Abstract
The type-2 fuzzy sets was extended of original fuzzy sets and there are many researches related to type-2 fuzzy sets and fuzzy logic systems (FLS), recently. The paper deals with the approximate presentation of type-2 fuzzy sets and operations by using triangulated irregular networks (TIN). TIN usually used to represent approximate 3-D surfaces with applications in computer graphics. By using TINs and half-edge structure, authors proposed representation and operations of type-2 fuzzy sets based on this approach. Some results compared with original approaches are shown to confirm the approach be good and correctly.
Keywords
- type-2 fuzzy sets
- TIN
- Delaunay algorithm
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Zadeh, L.A.: The concept of linguistic variable and its application to approximate reasoning. J. Inform. Sci. 8, 199–249 (1975)
Mizumoto, M., Tanaka, K.: Some properties of fuzzy sets of type-2. J. Inform. and Control 31, 312–334 (1976)
Karnik, N., Mendel, J.M.: Operations on Type-2 Fuzzy Sets. Fuzzy Sets and Systems 122, 327–348 (2001)
Karnik, N., Mendel, J.M.: Centroid of a type-2 fuzzy set. Information Sciences 132, 195–220 (2001)
Karmil, N.N., Mendel, J.M., Liang, Q.: Type-2 Fuzzy Logic Systems. IEEE Trans. on Fuzzy Systems 7(6), 643–658 (1999)
Liang, Q., Mendel, J.M.: Interval Type-2 Fuzzy Logic Systems: Theory and Design. IEEE Trans. on Fuzzy Systems 8(5), 635–650 (2000)
Mendel, J.M., John, R.B.: Type-2 Fuzzy Sets Made Simple. Fuzzy Sets and Systems 10(2), 117–127 (2002)
Mendel, J.M.: On Computing the Centroid of a Symmetrical Interval Type-2 Fuzzy Set. In: Proc. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU), Perugia, Italy, July 4-9 (2004)
Coupland, S., John, R.: Fuzzy Logic and Computational Geometry. In: 5th International Conference on Recent Advances in Soft Computing, pp. 3–8 (2004)
Coupland, S., John, R.: Geometric Type-1 and Type-2 Fuzzy Logic Systems. Accepted for publication in IEEE Transactions on Fuzzy Systems (2006)
Shewchuck, J.R.: Delaunay Refinement Algorithms for Triangular Mesh Generation. Computational Geometry: Theory and Applications 22(1-3), 21–74 (2002)
Ruppert, J.: A Delaunay refinement algorithm for Quality 2-Dimensional Mesh Generation. Journal of Algorithms 18(3), 548–585 (1995)
Ngo, L.T., Pham, L.T.: Approach in Generating 3-D Digital Terrain Model based on Refinement Delaunay Algorithm (in Vietnamese). In: Proc. of Symposium in IT, pp. 248–258 (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Thanh Ngo, L., Pham The, L., Hoang Nguyen, P., Hirota, K. (2007). On Approximate Representation of Type-2 Fuzzy Sets Using Triangulated Irregular Network. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_58
Download citation
DOI: https://doi.org/10.1007/978-3-540-72950-1_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
eBook Packages: Computer ScienceComputer Science (R0)