Araştırma Makalesi

ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION

Cilt: 5 Sayı: 2 31 Temmuz 2022
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EN

ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION

Öz

The concept of an Intuitionistic Fuzzy Set (IFS) was introduced in 1983 in \cite{ITKR} and again there in it, the first definition of operation intuitionistic fuzzy negation over IFS was introduced. Later, in \cite{IFPC}, two forms of the operation intuitionistic fuzzy implication were introduced. As of the 2000s, more than 200 different implications and more than 50 different negations arise and in [5 -- 21, 23, 24], their basic properties were discussed. In \cite{e,ee}, two negations, namely $\ep$-negation and $(\ep,\eta)$-negation, were introduced and over their bases $\ep$- and $(\ep,\eta)$-implications were defined, respectively. It was shown that the $(\ep,\eta)$-negation and $(\ep,\eta)$-implication are extensions of the $\ep$-negation and $\ep$-implication, respectively.

Anahtar Kelimeler

Destekleyen Kurum

european regional development fund

Proje Numarası

UNITe BG05M2OP001-1.001-0004 /28. 02.2018 (2018-2023).

Kaynakça

  1. \bibitem{ITKR} Atanassov, K. Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.). Reprinted: \textit{Int. J. Bioautomation}, 2016, 20(S1), S1-S6. \bibitem{IFPC} Atanassov K., Two variants of intuitionistic fuzzy propositional calculus.\textit{Preprint IM-MFAIS-5-88}, Sofia, 1988. Reprinted: \textit{Int. J. Bioautomation}, 2016, 20(S1), S17-S26.
  2. \bibitem{e} Atanassov, K. On intuitionistic fuzzy implication $\ri^{\ep}$ and intuitionistic fuzzy negation $\neg^{\ep}$. \textit{Issues in Intuitionistic Fuzzy Sets and Generalized Nets}, Vol. 6, 2008, 6-19.
  3. \bibitem{ee} Atanassov, K. Intuitionistic fuzzy implication $\riee$ and intuitionistic fuzzy negation $\nee$. \textit{Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics}, Vol. 1, 2008, 1-10. \bibitem{Spr2} Atanassov, K. (2012) \textit{On Intuitionistic Fuzzy Sets Theory}, Springer, Berlin. \bibitem{Spr4} Atanassov, K. (2017) \textit{Intuitionistic Fuzzy Logics}, Springer, Cham.
  4. \bibitem{L1} Atanassova, L. (2008). On an intuitionistic fuzzy implication from Kleene-Dienes type. \textit{Proceedings of the Jangjeon Mathematical Society}, 11 (1), 69-74.
  5. \bibitem{L4} Atanassova, L. (2008). Modifications of an intuitionistic fuzzy implication from Kleene--Dienes type. \textit{Advanced Studies in Contemporary Mathematics}, 16 (2), 155-160.
  6. \bibitem{L5} Atanassova, L. (2008). New modifications of an intuitionistic fuzzy implication from Kleene--Dienes type. Part 2. \textit{Annual of Section ``Informatics"}, 1, 59-64.
  7. \bibitem{L6} Atanassova, L. (2009). New modifications of an intuitionistic fuzzy implication from Kleene--Dienes type. Part 3. \textit{Advanced Studies in Contemporary Mathematics}, 18 (1), 33-40.
  8. \bibitem{L8} Atanassova, L. (2009). A new intuitionistic fuzzy implication, \textit{Cybernetics and Information Technologies}, 9 (2), 21-25. \bibitem{L9} Atanassova, L. (2009). On some properties of intuitionistic fuzzy negation $\neg_@$, \textit{Notes on Intuitionistic Fuzzy Sets}, 15 (1), 32-35.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

31 Temmuz 2022

Gönderilme Tarihi

22 Haziran 2022

Kabul Tarihi

27 Temmuz 2022

Yayımlandığı Sayı

Yıl 2022 Cilt: 5 Sayı: 2

Kaynak Göster

APA
Atanassov, K. T. (2022). ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION. Journal of Universal Mathematics, 5(2), 51-60. https://doi.org/10.33773/jum.1134441
AMA
1.Atanassov KT. ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION. JUM. 2022;5(2):51-60. doi:10.33773/jum.1134441
Chicago
Atanassov, Krassimir T. 2022. “ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION”. Journal of Universal Mathematics 5 (2): 51-60. https://doi.org/10.33773/jum.1134441.
EndNote
Atanassov KT (01 Temmuz 2022) ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION. Journal of Universal Mathematics 5 2 51–60.
IEEE
[1]K. T. Atanassov, “ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION”, JUM, c. 5, sy 2, ss. 51–60, Tem. 2022, doi: 10.33773/jum.1134441.
ISNAD
Atanassov, Krassimir T. “ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION”. Journal of Universal Mathematics 5/2 (01 Temmuz 2022): 51-60. https://doi.org/10.33773/jum.1134441.
JAMA
1.Atanassov KT. ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION. JUM. 2022;5:51–60.
MLA
Atanassov, Krassimir T. “ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION”. Journal of Universal Mathematics, c. 5, sy 2, Temmuz 2022, ss. 51-60, doi:10.33773/jum.1134441.
Vancouver
1.Krassimir T. Atanassov. ON NEW INTUITIONISTIC FUZZY(\ep,η)-NEGATION AND (\ep,η)-IMPLICATION. JUM. 01 Temmuz 2022;5(2):51-60. doi:10.33773/jum.1134441