| Title of paper:
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Modified level operator [math]\displaystyle{ N_{\gamma_1}^{\gamma_2} }[/math] 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, File info)
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| Abstract:
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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.
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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. (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.
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