A note on the fuzzy Xor

Radosław Łukasik

Published: 2025-11-15

2024

A note on the fuzzy Xor

Radosław Łukasik

Abstract

In this paper we will try to answer what conditions must be met by the fuzzy Xor to be used for cryptographic purposes. We will also show that defining the fuzzy Xor using other fuzzy connectives is not suitable for this purpose.

Keywords:

fuzzy Xor , fuzzy implication , fuzzy negation , t-norm , t-conorm

Download files

PDF

Citation rules

Łukasik, R. (2025). A note on the fuzzy Xor. Annales Mathematicae Silesianae. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/22867

Licence

This work is licensed under a Creative Commons Attribution 4.0 International License.

The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

License
This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
Author’s Warranties
The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
User Rights
Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
Co-Authorship
If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.

Similar Articles

Rajab Ali Borzooei, Gholam Reza Rezaei, Young Bae Jun, Fuzzy weak filters of Sheffer stroke Hilbert algebras , Annales Mathematicae Silesianae: Vol. 37 No. 2 (2023)
Silvestru Sever Dragomir, Hypo-q-norms on a cartesian product of algebras of operators on Banach spaces , Annales Mathematicae Silesianae: Vol. 34 No. 2 (2020)
Milena Carolina dos Santos Mangueira, Renata Passos Machado Vieira, Francisco Régis Vieira Alves, Paula Maria Machado Cruz Catarino, The hybrid numbers of Padovan and some identities , Annales Mathematicae Silesianae: Vol. 34 No. 2 (2020)
Eszter Gselmann, On approximate n-Jordan homomorphisms , Annales Mathematicae Silesianae: Vol. 28 (2014)
Małgorzata Wróbel, On functions of bounded n-th variation , Annales Mathematicae Silesianae: Vol. 15 (2001)
Tomasz Łukasz Żynda, On weights which admit harmonic Bergman kernel and minimal solutions of Laplace's equation , Annales Mathematicae Silesianae: Vol. 36 No. 2 (2022)

You may also start an advanced similarity search for this article.

References

M. Baczyński and B. Jayaram, Fuzzy Implications, Studies in Fuzziness and Soft Computing, Vol. 231, Springer-Verlag, Berlin, 2008.
Google Scholar

B.C. Bedregal, R.H.S. Reiser, and G.P. Dimuro, Xor-implications and E-implications: classes of fuzzy implications based on fuzzy Xor, Electron. Notes Theor. Comput. Sci. 247 (2009), 5–18.
Google Scholar

B.C. Bedregal, R.H.S. Reiser, and G.P. Dimuro, Revisiting Xor-implications: classes of fuzzy (co)implications based on f-Xor (f-XNor) connectives, Internat. J. Uncertain. Fuzziness Knowledge-Based Systems 21 (2013), no. 6, 899–925.
Google Scholar

G. Bongiovanni and P. Penna, XOR-based schemes for fast parallel IP lookups, Theory Comput. Syst. 38 (2005), no. 4, 481–501.
Google Scholar

E.G. Codding and G. Horlick, Application of AND and exclusive-or (XOR) logic operations to the identification of elemental emission spectra measured using a photodiode array direct reading spectrometer, Appl. Spectrosc. 27 (1973), no. 5, 366–370.
Google Scholar

M.M. Gupta, A. Kandel, W. Bandler, and J.B. Kiszka (Eds.), Approximate Reasoning in Expert Systems, North-Holland Publishing Co., Amsterdam, 1985.
Google Scholar

Y. Horikawa, Landscapes of basins of local minima in the XOR problem, in: Proceedings of 1993 International Conference on Neural Networks (IJCNN-93-Nagoya, Japan), IEEE, 1993, pp. 1677–1680.
Google Scholar

L. Kohout and E. Kim, Characterization of interval fuzzy logic systems of connectives by group transformations, Reliab. Comput. 10 (2004), no. 4, 299–334.
Google Scholar

A.G. Konheim, Computer Security and Cryptography, John Wiley & Sons, Inc., Hoboken, 2007.
Google Scholar

M. Maeda, M. Suenaga, and H. Miyajima, Qubit neuron according to quantum circuit for XOR problem, Appl. Math. Comput. 185 (2007), no. 2, 1015–1025.
Google Scholar

C.F. Mela and D.R. Lehmann, Using fuzzy set theoretic techniques to identify preference rules from interactions in the linear model: an empirical study, Fuzzy Sets and Systems 71 (1995), no. 2, 165–181.
Google Scholar

N.D. Mermin, Quantum Computer Science. An Introduction, Cambridge University Press, Cambridge, 2007.
Google Scholar

W. Pedrycz and G. Succi, fXOR fuzzy logic networks, Soft Comput. 7 (2002), no. 2, 115–120.
Google Scholar

C. Shannon, Communication theory of secrecy systems, Bell System Tech. J. 28 (1949), 656–715.
Google Scholar

W. Stallings, Cryptography and Network Security. Principles and Practice, Prentice Hall, Upper Saddle River, 1999.
Google Scholar

H. Vandierendonck and K. De Bosschere, XOR-based hash functions, IEEE Trans. Comput. 54 (2005), no. 7, 800–812.
Google Scholar

H. Vandierendonck, P. Manet, and J.-D. Legat, Application-specific reconfigurable XOR-indexing to eliminate cache conflict misses, in: Proceedings of the Design Automation & Test in Europe Conference, IEEE, 2006, pp. 357–362.
Google Scholar

2024
Published: 2024-01-18

ISSN: 0860-2107

eISSN: 2391-4238

10.2478/amsil

Publisher

University of Silesia Press

Licence CC

This work is licensed under a Creative Commons Attribution 4.0 International License.

Submit