Title of paper:
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Modified level operator Nγ1γ2 applied over interval-valued intuitionistic fuzzy sets
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Author(s):
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Vassia Atanassova
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Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
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vassia.atanassova@gmail.com
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Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 24 (2018), Number 4, pages 29–39
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DOI:
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https://doi.org/10.7546/nifs.2018.24.4.29-39
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Download:
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PDF (158 Kb Kb, File info)
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Abstract:
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The recently proposed intuitionistic fuzzy level operator Nγ generates a subset of an intuitionistic fuzzy set A, where the elements of the subset are those elements of A, for which the ratio of their degrees of membership to their degrees of non-membership is greater than or equal to a given constant γ > 0. 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. γ1, γ2 > 0. We show that there are twenty possible scenarios for the mutual position of the intervalized level operator Nγ1γ2 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 Nγ1γ2. 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.
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Keywords:
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Interval valued intuitionistic fuzzy sets, Intuitionistic fuzzy sets, Level operator, Decision making under uncertainty.
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AMS Classification:
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03E72.
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References:
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- 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.
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- 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.
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