Abstract
An efficient centroid type-reduction strategy for general type-2 fuzzy set is proposed by Liu. In Liu’s method, a type-2 fuzzy set will be decomposed into several interval type-2 fuzzy sets. However, if the membership function of the type-2 fuzzy set is concave, the primary membership of these interval type-2 fuzzy sets on some points may not have only one continuous interval. Existing type-reduction algorithms, such as Karnik-Mendel algorithm and Enhanced Karnik-Mendel algorithm, can not deal with this problem. We propose a method to decompose this problem into several subproblems which can then be solved by existing type-reduction algorithms. The union of the solutions to the subproblems is the final solution to the original problem.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Pearson Education Taiwan (2005)
Liu, F.: An Efficient Centroid Type-Reduction Strategy for General Type-2 Fuzzy Logic System. Information Sciences 178(9), 2224–2236 (2008)
Karnik, N.N., Mendel, J.M.: Centroid of a Type-2 Fuzzy Set. Information Sciences 132(1–4), 195–220 (2001)
Karnik, N.N., Mendel, J.M., Liang, Q.: Type-2 Fuzzy Logic Systems. IEEE Transactions on Fuzzy Systems 7(6), 643–658 (1999)
Mendel, J.M.: Type-2 Fuzzy Sets and Systems: an Overview. IEEE Transactions on Computational Intelligence Magazine 2(1), 20–29 (2007)
Mendel, J.M.: On KM Algorithms for Solving Type-2 Fuzzy Set Problems. IEEE Transactions on Fuzzy Systems 21(3), 426–445 (2013)
Mendel, J.M., Liang, Q.: Type-2 Fuzzy Sets Made Simple. IEEE Transactions on Fuzzy Systems 10(2), 117–127 (2002)
Wu, D., Mendel, J.M.: Enhanced Karnik-Mendel Algorithms. IEEE Transactions on Fuzzy Systems 17(4), 923–934 (2009)
Wu, H.-J., Su, Y.-K., Lee, S.-J.: A Fast Method for Computing the Centroid of a Type-2 Set. IEEE Transactions on Systems, Man, And Cybernetics-Part B 42(3), 764–777 (2012)
Yeh, C.-Y., Jeng, W.-H.R., Lee, S.-J.: An Enhanced Type-Reduction Algorithm for Type-2 Fuzzy Sets. IEEE Transactions on Fuzzy Systems 19(2), 227–240 (2011)
Zhai, D., Mendel, J.M.: Computing the Centroid of a General Type-2 Fuzzy Set by Means of the Centroid-Flow Algorithm. IEEE Transactions on Fuzzy Systems 19(2), 401–422 (2011)
Zhai, D., Mendel, J.M.: Enhanced Centroid-Flow Algorithm for Computing the Centroid of General Type-2 Fuzzy Sets. IEEE Transactions on Fuzzy Systems 20(5), 939–956 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Xie, BK., Lee, SJ. (2015). Type-Reduction for Concave Type-2 Fuzzy Sets. In: Barbucha, D., Nguyen, N., Batubara, J. (eds) New Trends in Intelligent Information and Database Systems. Studies in Computational Intelligence, vol 598. Springer, Cham. https://doi.org/10.1007/978-3-319-16211-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-16211-9_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16210-2
Online ISBN: 978-3-319-16211-9
eBook Packages: EngineeringEngineering (R0)