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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). [http://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., & Todorov, V. (2017). [[Issue:Intuitionistic fuzzy conjunctions and disjunctions from second type|Intuitionistic fuzzy conjunctions and disjunctions from second type]]. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 13, 143–170.
# Angelova, N., Stoenchev, M., & Todorov, V. (2017). Intuitionistic fuzzy conjunctions and disjunctions from second type. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 13, 143–170.
# 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. (1999). [[Intuitionistic Fuzzy Sets: Theory and Applications]], Springer, Heidelberg.
# Atanassov, K. (1999). [[Intuitionistic Fuzzy Sets: Theory and Applications]], Springer, Heidelberg.
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# Atanassov, K. (2019) On the intuitionistic fuzzy implication →<sub>191</sub>. Notes on Intuitionistic Fuzzy Sets, 25(4), 1–6.
# Atanassov, K. (2019) On the intuitionistic fuzzy implication →<sub>191</sub>. Notes on Intuitionistic Fuzzy Sets, 25(4), 1–6.
# Atanassov, K., Angelova, N., & Atanassova, V. (2021). On an Intuitionistic Fuzzy Form of the Goguen’s Implication. Mathematics 9(6), Article ID 676.
# Atanassov, K., Angelova, N., & Atanassova, V. (2021). On an Intuitionistic Fuzzy Form of the Goguen’s Implication. Mathematics 9(6), Article ID 676.
# Atanassov, K. (2021). Third Zadeh’s Intuitionistic Fuzzy Implication. Mathematics, 9(6), Article ID 619.
# Atanassov, K. (2021). [https://www.mdpi.com/2227-7390/9/6/619 Third Zadeh’s Intuitionistic Fuzzy Implication]. Mathematics, 9(6), Article ID 619.
# Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, 9(2), 21–25.
# Atanassova, L. (2009). [https://cit.iict.bas.bg/CIT_09/v9-2/21-25.pdf A new intuitionistic fuzzy implication]. Cybernetics and Information Technologies, 9(2), 21–25.
# Atanassova, L. (2009). [[On some properties of intuitionistic fuzzy negation ¬@|On some properties of intuitionistic fuzzy negation ¬<sub>@</sub>]]. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.
# Atanassova, L. (2009). [[Issue:On some properties of intuitionistic fuzzy negation ¬@|On some properties of intuitionistic fuzzy negation ¬<sub>@</sub>]]. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.
# Atanassova, L. (2012). [[Issue:On two modifications of the intuitionistic fuzzy implication →@|On two modifications of the intuitionistic fuzzy implication →<sub>@</sub>]]. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.
# Atanassova, L. (2012). [[Issue:On two modifications of the intuitionistic fuzzy implication →@|On two modifications of the intuitionistic fuzzy implication →<sub>@</sub>]]. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.
# Atanassova, L. (2013). On the modal form of the intuitionistic fuzzy implications →'<sub>@</sub> and →"<sub>@</sub>. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 10, 5–11.
# Atanassova, L. (2013). On the modal form of the intuitionistic fuzzy implications →'<sub>@</sub> and →"<sub>@</sub>. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 10, 5–11.
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# Atanassova, L. (2015/2016). [[Issue:Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2|Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2]]. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 61–67.
# Atanassova, L. (2015/2016). [[Issue:Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2|Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2]]. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 61–67.
# Chen, J., & Kundu, S. (1996). A sound and complete fuzzy logic system using Zadeh’s implication operator. Lecture Notes in Computer Science, 1079, 233–242.
# Chen, J., & Kundu, S. (1996). A sound and complete fuzzy logic system using Zadeh’s implication operator. Lecture Notes in Computer Science, 1079, 233–242.
# 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). [https://cit.iict.bas.bg/CIT_2010/v10-3/3-9.pdf 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). [https://cit.iict.bas.bg/CIT_2010/v10-4/13-21.pdf On one class of intuitionistic fuzzy implications]. Cybernetics and Information Technologies, 10(4), 13–21.
# Dworniczak, P. (2011). [[Issue:On some two-parametric intuitionistic fuzzy implications|On some two-parametric intuitionistic fuzzy implications]]. Notes on Intuitionistic Fuzzy Sets, 17(2), 8–16.
# Dworniczak, P. (2011). [[Issue:On some two-parametric intuitionistic fuzzy implications|On some two-parametric intuitionistic fuzzy implications]]. Notes on Intuitionistic Fuzzy Sets, 17(2), 8–16.
# Feys, R. (1965). Modal logics, Gauthier-Villars, Paris.
# Feys, R. (1965). Modal logics, Gauthier-Villars, Paris.
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# Mendelson, E. (1964). Introduction to Mathematical Logic, D. Van Nostrand, Princeton, New Jersey.
# Mendelson, E. (1964). Introduction to Mathematical Logic, D. Van Nostrand, Princeton, New Jersey.
# Rasiova, H., & Sikorski, R.(1963). The Mathematics of Metamathematics, Pol. Acad. of Sci., Warszawa.
# Rasiova, H., & Sikorski, R.(1963). The Mathematics of Metamathematics, Pol. Acad. of Sci., Warszawa.
# Vassilev, P., & Atanassov, K. (2019). Extensions and Modifications of Intuitionistic Fuzzy Sets, “Prof. Marin Drinov” Academic Publishing House, Sofia.
# Vassilev, P., & Atanassov, K. (2019). [[Extensions and Modifications of Intuitionistic Fuzzy Sets]], “Prof. Marin Drinov” Academic Publishing House, Sofia.
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Latest revision as of 21:01, 25 June 2021

shortcut
http://ifigenia.org/wiki/issue:nifs/27/1/9-23
Title of paper: Modifications of the Third Zadeh’s intuitionistic fuzzy implication
Author(s):
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
Nora Angelova
Faculty of Mathematics and Informatics, Sofia University, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria
noraa@fmi.uni-sofia.bg
Published in: Notes on Intuitionistic Fuzzy Sets, Volume 27 (2021), Number 1, pages 9–23
DOI: https://doi.org/10.7546/nifs.2021.27.1.9-23
Download:  PDF (151  Kb, File info)
Abstract: In [24], G. Klir and B. Yuan named after L. Zadeh the implication p → q = max(1 − p, min(p, q)). In a series of papers, the author introduced two intuitionistic fuzzy forms of Zadeh’s implication and their basic properties have been studied. In the present paper, a new (third) intuitionistic fuzzy form of Zadeh’s implication is given and some of its properties are studied.
Keywords: Intuitionistic fuzzy implication, Intuitionistic fuzzy set, Zadeh’s fuzzy implication.
AMS Classification: 03E72
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., & Todorov, V. (2017). Intuitionistic fuzzy conjunctions and disjunctions from second type. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 13, 143–170.
  3. Angelova, N., & Stoenchev, M. (2017). Intuitionistic fuzzy conjunctions and disjunctions from third type. Notes on Intuitionistic Fuzzy Sets, 23(5), 29–41.
  4. Atanassov, K. (1999). Intuitionistic Fuzzy Sets: Theory and Applications, Springer, Heidelberg.
  5. Atanassov, K. (2006). On some intuitionistic fuzzy implication. Comptes Rendus de l’Academie bulgare des Sciences, 59(1), 21–26.
  6. Atanassov, K. (2006). A new intuitionistic fuzzy implication from a modal type. Advanced Studies in Contemporary Mathematics, 12(1), 117–122.
  7. Atanassov, K. (2011). Second Zadeh's intuitionistic fuzzy implication. Notes on Intuitionistic Fuzzy Sets, 17(3), 11–14.
  8. Atanassov, K. (2012). On Intuitionistic Fuzzy Sets Theory, Springer, Berlin.
  9. Atanassov, K. (2017). Intuitionistic Fuzzy Logics, Springer, Cham.
  10. Atanassov, K. (2019) On the intuitionistic fuzzy implication →191. Notes on Intuitionistic Fuzzy Sets, 25(4), 1–6.
  11. Atanassov, K., Angelova, N., & Atanassova, V. (2021). On an Intuitionistic Fuzzy Form of the Goguen’s Implication. Mathematics 9(6), Article ID 676.
  12. Atanassov, K. (2021). Third Zadeh’s Intuitionistic Fuzzy Implication. Mathematics, 9(6), Article ID 619.
  13. Atanassova, L. (2009). A new intuitionistic fuzzy implication. Cybernetics and Information Technologies, 9(2), 21–25.
  14. Atanassova, L. (2009). On some properties of intuitionistic fuzzy negation ¬@. Notes on Intuitionistic Fuzzy Sets, 15(1), 32–35.
  15. Atanassova, L. (2012). On two modifications of the intuitionistic fuzzy implication →@. Notes on Intuitionistic Fuzzy Sets, 18(2), 26–30.
  16. Atanassova, L. (2013). On the modal form of the intuitionistic fuzzy implications →'@ and →"@. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 10, 5–11.
  17. Atanassova, L. (2015). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 1. Notes on Intuitionistic Fuzzy Sets, 21(3), 18–23.
  18. Atanassova, L. (2015/2016). Remark on Dworniczak’s intuitionistic fuzzy implications. Part 2. Issues in Intuitionistic Fuzzy Sets and Generalized Nets, 12, 61–67.
  19. Chen, J., & Kundu, S. (1996). A sound and complete fuzzy logic system using Zadeh’s implication operator. Lecture Notes in Computer Science, 1079, 233–242.
  20. Dworniczak, P. (2010). Some remarks about the L. Atanassova’s paper “A new intuitionistic fuzzy implication”. Cybernetics and Information Technologies, 10(3), 3–9.
  21. Dworniczak, P. (2010). On one class of intuitionistic fuzzy implications. Cybernetics and Information Technologies, 10(4), 13–21.
  22. Dworniczak, P. (2011). On some two-parametric intuitionistic fuzzy implications. Notes on Intuitionistic Fuzzy Sets, 17(2), 8–16.
  23. Feys, R. (1965). Modal logics, Gauthier-Villars, Paris.
  24. Klir, G., & Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic, Prentice Hall, New Jersey.
  25. Mendelson, E. (1964). Introduction to Mathematical Logic, D. Van Nostrand, Princeton, New Jersey.
  26. Rasiova, H., & Sikorski, R.(1963). The Mathematics of Metamathematics, Pol. Acad. of Sci., Warszawa.
  27. Vassilev, P., & Atanassov, K. (2019). Extensions and Modifications of Intuitionistic Fuzzy Sets, “Prof. Marin Drinov” Academic Publishing House, Sofia.
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