| Title of paper:
|
Modified level operator [math]\displaystyle{ N_{\gamma_1}^{\gamma_2} }[/math] applied over interval-valued intuitionistic fuzzy sets
|
| Author(s):
|
| Vassia Atanassova
|
| Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
|
| vassia.atanassova@gmail.com
|
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 29–39
|
| DOI:
|
https://doi.org/10.7546/nifs.2018.24.4.29-39
|
| Download:
|
 PDF (158 Kb Kb, Info)
|
| Abstract:
|
The recently proposed intuitionistic fuzzy level operator [math]\displaystyle{ N_\gamma }[/math] generates a subset of an intuitionistic fuzzy set [math]\displaystyle{ A }[/math], where the elements of the subset are those elements of [math]\displaystyle{ A }[/math], for which the ratio of their degrees of membership to their degrees of non-membership is greater than or equal to a given constant [math]\displaystyle{ \gamma \gt 0 }[/math]. Here we propose a continuation of this idea from the case of intuitionistic fuzzy sets to the case of interval-valued intuitionistic fuzzy sets. This modification requires us to introduce a second constant, i.e. [math]\displaystyle{ \gamma_1,\gamma_2 \gt 0 }[/math]. We show that there are twenty possible scenarios for the mutual position of the intervalized level operator [math]\displaystyle{ N_{\gamma_1}^{\gamma_2} }[/math] and the element of the interval-valued intuitionistic fuzzy set, and give the respective formulas which calculate in each case the membership and non-membership degrees with which the IVIFS element belongs to the set defined by the operator [math]\displaystyle{ N_{\gamma_1}^{\gamma_2} }[/math]. These twenty scenarios are graphically interpreted in the intuitionistic fuzzy interpretational triangle, and the respective formulas have been derived. In conclusion, further ideas of research have been suggested.
|
| Keywords:
|
Interval valued intuitionistic fuzzy sets, Intuitionistic fuzzy sets, Level operator, Decision making under uncertainty.
|
| AMS Classification:
|
03E72.
|
| References:
|
- Atanassov, K. T. (1983). 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) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1–S6.
- Atanassov K. T. (1989). Geometrical Interpretation of the Elements of the Intuitionistic Fuzzy Objects, Mathematical Foundations of Artificial Intelligence Seminar, Sofia, 1989, Preprint IM-MFAIS-1-89. Reprinted: Int J Bioautomation, 2016, 20(S1), S27–S42.
- Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Physica- Verlag, Heidelberg.
- Atanassov, K. T., & Gargov, G. (1999). Interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 31(3), 343–349.
- Atanassova, V. (2017). New modified level operator Nγ over intuitionistic fuzzy sets. In: Christiansen H., Jaudoin H., Chountas P., Andreasen T., Legind Larsen H. (eds) Flexible Query Answering Systems. FQAS 2017. Lecture Notes in Computer Science, vol 10333. Springer, Cham, 209–214.
- Doukovska, L., Atanassova, V., Mavrov, D., & Radeva, I. (2018). Intercriteria Analysis of EU Competitiveness Using the Level Operator Nγ. 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 641. Springer, Cham, 631–647.
- Gottman, J. (1995). Why Marriages Succeed or Fail: And How You Can Make Yours Last. Simon and Schuster.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
