Part of the book series: Studies in Computational Intelligence ((SCI,volume 934))

  • 250 Accesses

Abstract

In the present work we try to provide an overview of the main results related to intiuitionistic fuzzy sets and related concepts contributed by scientists from the Bulgarian Academy of Sciences from the very birth of the concept to present day. Of course, it is impossible not to mention briefly the contributions of other authors but we will try to keep the focus of our exposition on the results of the groups that have worked within the Academy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Andonov, V.: On some properties of one Cartesian product over intuitionistic fuzzy sets. Notes Intuit. Fuzzy Sets 14(1), 12–19 (2008)

    MathSciNet  Google Scholar 

  2. Angelova, M., Atanassov, K., Pencheva, T.: Intuitionistic fuzzy logic based quality assessment of simple genetic algorithm. In: Proceedings of the 16th International Conference on System Theory, Control and Computing (ICSTCC), Electronic edn., vol. 2, Sinaia, Romania, 12–14 October (2012)

    Google Scholar 

  3. Angelova, M., Atanassov, K. & Pencheva, T.: Multipopulation genetic algorithm quality assessment implementing intuitionistic fuzzy logic. In: Proceedings of the Federated Conference on Computer Sciences and Information Systems—FEDCSIS 2012, Workshop on Computational Optimization—WCO’2012, Wrocław, pp. 365–370, Poland, 9–12 September (2012)

    Google Scholar 

  4. Angelova, M., Atanassov, K., Pencheva, T.: Intuitionistic fuzzy estimations of purposeful model parameters genesis. In: Proceedings of the IEEE 6th International Conference on Intelligent Systems, pp. 206–211, Sofia, Bulgaria, 6–8 September (2012)

    Google Scholar 

  5. Angelova, M., Pencheva, T.: Quality assesment procedure for genetic algorithms performance using intuitionistic fuzzy logics. In: 10th National Young Scientific-Practical Session, pp. 244–249, Sofia, Bulgaria, 23–25 April (2012) (in Bulgarian)

    Google Scholar 

  6. Angelova, M., Atanassov, K., Pencheva, T.: Purposeful model parameters genesis in simple genetic algorithms. Comput. Math. Appl. 64, 221–228 (2012)

    Article  Google Scholar 

  7. Angelova, M., Atanassov, K., Pencheva, T.: Intuitionistic fuzzy logic as a tool for quality assessment of genetic algorithms performances. Stud. Comput. Intell. 470, 1–13 (2013)

    Article  Google Scholar 

  8. Angelova, M., Pencheva, T.: Genetic operators’ significance assessment in multipopulation genetic algorithms. Int. J. Metaheur. 3(2), 162–173 (2014)

    Article  Google Scholar 

  9. Angelova, M., Pencheva, T.: Genetic operators significance assessment in simple genetic algorithm. In: Lecture Notes Computer Science, vol. 8353, pp. 223–231 (2014)

    Google Scholar 

  10. Angelova, M., Pencheva, T.: How to assess multi-population genetic algorithms performance using intuitionistic fuzzy logic. Adv. Comput. Ind. Math. Stud. Comput. Intell. 793, 23–25 (2018)

    Google Scholar 

  11. Angelova, N., & Stoenchev, M.: Intuitionistic fuzzy conjunctions and disjunctions from first type. Annu. Inf. Sect. Union Sci. Bulg. 8, 1–17 (2015–2016)

    Google Scholar 

  12. Angelova, N., Stoenchev, M., Todorov, V.: Intuitionistic fuzzy conjunctions and disjunctions from second type. Issues IFSs GNs 13, 143–170 (2017)

    MATH  Google Scholar 

  13. Angelova, N., Stoenchev, M.: Intuitionistic fuzzy conjunctions and disjunctions from third type. Notes Intuit. Fuzzy Sets 23(5), 29–41 (2017)

    MATH  Google Scholar 

  14. Atanassov, K.: Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.—Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.). Reprinted: Int. J. Bioautom. 20(S1), S1–S6 (in English) (1983 & 2016)

    Google Scholar 

  15. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  MATH  Google Scholar 

  16. Atanassov, K.: Generalized Nets. World Scientific, Singapore (1991)

    Google Scholar 

  17. Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)

    Google Scholar 

  18. Atanassov, K.: On the intuitionistic fuzzy implications and negations. In: Part 1. 35 Years of Fuzzy Set Theory pp. 19–38. Springer, Berlin, Heidelberg (2010)

    Google Scholar 

  19. Atanassov, K.: New Topol. Oper. Over Intuit. Fuzzy Sets. Notes Intuit. Fuzzy Sets 21(3), 90–92 (2015)

    Google Scholar 

  20. Atanassov, K.: Errata or a new form of the uniformly expanding intuitionistic fuzzy operator. Notes Intuit. Fuzzy Sets 23(1), 100–103 (2017)

    MATH  Google Scholar 

  21. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)

    Google Scholar 

  22. Atanassov, K.: On Generalized Nets Theory. Prof. M. Drinov Academic Publishing House, Sofia (2007)

    Google Scholar 

  23. Atanassov, K.T.: Intuitionistic Fuzzy Logics. Springer International Publishing, Cham (2017)

    Google Scholar 

  24. Atanassov, K., Ban, A.: On an operator over intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, Tome 53(5), 39–42 (2000)

    MathSciNet  MATH  Google Scholar 

  25. Atanassov, K., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(3), 343–349 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  26. 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 Intuit. Fuzzy Sets Gener. Nets 11, 1–8 (2014)

    Google Scholar 

  27. Atanassov, K., Szmidt, E., Kacprzyk, J.: On intuitionistic fuzzy pairs. Notes Intuit. Fuzzy Sets 19(3), 1–13 (2013)

    MATH  Google Scholar 

  28. Atanassov, K., Vassilev, P., Tsvetkov, R. (2013). Intuitionistic Fuzzy Sets, Measures and Integrals,“Prof. Marin Drinov” Academic Publishing House, Sofia, (2013)

    Google Scholar 

  29. Atanassov, K.T., Vassilev, P.: On the intuitionistic fuzzy sets of \(n\)-th type. In: Gaweda, A., Kacprzyk, J., Rutkowski, L., Yen, G. (eds.) Advances in Data Analysis with Computational Intelligence Methods. Studies in Computational Intelligence, vol. 738, pp. 265–274 (2018)

    Google Scholar 

  30. Atanassova, V.: Representation of fuzzy and intuitionistic fuzzy data by Radar charts. Notes Intuit. Fuzzy Sets 16(1), 21–26 (2010)

    Google Scholar 

  31. Atanassova, V.: New modified level operator \(N_{\gamma }\) over intuitionistic fuzzy sets. Lect. Notes Comput. Sci. 10333, 209–214 (2017)

    Article  Google Scholar 

  32. Atanassova, V., Doukovska, L.: Compass-and-straightedge constructions in the intuitionistic fuzzy interpretational triangle: two new intuitionistic fuzzy modal operators. Notes Intuit. Fuzzy Sets 23(2), 1–7 (2017)

    MATH  Google Scholar 

  33. Brouwer, L.E.J.: Intuitionism and formalism. Bull. Am. Math. Soc. 20(2), 81–96 (1913)

    Article  MathSciNet  MATH  Google Scholar 

  34. Castillo, O., Ramirez, E., Roeva, O.: Water cycle algorithm augmentation with fuzzy and intuitionistic fuzzy dynamic adaptation of parameters. Notes Intuit. Fuzzy Sets 23(1), 79–94 (2017)

    MATH  Google Scholar 

  35. Chountas, P., Atanassov, K., Atanassova, V., Sotirova, E., Sotirov, S., Roeva, O.: Big data, intuitionistic fuzzy sets and MapReduce operators. Notes Intuit. Fuzzy Sets 24(2), 129–135 (2018)

    Article  Google Scholar 

  36. Dworniczak, P.: A note on the unconscientious experts’ evaluations in the intuitionistic fuzzy environment. Notes Intuit. Fuzzy Sets 18(3), 23–29 (2012)

    Google Scholar 

  37. Dworniczak, P.: Further remarks about the unconscientious experts’ evaluations in the intuitionistic fuzzy environment. Notes Intuit. Fuzzy Sets 19(1), 27–31 (2012)

    Google Scholar 

  38. Feferman, S.: In the Light of Logic. Oxford University Press, Oxford (1998)

    Google Scholar 

  39. Feys, R.: Modal Logics. Gauthier, Paris (1965)

    Google Scholar 

  40. Georgieva, O., Pencheva, T., Krawczak, M.: An application of generalized nets with intuitionistic fuzzy sets for modelling of biotechnological processes with distributed parameters. Issues Intuit. Fuzzy Sets Gener. Nets 3, 5–10 (2006)

    Google Scholar 

  41. Hadjitodorov, S.T.: A F-operator intuitionistic fuzzy version of the nearest neighbor classifier. Notes Intuit. Fuzzy Sets 6, 1–6 (2000)

    MathSciNet  MATH  Google Scholar 

  42. Hadjitodorov, S.: An intuitionistic fuzzy sets application to the k-NN method. Notes Intuit. Fuzzy Sets 1(1), 66–69 (1995)

    MathSciNet  Google Scholar 

  43. Hadjitodorov, S.T.: Intuitionistic fuzzy versions of k-nn method and their application to respiratory distress syndrome detection. Notes Intuit. Fuzzy Sets 4(4), 62–67 (1998)

    Google Scholar 

  44. Kuratowski, K., Topology, Vol. 1, New York, Acad. Press (1966)

    Google Scholar 

  45. Marinov, E.: On the algorithmic aspect of the modified weighted hausdorff distance. Inf. Models Anal. 126–135 (2012)

    Google Scholar 

  46. Marinov, E.: \(\pi \)-ordering and index of indeterminacy for intuitionistic fuzzy sets. In: Proceedings of 12th International Workshop on IFS and GN, IWIFSGN’13, Warsaw, Oct. 2013, Modern Approaches in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics. Volume I: Foundations, IBS PAN-SRI PAS, Warsaw, pp. 129–138 (2014)

    Google Scholar 

  47. Marinov, E., Atanassov, K., Vassilev, P., Su, J.: Directed intuitionistic fuzzy neighbourhoods. In: Proceedings of the IEEE 8th International Conference on Intelligent Systems (IS), pp. 544–549, Sofia, Bulgaria (2016)

    Google Scholar 

  48. Marinov, E., Szmidt, E., Kacprzyk, J., Tcvetkov, R.: A modified weighted Hausdorff distance between intuitionistic fuzzy sets. In: Proceedings of the 6th IEEE International Conference on Intelligent Systems, pp. 138–141 (2012)

    Google Scholar 

  49. Marinov, E., Vassilev, P., Atanassov, K.: On intuitionistic fuzzy metric neighbourhoods. In: Proceedings of the Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15), Gijon, Spain

    Google Scholar 

  50. Marinov, E., Vassilev, P., Atanassov, K.: On separability of intuitionistic fuzzy sets. In: Atanassov, K., et al. (eds) Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, Vol. 401, pp. 111–123 (2016)

    Google Scholar 

  51. Pencheva, T.: Modelling of expanded advisory system for yeast cultivation on-line control using generalized nets and intuitionistic fuzzy logic. Issues Intuit. Fuzzy Sets Gener. Nets 9, 101–115 (2011)

    Google Scholar 

  52. Pencheva, T.: Intuitionistic fuzzy logic in generalized net model of an advisory system for yeast cultivation on-line control. Notes Intuit. Fuzzy Sets 15(4), 45–51 (2009)

    Google Scholar 

  53. Pencheva, T., Angelova, M.: Intuitionistic fuzzy logic implementation to assess purposeful model parameters genesis. Stud. Comput. Intell. 657, 179–203 (2017)

    Article  Google Scholar 

  54. Pencheva, T., Angelova, M., Atanassov, K.: Quality assessment of multi-population genetic algorithms performance. Int. J. Sci. Eng. Res. 4(12), 1870–1875 (2013)

    Google Scholar 

  55. Pencheva, T., Angelova, M., Atanassov, K.: Genetic algorithms quality assessment implementing intuitionistic fuzzy logic, Chapter 11. In: Vasant, P. (ed.) Handbook of Research on Novel Soft Computing Intelligent Algorithms: Theory and Practical Applications, pp. 327–354. Hershey, Pennsylvania (USA), IGI Global (2013)

    Google Scholar 

  56. Pencheva, T., Novachev, N., Stratiev, D., Atanassov, K.: Generalized net model of the process of evaluation of the environmental impact of refinery activity using intuitionistic fuzzy estimations. Notes Intuit. Fuzzy Sets 18(4), 32–39 (2012)

    Google Scholar 

  57. Perez, J., Valdez, F., Roeva, O., Castillo, O.: Parameter adaptation of the Bat Algorithm, using type-1, interval type-2 fuzzy logic and intuitionistic fuzzy logic. Notes Intuit. Fuzzy Sets 22(2), 87–98 (2016)

    MATH  Google Scholar 

  58. Perez, J., Valdez, F., Castillo, O., Roeva, O.: Bat Algorithm with parameter adaptation using interval type-2 fuzzy logic for benchmark mathematical functions. In: 2016 IEEE 8th International Conference on Intelligent Systems, Sofia, 04–06 September, pp. 120–127 (2016)

    Google Scholar 

  59. Priest, G.: An Introduction to Non-classical Logic: From if to is. Cambridge University Press (2008)

    Google Scholar 

  60. Ribagin, S., Vassilev, P., Pencheva, T., Zadrożny, S.: Intuitionistic fuzzy generalized net model of adolescent idiopathic scoliosis classification and the curve progression probability. Notes Intuit. Fuzzy Sets 23(3), 88–95 (2017)

    Google Scholar 

  61. Roeva, O., Michalíková, A.: Intuitionistic fuzzy logic control of metaheuristic algorithms’ parameters via a generalized net. Notes Intuit. Fuzzy Sets 20(4), 53–58 (2014)

    MATH  Google Scholar 

  62. Roeva, O., Michalíková, A.: Generalized net model of intuitionistic fuzzy logic control of genetic algorithm parameters. Notes Intuit. Fuzzy Sets 19(2), 71–76 (2013)

    MATH  Google Scholar 

  63. Roeva, O., Pencheva, T., Bentes, I., Manuel Nascimento, M.: Modelling of temperature control system in fermentation processes using generalized nets and intuitionistic fuzzy logics. Notes Intuiti. Fuzzy Sets 11(4), 151–157 (2005)

    Google Scholar 

  64. Roeva, O., Vassilev, P., Chountas, P.: Application of topological operators over data from intercriteria analysis. In: Christiansen, H., et al. (eds.): FQAS 2017, Lecture Notes in Artificial Intelligence, vol. 10333, pp. 215–225 (2017)

    Google Scholar 

  65. Roeva, O., Pencheva, T., Atanassov, K.: Generalized net of a genetic algorithm with intuitionistic fuzzy selection operator, new developments in fuzzy sets, intuitionistic fuzzy sets, generalized nets and related topics. In: Atanassov, K.T., Baczyński, M., Drewniak, J., Kacprzyk, J., Krawczak, M., Szmidt, E., Wygralak, M., Zadrożny, S. (eds.) Foundations, vol. 1, IBS PAN-SRI PAS, pp. 167–178, Warsaw (2012)

    Google Scholar 

  66. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114(3), 505–518 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  67. Vassilev, P.: Operators similar to operators defined over intuitionistic fuzzy sets 18(4), 40–47 (2012)

    Google Scholar 

  68. Vassilev, P.: Intuitionistic fuzzy sets generated by archimedean metrics and ultrametrics. In: Sgurev, V., Yager, R., Kacprzyk, J., Atanassov, K. (eds.) Recent Contributions in Intelligent Systems. Studies in Computational Intelligence, vol. 657, pp. 339–378 (2017)

    Google Scholar 

  69. Vassilev, P.: On reassessment of expert evaluations in the case of intuitionistic fuzziness. Adv. Stud. Contemp. Math. 20(4), 569–574 (2010)

    MathSciNet  MATH  Google Scholar 

  70. Vassilev, P., Ribagin, S.: A Note on intuitionistic fuzzy modal-like operators generated by power mean. Adv. Intell. Syst. Comput. 643, 470–475 (2018)

    Google Scholar 

  71. Vassilev, P., Ribagin, S., Kacprzyk, J.: A remark on intuitionistic fuzzy implications. Notes Intuit. Fuzzy Sets 24(2), 1–7 (2018)

    Article  Google Scholar 

  72. Vassilev, P., Stoyanov, T.: On a new ordering between intuitionistic fuzzy pairs. In: Proceedings of the 8th European Symposium on Computational Intelligence and Mathematics, pp. 77–80, Sofia (Bulgaria), 5–8 October (2016)

    Google Scholar 

  73. Vassilev, P., Stoyanov, T.: On power mean generated orderings between intuitionistic fuzzy pairs. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds.) Advances in Fuzzy Logic and Technology 2017. EUSFLAT 2017, IWIFSGN 2017. Advances in Intelligent Systems and Computing, vol. 643, pp. 476–481 (2018)

    Google Scholar 

  74. Vassilev, P., Todorova, L., Kosev, K.: Note on the (\(\mu, \nu \))-coherence relation, defined over intuitionistic fuzzy sets. Notes Intuit. Fuzzy Sets 20(4), 7–9 (2014)

    MATH  Google Scholar 

  75. Vassilev, P., Todorova, L., Surchev, J.: Determining intuitionistic fuzzy estimates for decision making in medical tasks. Notes Intuit. Fuzzy Sets 20(5), 62–68 (2014)

    Google Scholar 

  76. Todorova, L.: Determining the specificity, sensitivity, positive and negative predictive values in intuitionistic fuzzy logic. In: Twelfth International Conference on IFSs, pp. 73–79, Sofia, 17–18 May 2008, Notes on Intuitionistic Fuzzy Sets, vol. 14, no. 2 (2008)

    Google Scholar 

  77. Todorova, L., Vassilev, P., Hadjistoykov, P., Surchev, J.: Application of intuitionistic fuzzy sets for more objective comparison of Kaplan-Meier curves. In: Intelligent Systems (IS), Proceedings of the 6th International IEEE Conference Intelligent Systems, Sept. 2012, pp. 212–215 (2012)

    Google Scholar 

  78. Traneva, V., Atanassova, V., Tranev, S.: Index matrices as a decision-making tool for job appointment. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds.) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science, Vol. 11189, pp. 158–166 (2019)

    Google Scholar 

  79. Traneva, V., Tranev, S., Atanassova, V. (2019) An intuitionistic fuzzy approach to the Hungarian Algorithm. In: Nikolov, G., Kolkovska, N., Georgiev, K. (eds) Numerical Methods and Applications. NMA 2018. Lecture Notes in Computer Science, vol. 11189, pp. 167–175 (2019)

    Google Scholar 

  80. Yang, Y., Chiclana, F.: Intuitionistic fuzzy sets: spherical representation and distances. Int. J. Intell. Syst. 24(4), 399–420 (2009)

    Article  MATH  Google Scholar 

  81. Yosida, K.: Functional Analysis. Springer, Berlin (1965)

    Google Scholar 

  82. Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Google Scholar 

  83. Zoteva, D., Roeva, A., Atanassova, V.: Generalized net model of artificial bee colony optimization algorithm with intuitionistic fuzzy parameter adaptation. Notes Intuit. Fuzzy Sets 24(3), 79–91 (2018)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Vassilev, P., Todorova, L., Marinov, E. (2021). On Intuitionistic Fuzziness. In: Atanassov, K.T. (eds) Research in Computer Science in the Bulgarian Academy of Sciences. Studies in Computational Intelligence, vol 934. Springer, Cham. https://doi.org/10.1007/978-3-030-72284-5_11

Download citation

Publish with us

Policies and ethics

Navigation