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# Angelova, N. (2019). IFSTOOL - Software for intuitionistic fuzzy sets – Necessity, Possibility and Circle operators. Advances in Intelligent Systems and Computing,issue:1081, Springer, 76–81.
# Angelova, N. (2019). IFSTOOL - Software for intuitionistic fuzzy sets – Necessity, Possibility and Circle operators. Advances in Intelligent Systems and Computing,issue:1081, Springer, 76–81.
# Angelova, N., & Atanassov, K. (2015). Intuitionistic Fuzzy Implications and the Axioms of Intuitionistic Logic. In:Proc. of the 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1578–1584.
# Angelova, N., & Atanassov, K. (2015). Intuitionistic Fuzzy Implications and the Axioms of Intuitionistic Logic. In: Proc. of the 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1578–1584.
# Angelova, N., & Atanassov, K. (2016). Intuitionistic Fuzzy Implications and Klir-Yuan’s Axioms.Novel Developments in Uncertainty Representation and Processing. Advances in Intuitionistic Fuzzy Sets and Generalized Nets, Advances in Intelligent Systems and Computing, 401. Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., De Tr´e, G., Zadro˙zny, S. (Eds.), 97–110.
# Angelova, N., & Atanassov, K. (2016). Intuitionistic Fuzzy Implications and Klir-Yuan’s Axioms. Novel Developments in Uncertainty Representation and Processing. Advances in Intuitionistic Fuzzy Sets and Generalized Nets, Advances in Intelligent Systems and Computing, 401. Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., De Tre, G., Zadrozny, S. (Eds.), 97–110.
# Angelova, N., Marinov, E., & Atanassov, K. (2015). Intuitionistic fuzzy implications and Kolmogorov’s and Lukasiewisz–Tarski’s axioms of logic. Notes on Intuitionistic Fuzzy Sets, 21 (2), 35–42.
# Angelova, N., Marinov, E., & Atanassov, K. (2015). Intuitionistic fuzzy implications and Kolmogorov’s and Łukasiewicz–Tarski’s axioms of logic. Notes on Intuitionistic Fuzzy Sets, 21 (2), 35–42.
# Atanassov, K. (1988). Two variants of intuitonistc fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia.
# Atanassov, K. (1988). Two variants of intuitonistc fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia.
# Atanassov, K. (2005). On some intuitionistic fuzzy negations. Proc. of the First Int. Workshop on IFSs, Banska Bystrica, 22 Sept. 2005. Notes on Intuitionistic Fuzzy Sets, 11(6), 13–20.
# Atanassov, K. (2005). On some intuitionistic fuzzy negations. Proc. of the First Int. Workshop on IFSs, Banska Bystrica, 22 Sept. 2005. Notes on Intuitionistic Fuzzy Sets, 11(6), 13–20.
# Atanassov, K. (2006). On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, 59 (1), 19–24.
# Atanassov, K. (2006). On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, 59 (1), 19–24.
# Atanassov, K. (2006). A new intuitionistic fuzzy implication from a modal type. Advanced Studies on Contemporary Mathematics, 12 (1), 117–122.
# Atanassov, K. (2006). A new intuitionistic fuzzy implication from a modal type. Advanced Studies on Contemporary Mathematics, 12 (1), 117–122.
# Atanassov, K. (2006). On eight new intuitionistic fuzzy implications. Proc. of 3rd Int. IEEEConf. “Intelligent Systems” IS06, London, 4-6 Sept. 2006, 741–746.
# Atanassov, K. (2006). On eight new intuitionistic fuzzy implications. Proc. of 3rd Int. IEEE Conf. “Intelligent Systems” IS06, London, 4-6 Sept. 2006, 741–746.
# Atanassov, K. (2008). On intuitionistic fuzzy implication →<sup>ε</sup> and intuitionistic fuzzy negation ¬<sup>ε</sup>. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 6, 6–19.
# Atanassov, K. (2008). On intuitionistic fuzzy implication →<sup>ε</sup> and intuitionistic fuzzy negation ¬<sup>ε</sup>. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 6, 6–19.
# Atanassov, K. (2008). Intuitionistic fuzzy implication →<sup>ε,η</sup> and intuitionistic fuzzy negation ¬<sup>ε,η</sup>. Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, 1, 1–10.
# Atanassov, K. (2008). Intuitionistic fuzzy implication →<sup>ε,η</sup> and intuitionistic fuzzy negation ¬<sup>ε,η</sup>. Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, 1, 1–10.
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# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2015). On Fodor’s type of intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21 (2), 25–34.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2015). On Fodor’s type of intuitionistic fuzzy implication and negation. Notes on Intuitionistic Fuzzy Sets, 21 (2), 25–34.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2016). New Fodor’s Type Of Intuitionistic Fuzzy Implication and Negation. Notes on Intuitionistic Fuzzy Sets, 22 (3), 1–8.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2016). New Fodor’s Type Of Intuitionistic Fuzzy Implication and Negation. Notes on Intuitionistic Fuzzy Sets, 22 (3), 1–8.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). On intuitionistic fuzzy implication →<sub>187</sub>7. Notes on Intuitionistic Fuzzy Sets, 23 (2), 37–43.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). On intuitionistic fuzzy implication →<sub>187</sub>. Notes on Intuitionistic Fuzzy Sets, 23 (2), 37–43.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). On intuitionistic fuzzy implication →<sub>188</sub>7. Notes on Intuitionistic Fuzzy Sets, 23 (1), 6–13.
# Atanassov, K., Szmidt, E., & Kacprzyk, J. (2017). On intuitionistic fuzzy implication →<sub>188</sub>. Notes on Intuitionistic Fuzzy Sets, 23 (1), 6–13.
# Atanassov, K., Szmidt, E., Kacprzyk, J., & Angelova, N. (2019). Intuitionistic fuzzy implications revisited. Part 1. Notes on Intuitionistic Fuzzy Sets, 25(3), 71–78.
# Atanassov, K., Szmidt, E., Kacprzyk, J., & Angelova, N. (2019). Intuitionistic fuzzy implications revisited. Part 1. Notes on Intuitionistic Fuzzy Sets, 25(3), 71–78.
# Atanassov, K., & Trifonov, T. (2005). On a new intuitionistic fuzzy implication of Godel’s type. Proceedings of the Jangjeon Mathematical Society, 8 (2), 147–152.
# Atanassov, K., & Trifonov, T. (2005). On a new intuitionistic fuzzy implication of Godel’s type. Proceedings of the Jangjeon Mathematical Society, 8 (2), 147–152.
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# Atanassova, L. (2015) Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 61–67.
# Atanassova, L. (2015) Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 61–67.
# Atanassova, L. (2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, 22 (1), 1–6.
# Atanassova, L. (2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 3. Notes on Intuitionistic Fuzzy Sets, 22 (1), 1–6.
# Atanassova, L. (2017). Intuitionistic fuzzy implication !189. Notes on Intuitionistic Fuzzy Sets, 2 (1), 14–20.
# Atanassova, L. (2017). Intuitionistic fuzzy implication →<sub>189</sub>. Notes on Intuitionistic Fuzzy Sets, 2 (1), 14–20.
# Atanassova, L. (2017). Properties of the intuitionistic fuzzy implication !189. Notes on Intuitionistic Fuzzy Sets, 23 (4), 10–14.
# Atanassova, L. (2017). Properties of the intuitionistic fuzzy implication →<sub>189</sub>. Notes on Intuitionistic Fuzzy Sets, 23 (4), 10–14.
# Dworniczak, P. (2010). Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”. Cybernetics and Information Technologies, 10 (3), 3–9.
# Dworniczak, P. (2010). Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”. Cybernetics and Information Technologies, 10 (3), 3–9.
# Dworniczak, P. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, 10 (4), 13–21.
# Dworniczak, P. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, 10 (4), 13–21.

Latest revision as of 21:39, 21 August 2021

shortcut
http://ifigenia.org/wiki/issue:nifs/27/2/20-93
Title of paper: Research on intuitionistic fuzzy implications
Author(s):
Nora Angelova
Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
noraa@fmi.uni-sofia.bg
Krassimir Atanassov
Dept. of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, 105 Acad. G. Bonchev Str., 1113 Sofia, Bulgaria
Intelligent Systems Laboratory, Prof. Dr. Asen Zlatarov University, 8010 Burgas, Bulgaria
krat@bas.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 2, pages 20–93
DOI: https://doi.org/10.7546/nifs.2021.27.2.20-93
Download:  PDF (289  Kb, File info)
Abstract: Currently in the theories of intuitionistic fuzzy sets, logics and pairs, there are 198 different implications. Here, we check the relationships between every two of them.
Keywords: Intuitionistic fuzzy implication, Intuitionistic fuzzy pair, Intuitionistic fuzzy set.
References:
  1. Angelova, N. (2019). IFSTOOL - Software for intuitionistic fuzzy sets – Necessity, Possibility and Circle operators. Advances in Intelligent Systems and Computing,issue:1081, Springer, 76–81.
  2. Angelova, N., & Atanassov, K. (2015). Intuitionistic Fuzzy Implications and the Axioms of Intuitionistic Logic. In: Proc. of the 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 30.06-03.07.2015, Gijon, Spain, 1578–1584.
  3. Angelova, N., & Atanassov, K. (2016). Intuitionistic Fuzzy Implications and Klir-Yuan’s Axioms. Novel Developments in Uncertainty Representation and Processing. Advances in Intuitionistic Fuzzy Sets and Generalized Nets, Advances in Intelligent Systems and Computing, 401. Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., De Tre, G., Zadrozny, S. (Eds.), 97–110.
  4. Angelova, N., Marinov, E., & Atanassov, K. (2015). Intuitionistic fuzzy implications and Kolmogorov’s and Łukasiewicz–Tarski’s axioms of logic. Notes on Intuitionistic Fuzzy Sets, 21 (2), 35–42.
  5. Atanassov, K. (1988). Two variants of intuitonistc fuzzy propositional calculus. Preprint IM-MFAIS-5-88, Sofia.
  6. Atanassov, K. (2005). On some intuitionistic fuzzy negations. Proc. of the First Int. Workshop on IFSs, Banska Bystrica, 22 Sept. 2005. Notes on Intuitionistic Fuzzy Sets, 11(6), 13–20.
  7. Atanassov, K. (2006). On some intuitionistic fuzzy implications. Comptes Rendus de l’Academie bulgare des Sciences, 59 (1), 19–24.
  8. Atanassov, K. (2006). A new intuitionistic fuzzy implication from a modal type. Advanced Studies on Contemporary Mathematics, 12 (1), 117–122.
  9. Atanassov, K. (2006). On eight new intuitionistic fuzzy implications. Proc. of 3rd Int. IEEE Conf. “Intelligent Systems” IS06, London, 4-6 Sept. 2006, 741–746.
  10. Atanassov, K. (2008). On intuitionistic fuzzy implication →ε and intuitionistic fuzzy negation ¬ε. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 6, 6–19.
  11. Atanassov, K. (2008). Intuitionistic fuzzy implication →ε,η and intuitionistic fuzzy negation ¬ε,η. Developments in Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets and Related Topics, 1, 1–10.
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