Modal Type of Weak Intuitionistic Fuzzy Implications Generated by the Operation Δ

Dworniczak, Piotr; Atanassova, Lilija; Angelova, Nora

doi:10.2478/cait-2021-0047

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Modal Type of Weak Intuitionistic Fuzzy Implications Generated by the Operation Δ

Cybernetics and Information Technologies

Volume 21 (2021): Issue 4 (December 2021)

By: Piotr Dworniczak , Lilija Atanassova and Nora Angelova

Open Access

|Dec 2021

Abstract

In 2020 L. Atanassova has been introduced the new operation Δ over intuitionistic fuzzy sets and over intuitionistic fuzzy pairs. Some of its properties have been studied in 2021 from L. Atanassova and P. Dworniczak. In 2021 L. Atanassova and P. Dworniczak generated an intuitionistic fuzzy implication by the operation Δ, and it has been introduced and some of its basic properties have been described. Here, eight modal type of intuitionistic fuzzy implications are generated by the first one and some of their properties are discussed.

References

1. Atanassov, K. Intuitionistic Fuzzy Sets. Springer, Heidelberg, 1999.10.1007/978-3-7908-1870-3
Search in Google Scholar Back to article
2. Atanassov, K. On Intuitionistic Fuzzy Sets Theory. Springer, Berlin, 2012.10.1007/978-3-642-29127-2
Search in Google Scholar Back to article
3. Atanassov, K. Intuitionistic Fuzzy Logics. Springer, Cham, 2017.10.1007/978-3-319-48953-7
Search in Google Scholar Back to article
4. Atanassov, K. T., E. Szmidt, J. Kacprzyk. On Intuitionistic Fuzzy Pairs. – Notes on Intuitionistic Fuzzy Sets, Vol. 19, 2013, No 3, pp. 1-13.
Search in Google Scholar Back to article
5. Atanassova, L. A New Operator over Intuitionistic Fuzzy Sets. – Notes on Intuitionistic Fuzzy Sets, Vol. 26, 2020, No 1, pp. 23-28.10.7546/nifs.2020.26.3.1-12
Search in Google Scholar Back to article
6. Atanassova, L., P. Dworniczak. On the Operation Δ over Intuitionistic Fuzzy Sets. – Mathematics, Vol. 9, 2021, No 13, p. 1518.10.3390/math9131518
Search in Google Scholar Back to article
7. Atanassova, L., P. Dworniczak. On the Weak Intuitionistic Fuzzy Implication Based on Δ Operation. – Notes on Intuitionistic Fuzzy Sets, Vol. 27, 2021, No 2, pp. 11-19.10.7546/nifs.2021.27.2.11-19
Search in Google Scholar Back to article
8. Feys, R. Modal Logics. Gauthier-Villars, Paris, 1965.
Search in Google Scholar Back to article
9. Klir, G., B. Yuan. Fuzzy Sets and Fuzzy Logic. Prentice Hall, New Jersey, 1995.10.1109/45.468220
Search in Google Scholar Back to article
10. Mendelson, E. Introduction to Mathematical Logic. 6th Ed. CRC Press, Boca Raton, FL, USA, 2015.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/cait-2021-0047 | Journal eISSN: 1314-4081 | Journal ISSN: 1311-9702

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Language: English

Page range: 137 - 144

Submitted on: Jul 31, 2021

Accepted on: Oct 4, 2021

Published on: Dec 9, 2021

Published by: Bulgarian Academy of Sciences, Institute of Information and Communication Technologies

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Intuitionistic fuzzy implication,

intuitionistic fuzzy operation,

intuitionistic fuzzy operator

Related subjects:

Computer sciences,

Information technology

© 2021 Piotr Dworniczak, Lilija Atanassova, Nora Angelova, published by Bulgarian Academy of Sciences, Institute of Information and Communication Technologies
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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