Application of Topological Operators over Data from InterCriteria Analysis

  • Olympia Roeva
  • Peter Vassilev
  • Panagiotis Chountas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10333)


In this paper, two topological operators T and U over intuitionistic fuzzy sets are considered and applied. As a case study a parameter identification problem of E. coli fed-batch cultivation process model using genetic algorithms is investigated. A new result regarding T and U is established. The results obtained by the application of the topological operators over data processed by InterCriteria Analysis are discussed.


InterCriteria Analysis Topological operators Intuitionistic fuzzy sets Genetic Algorithms 



The work is partially supported by the Bulgarian National Scientific Fund under the grant DFNI-I02/5 “InterCriteria Analysis. A New Approach to Decision Making”.


  1. 1.
    Atanassov, K., Atanassova, V., Gluhchev, G.: InterCriteria analysis: ideas and problems. Notes Intuitionistic Fuzzy Sets 21(1), 81–88 (2015)Google Scholar
  2. 2.
    Atanassov, K., Mavrov, D., Atanassova, V.: Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Issues IFSs GNs 11, 1–8 (2014)Google Scholar
  3. 3.
    Atanassov, K.: A new topological operator over intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets 21(3), 90–92 (2015)Google Scholar
  4. 4.
    Atanassov, K.: Errata, or a new form of the uniformly expanding intuitionistic fuzzy operator. Notes on Intuitionistic Fuzzy Sets 23(1), 100–104 (2017)Google Scholar
  5. 5.
    Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham (2014)zbMATHGoogle Scholar
  6. 6.
    Atanassov, K.: Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20–23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84). Reprinted: Int J Bioautomation 20(S1), S1–S6 (2016)Google Scholar
  7. 7.
    Atanassov, K.: On four intuitionistic fuzzy topological operators. Mathw. Soft Comput. 8, 65–70 (2001)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  9. 9.
    Atanassov, K.: On two topological operators over intuitionistic fuzzy sets. Issues in Intuitionistic Fuzzy Sets and Generalized Nets 8, 1–7 (2010)Google Scholar
  10. 10.
    Atanassova, V., Doukovska, L., Karastoyanov, D., Čapkovič, F.: InterCriteria decision making approach to EU member states competitiveness analysis: trend analysis. In: Angelov, P., Atanassov, K.T., Doukovska, L., Hadjiski, M., Jotsov, V., Kacprzyk, J., Kasabov, N., Sotirov, S., Szmidt, E., Zadrożny, S. (eds.) Intelligent Systems’2014. AISC, vol. 322, pp. 107–115. Springer, Cham (2015). doi: 10.1007/978-3-319-11313-5_10 Google Scholar
  11. 11.
    Atanassova, V.: New modified level operator \(N_\gamma \) over intuitionistic fuzzy sets. In: Christiansen, H., Jaudoin, H., Chountas, P., Andreasen, T., Larsen, H.L. (eds.) FQAS 2017. LNCS (LNAI), vol. 10333, pp. 209–214. Springer, Cham (2017)Google Scholar
  12. 12.
    Fidanova, S., Paprzycki, M., Roeva, O.: Hybrid GA-ACO algorithm for a model parameters identification problem. In: IEEE Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 413–420 (2014)Google Scholar
  13. 13.
    Ilkova, T., Petrov, M.: InterCriteria analysis for evaluation of the pollution of the Struma river in the Bulgarian section. Notes on Intuitionistic Fuzzy Sets 22(3), 120–130 (2016)Google Scholar
  14. 14.
    Krawczak, M., Bureva, V., Sotirova, E., Szmidt, E.: Application of the intercriteria decision making method to universities ranking. In: Atanassov, K.T., et al. (eds.) Novel Developments in Uncertainty Representation and Processing. AISC, vol. 401, pp. 365–372. Springer, Cham (2016). doi: 10.1007/978-3-319-26211-6_31 CrossRefGoogle Scholar
  15. 15.
    Pencheva, T., Angelova, M.: InterCriteria analysis of simple genetic algorithms performance. In: Georgiev, K., Todorov, M., Georgiev, I. (eds.) Advanced Computing in Industrial Mathematics. Studies in Computational Intelligence, vol. 681, pp. 147–159. Springer, Cham (2017)CrossRefGoogle Scholar
  16. 16.
    Roeva, O., Fidanova, S., Paprzycki, M.: Influence of the population size on the genetic algorithm performance in case of cultivation process modelling. In: IEEE Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 371–376 (2013)Google Scholar
  17. 17.
    Roeva, O., Vassilev, P., Fidanova, S., Paprzycki, M.: InterCriteria analysis of genetic algorithms performance. In: Fidanova, S. (ed.) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol. 655, pp. 235–260. Springer, Cham (2016)CrossRefGoogle Scholar
  18. 18.
    Roeva, O., Fidanova, S., Vassilev, P., Gepner, P.: InterCriteria analysis of a model parameters identification using genetic algorithm. In: IEEE Proceedings of the Federated Conference on Computer Science and Information Systems, pp. 501–506 (2015)Google Scholar
  19. 19.
    Sotirov, S., Sotirova, E., Melin, P., Castilo, O., Atanassov, K.: Modular neural network preprocessing procedure with intuitionistic fuzzy intercriteria analysis method. In: Andreasen, T., et al. (eds.) Flexible Query Answering Systems. AISC, vol. 400, pp. 175–186. Springer, Cham (2016)Google Scholar
  20. 20.
    Stratiev, D., Sotirov, S., Shishkova, I., Nedelchev, A., Sharafutdinov, I., Veli, A., Mitkova, M., Yordanov, D., Sotirova, E., Atanassova, V., Atanassov, K., Stratiev, D., Rudnev, N., Ribagin, S.: Investigation of relationships between bulk properties and fraction properties of crude oils by application of the intercriteria analysis. Pet. Sci. Technol. 34(13), 1113–1120 (2016)CrossRefGoogle Scholar
  21. 21.
    Todinova, S., Mavrov, D., Krumova, S., Marinov, P., Atanassova, V., Atanassov, K., Taneva, S.: Blood plasma thermograms dataset analysisby means of intercriteria and correlation analyses for the case of colorectal cancer. Int. J. Bioautomation 20(1), 115–124 (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Olympia Roeva
    • 1
  • Peter Vassilev
    • 1
  • Panagiotis Chountas
    • 2
  1. 1.Institute of Biophysics and Biomedical EngineeringBulgarian Academy of ScienceSofiaBulgaria
  2. 2.Department of Computer Science, Faculty of Science and Technology (FST)University of WestminsterLondonUK

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