materials, vol.40, pp.195-200, 2010.
F.E. Petry, Fuzzy Databases: Principles and Applications, Kluwer Academic Publishers, 1996.
H. Nguyen, “A type-2 fuzzy relational database model,” Journal of Information & Communication Technology: Research and Development on Information & Communication Technology, vol.E–3, no.14, pp.19-26, 2017.
H. Nguyen, T.U.N. Nguyen and N.D Le, “Fuzzy relational database model and management system for imprecise information,” Journal of Computer Science and Cybernetics, vol.37, no.2, pp.145-162, 2021.
P.C. 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.1, pp.99-138, 2012.
G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic–Theory and Applications, Prentice Hall PTR, 1994.
L.A. Zadeh, “Fuzzy sets,” Information and Control, vol.8, pp.338-353, 1965.
H. Uesu, “Triangular shaped type-2 fuzzy number and UESU product,” ICIC Express Letters, vol.16, no.8, pp. 869-876, 2022.
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