Abstract
The purpose of this paper is to investigate the relationship between the recently introduced Generalised Atanassov Intuitionistic Fuzzy Sets and the Intuitionistic Fuzzy Sets (also sometimes called Atanassov sets). As a result it will be established that the two notions are completely equivalent.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Atanassov, K.: Geometrical interpretation of the elements of the intuitionistic fuzzy objects, Preprint IM-MFAIS-1-89, Sofia, 1989. Reprinted: Int. J. Bioautomation, 2016, 20(S1), S27–S42 (1989)
Atanassov, K.: A second type of intuitionistic fuzzy sets. BUSEFAL 56, 66–70 (1993)
Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)
Atanassov, K.: Remark on a property of the intuitionistic fuzzy interpretation triangle. Notes on Intuitionistic Fuzzy Sets 8(1), 34–36 (2002)
Atanassov, K., Szmidt, E., Kacprzyk, J.: On Intuitionistic Fuzzy Pairs. Notes on Intuitionistic Fuzzy Sets 19(3), 1–13 (2013)
Atanassov, K.T.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)
Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst. 79(3), 403–405 (1996)
Cornelis, C., Atanassov, K., Kerre, E.: Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison. In: Wagenknecht, M., Hampel, R. (eds.) Proceedings of Third International Conference on Fuzzy Logic and Technology, pp. 159–163 (2003)
Despi, I., Opris, D., Yalcin, E.: Generalised Atanassov intuitionistic fuzzy sets. In: Proceedings of the Fifth International Conference on Information, Process, and Knowledge Management 2013, (eKNOW 2013), pp. 51–56 (2013)
Dworniczak, P.: A note on the unconscientious experts’ evaluations in the intuitionistic fuzzy environment. Notes on Intuitionistic Fuzzy Sets 18(3), 23–29 (2012)
Dworniczak, P.: Further remarks about the unconscientious experts’ evaluations in the intuitionistic fuzzy environment. Notes on Intuitionistic Fuzzy Sets 19(1), 27–31 (2013)
Niewiadomski, A.: Interval-valued and interval type-2 fuzzy sets: a subjective comparison. In: Proceedings of FUZZ-IEEE’07, London, pp. 1198–1203 (2007)
Vassilev, P.: Intuitionistic fuzzy sets with membership and non-membership functions in metric relation, Ph.D. Thesis (in Bulgarian) (2013)
Acknowledgements
Work presented here is supported by Program for career development of young scientists, Bulgarian Academy of Sciences, Grant number DFNP-17-139 “Investigation of different extensions of fuzzy sets and assessment of their correctness”.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Vassilev, P., Atanassov, K. (2020). Generalised Atanassov Intuitionistic Fuzzy Sets Are Actually Intuitionistic Fuzzy Sets. In: Castillo, O., Melin, P., Kacprzyk, J. (eds) Intuitionistic and Type-2 Fuzzy Logic Enhancements in Neural and Optimization Algorithms: Theory and Applications. Studies in Computational Intelligence, vol 862. Springer, Cham. https://doi.org/10.1007/978-3-030-35445-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-35445-9_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35444-2
Online ISBN: 978-3-030-35445-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)