Application of Intuitionistic Fuzzy Topological Operators in Spatial Objects Modeling

Abstract

The concept of topology is widely used in mathematical modeling of spatial objects and in GIS. One such application of fuzzy topological operators, detecting areas affected by Mikania micrantha, was studied by Shi and Liu. The precision of the results was evaluated by applying the intuitionistic fuzzy pre-interior and pre-clouser operators defined by the author to the data included in this study. With this application example, it has been shown that the newly defined operators give results closer to the real bounds.

Keywords

• Intuitionistic Fuzzy Sets
• Intuitionistic Fuzzy Topological Operators
• Spatial Objects Modeling.

References

1. [1] A. Arkhangelskii, V. Fedorchuk, General Topology I, Springer-Verlag, Berlin, 1990
2. [2] K. Atanassov, Intuitionistic Fuzzy Sets, VII ITKR.s Session, Sofia, June, 1983.
3. [3] K. Atanassov K., Studies in Fuzziness and Soft Computing-On Intuitionistic Fuzzy Sets Theory, ISBN 978-3-642-29126-5, Springer Heidelberg, New York, 2012.
4. [4] H. Bustince, J. Kacprzyk and V. Mohedano, “Intuitionistic Fuzzy Generators-Application to Intuitionistic Fuzzy Complementation, ” Fuzzy Sets Syst., vol. 114, no. 3, pp. 485-504, 2000.
5. [5] D. Çoker, “An Introduction to Intuitionistic Fuzzy Topological Spaces”, Fuzzy Sets and Systems, vol. 88, no. 1, pp. 81-89, 1997.
6. [6] G. Çuvalcoğlu, New Tools Based on Intuitionistic Fuzzy Sets and Generalized Nets, ISBN 978-3-319- 26301-4, Springer International Publishing Switzerland, 55-71, 2016.
7. [7] G. Çuvalcoğlu, E. Aykut, “An application of some intuitionistic fuzzy modal operators to agriculture” Notes on IFS, vol. 21, no. 2, pp. 140-149, 2015.
8. [8] F.G. Lupianez, “Intuitionistic fuzzy Topological Operators and Topology,” International Journal of Pure and Applied Mathematics, vol. 17, no. 1, pp. 35-40, 2004.

9. [9] M.R. Malek, Spatial Object Modeling in Intuitionistic Fuzzy Topological Spaces. In: Tsumoto S., Słowiński R., Komorowski J., Grzymała-Busse J.W. (eds) Rough Sets and Current Trends in Computing. RSCTC 2004. Lecture Notes in Computer Science, 3066. Springer, Berlin, Heidelberg, 2004.
10. [10] E. Marinov, K.T: Atanassov, “Partially Continuous Pretopological and Topological Operators for Intuitionistic Fuzzy Sets,” Iranian Journal of Fuzzy Systems, vol. 17, no. 2, pp. 1-15, 2020.
11. [11] E. Marinov, “Software Implementation of Intuitionistic Fuzzy Sets and Some Operators,” Notes on IFS, vol. 28, no. 1, 51-85, 2022.
12. [12] R. Saadati, J.H. Park, “On Intuitionistic Fuzzy Topological Spaces”, Kybernetes, vol.35, no. 5, pp. 743-747, 2006.
13. [13] W. Shi, K. Liu, “A Fuzzy Topology for Computing the Interior, Boundary and Exterior of Spatial Objects Quantitatively in GIS,” Computers & Geosciences, vol. 33, no. 7, pp. 898-915, 2007.
14. [14] A. K. Singh, and R. Srivastava, “Separation Axioms in Intuitionistic Fuzzy Topological Spaces,” Advances in Fuzzy Systems, vol. 2012, pp. 1-7, 2012. Article ID 604396, 7 pages, doi:10.1155/2012/604396
15. [15] M. Sugeno, T. Terano, “A Model of Learning Based on Fuzzy Information,” Kybernetes, vol. 6, no. 3, pp. 157-166, 1977.
16. [16] S. Tarsuslu (Yılmaz), “A Study on Intuitionistic Fuzzy Topological Operators,” Italian Journal of Pure And Applied Mathematics, vol. 49, pp. 863-875, 2023.
17. [17] L.A. Zadeh, Fuzzy Sets, Information and Control, 8, 338-353, 1965.
18. [18] L.A. Zadeh, “The concept of linguistic variable and its application to approximate reasoning,” Inform. Sci., vol. 8, pp. 133-139, 1975.