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Issue:Intuitionistic fuzzy topological operators via controlled sets

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Title of paper: Intuitionistic fuzzy topological operators via controlled sets
Author(s):
Sinem Tarsuslu (Yılmaz)     0000-0001-9192-7001
Department of Natural and Math. Sciences, Faculty of Engineering, Tarsus University, Tarsus, Türkiye
sinemtarsuslu@tarsus.edu.tr
Gökhan Çuvalcıoğlu     0000-0001-5451-3336
Department of Mathematics, Faculty of Sciences, Mersin University, Mersin, Türkiye
gcuvalcioglu@mersin.edu.tr
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 32 (2026), Number 3, pages 231–244
DOI: https://doi.org/10.7546/nifs.2026.32.3.231-244
Download:  PDF (1001  Kb, File info)
Abstract: Topological concepts are widely used in the mathematical modeling of spatial objects with uncertain boundaries. Determining suitable operators for the interior, closure, and boundary is one of the main problems that researchers are interested in. Therefore, fuzzy topological and intuitionistic fuzzy topological operators have been examined in such problems. Different methods are used to fuzzify the elements of a region under study. However, determining the non-membership degrees of a region based on its membership degrees remains a separate problem.

In this study, this problem is addressed by applying controlled set theory. The resulting intuitionistic fuzzy representations are then processed using intuitionistic fuzzy pre-interior and pre-closure operators to examine the interior, closure, and boundary characteristics of the spatial regions affected by Mikania micrantha. The results show how the proposed method changes these values for different parameter settings and offers a new way to model uncertainty in spatial regions.

Keywords: Intuitionistic fuzzy sets, Topological operators, Controlled sets, Spatial objects modeling.
AMS Classification: 03E72.
References:
  1. Arkhangel’skii, A. V., & Pontryagin, L. S. (Eds.). (1990). General Topology I: Basic Concepts and Constructions, Dimension Theory. Encyclopaedia of Mathematical Sciences, Vol. 17. Springer-Verlag, Berlin, Heidelberg.
  2. Atanassov, K. T. (1983). Intuitionistic fuzzy sets. In: VII ITKR Session, Sofia, June, 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20 (S1), S1–S6.
  3. Atanassov, K. T. (2012). On Intuitionistic Fuzzy Sets Theory. Studies in Fuzziness and Soft Computing, Vol. 283. Springer, Berlin, Heidelberg.
  4. Bustince, H., Kacprzyk, J., & Mohedano, V. (2000). Intuitionistic fuzzy generators: Application to intuitionistic fuzzy complementation. Fuzzy Sets and Systems, 114(3), 485–504.
  5. Çoker, D. (1997). An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 88, 81–89.
  6. Çuvalcıoğlu, G. (2014). Some properties of Controlled Set Theory. Notes on Intuitionistic Fuzzy Sets, 20(2), 37–42.
  7. Çuvalcıoğlu, G., & Varol, S. U. (2021). Decision making process for serving restaurants using intuitionistic fuzzy set theory via controlled sets. Journal of Universal Mathematics, 4(2), 296–325.
  8. Kutlu, F., & Bilgin, T. (2015). Temporal intuitionistic fuzzy topology in Šostak's sense. Notes on Intuitionistic Fuzzy Sets, 21(2), 63–70.
  9. Lupian ̃ez, F. G. (2004). Intuitionistic fuzzy topological operators and topology. International Journal of Pure and Applied Mathematics, 17(1), 35–40.
  10. Malek, M. R. (2004). 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, pp. 427–434. Springer, Berlin, Heidelberg.
  11. Marinov, E., & Atanassov, K. T. (2020). Partially continuous pretopological and topological operators for intuitionistic fuzzy sets. Iranian Journal of Fuzzy Systems, 17(2), 1–15.
  12. Radhika, C., & Parvathi, R. (2016) Intuitionistic fuzzification functions. Global Journal of Pure and Applied Mathematics, 12(2), 1211–1227.
  13. Shi, W., & Liu, K. (2007). A fuzzy topology for computing the interior, boundary, and exterior of spatial objects quantitatively in GIS. Computers & Geosciences, 33, 898–915.
  14. Sugeno, M. (1974). Theory of Fuzzy Integrals and Its Applications. PhD thesis, Tokyo Institute of Technology, Tokyo, Japan.
  15. Tarsuslu (Yılmaz), S. (2023). A study on intuitionistic fuzzy topological operators. Italian Journal of Pure and Applied Mathematics, 49, 863–875.
  16. Tarsuslu (Yılmaz), S. (2023). Application of intuitionistic fuzzy topological operators in spatial objects modeling. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 12(2), 524–530.
  17. Tarsuslu (Yılmaz), S., & Çuvalcıoğlu, G. (2024). An application of controlled sets in medical diagnosis. In: Melin, P., Castillo, O. (Eds.). New Directions on Hybrid Intelligent Systems Based on Neural Networks, Fuzzy Logic, and Optimization Algorithms. Studies in Computational Intelligence, Vol. 1146, pp. 9–17. Springer, Cham.
  18. Tuğrul, F. (2021). Connectedness in Temporal Intuitionistic Fuzzy Topology in Chang’s Sense. Journal of Universal Mathematics, 4(2), 157–165.
  19. Tuğrul, F., & Çitil, M. (2021). A new perspective on evaluation system in education with ıntuitionistic fuzzy logic and PROMETHEE algorithm. Journal of Universal Mathematics, 4(1), 13–24.
  20. Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
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