Issue:A new operation over intuitionistic fuzzy pairs

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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: 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. (2017). 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. (2017). Intuitionistic Fuzzy Logics, Springer, Cham. Atanassov, K., Szmidt, E., & Kacprzyk, J. (2013). On intuitionistic fuzzy pairs. Notes on Intuitionistic Fuzzy Sets, 19(3), 1–13. Herrera-Viedma, E., Garcia-Lapresta, J. L., Kacprzyk, J., Fedrizzi, M., Nurmi, H., & Zadrożny, S. (Eds.) (2011). Consensual Processes, Springer. 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.