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Issue:A new operation over intuitionistic fuzzy pairs: Difference between revisions

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  | issue          = [[Notes on Intuitionistic Fuzzy Sets/28/4|Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 4]], pages 436–441
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/28/4|Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 4]], pages 436–441
  | doi            = https://doi.org/10.7546/nifs.28.4.436-441
  | doi            = https://doi.org/10.7546/nifs.2022.28.4.436-441
  | file            = NIFS-28-4-436-441.pdf
  | file            = NIFS-28-4-436-441.pdf
  | format          = PDF
  | format          = PDF
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  | ams            = 03B52.
  | ams            = 03B52.
  | references      =  
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# Angelova, N., & Stoenchev, M. (2015/2016). Intuitionistic fuzzy conjunctions and disjunctions from first type. Annual of “Informatics” Section, Union of Scientists in Bulgaria, 8, 1–17.
# Angelova, N., & Stoenchev, M. (2015/2016). [https://old.usb-bg.org/Bg/Annual_Informatics/2015-2016/SUB-Informatics-2015-2016-8-001-017.pdf Intuitionistic fuzzy conjunctions and disjunctions from first type]. Annual of “Informatics” Section, Union of Scientists in Bulgaria, 8, 1–17.
# Angelova, N., & Stoenchev, M. (2017). [[Issue:Intuitionistic fuzzy conjunctions and disjunctions from third type|Intuitionistic fuzzy conjunctions and disjunctions from third type]]. Notes on Intuitionistic Fuzzy Sets, 23(5), 29–41.
# Angelova, N., & Stoenchev, M. (2017). [[Issue:Intuitionistic fuzzy conjunctions and disjunctions from third type|Intuitionistic fuzzy conjunctions and disjunctions from third type]]. Notes on Intuitionistic Fuzzy Sets, 23(5), 29–41.
# Atanassov, K. (2012). [[On Intuitionistic Fuzzy Sets Theory]]. Springer, Berlin.
# Atanassov, K. (2012). [[On Intuitionistic Fuzzy Sets Theory]]. Springer, Berlin.

Latest revision as of 12:54, 29 August 2024

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Title of paper: A new operation over intuitionistic fuzzy pairs
Author(s):
Velin Andonov
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, Sofia-1113, Bulgaria
Dept. of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
velin_andonov@math.bas.bg
Sławomir Zadrożny
Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
Slawomir.Zadrozny@ibspan.waw.pl
Lilija Atanassova
Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 2, Sofia-1113, Bulgaria
l.c.atanassova@gmail.com
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 28 (2022), Number 4, pages 436–441
DOI: https://doi.org/10.7546/nifs.2022.28.4.436-441
Download:  PDF (124  Kb, File info)
Abstract: The basic study of fuzzy sets theory was introduced by Lotfi Zadeh in 1965. Many authors investigated possibilities how two fuzzy sets can be compared and the most common kind of measures used in the mathematical literature are dissimilarity measures. The previous approach to the dissimilarities is too restrictive, because the third axiom in the definition of dissimilarity measure assumes the inclusion relation between fuzzy sets. While there exist many pairs of fuzzy sets, which are incomparable to each other with respect to the inclusion relation. Therefore we need some new concept for measuring a difference between fuzzy sets so that it could be applied for arbitrary fuzzy sets. We focus on the special class of so called local divergences. In the next part we discuss the divergences defined on more general objects, namely intuitionistic fuzzy sets. In this case we define the local property modified to this object. We discuss also the relation of usual divergences between fuzzy sets to the divergences between intuitionistic fuzzy sets.
Keywords: Intuitionistic fuzzy set, Dissimilarity measure, Divergence measure, Local divergence, Entropy measure.
AMS Classification: 03B52.
References:
  1. Angelova, N., & Stoenchev, M. (2015/2016). Intuitionistic fuzzy conjunctions and disjunctions from first type. Annual of “Informatics” Section, Union of Scientists in Bulgaria, 8, 1–17.
  2. Angelova, N., & Stoenchev, M. (2017). Intuitionistic fuzzy conjunctions and disjunctions from third type. Notes on Intuitionistic Fuzzy Sets, 23(5), 29–41.
  3. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory. Springer, Berlin.
  4. Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham.
  5. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13.
  6. Herrera-Viedma, E., Garcia-Lapresta, J. L., Kacprzyk, J., Fedrizzi, M., Nurmi, H., & Zadrożny, S. (Eds.) (2011). Consensual Processes, Springer.
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