Research Article
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Year 2026, Volume: 15 Issue: 1 , 15 - 28 , 30.04.2026
https://izlik.org/JA83LY47TG

Abstract

References

  • D. Molodstov, Soft set theory-first results, Computers and Mathematics with Applications 37 (4-5) (1999) 19–31.
  • H. Aktaş, N. Çağman, Soft sets and soft groups, Information Science 177 (13) (2007) 2726–2735.
  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications 59 (11) (2010) 3458–3463.
  • D. Singh, I. A. Onyeozili, On the ring structure of soft set theory, International Journal of Scientific and Technology Research 2 (3) (2013) 96–101.
  • Y. Yang, X. Xin, P. He, Applications of soft union sets in the ring theory, Journal of Applied Mathematics 2013 (1) (2013) 474890.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers Mathematics with Applications 44 (8-9) (2002) 1077–1083.
  • F. Fatimah, D. Rosadi, R. F. Hakim, J. C. R. Alcantud, Probabilistic soft sets and dual probabilistic soft sets in decision-making, Neural Computing and Applications 31 (1) (2019) 397–407.
  • Y. Liu, K. Qin, L. Mart´ınez, Improving decision making approaches based on fuzzy soft sets and rough soft sets, Applied Soft Computing 65 (2018) 320–332.
  • Y. B. Jun, C. H. Park, Applications of soft sets in Hilbert algebras, Iranian Journal of Fuzzy Systems 6 (2) (2009) 75–86.
  • P. Yadav, R. Singh, El-Algebra in soft sets, Journal of Algebraic Statistics 13 (2) (2022) 1455–1462.
  • J. Zhan, Y. B. Jun, Soft BL-algebras based on fuzzy sets, Computers and Mathematics with Applications 59 (6) (2010) 2037–2046.
  • N. Çağman, S. Karataş, S. Enginoglu, Soft topology, Computers and Mathematics with Applications 62 (1) (2011) 351–358.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın, On soft topology, El-Cezeri Journal of Science and Engineering 2 (3) (2015) 23–38.
  • Z. Li, T. Xie, The relationship among soft sets, soft rough sets and topologies, Soft Computing 18 (4) (2014) 717–728.
  • S. Singh, The code book: The science of secrecy from ancient Egypt to quantum cryptography, Doubleday, 1999.
  • D. Kahn, The codebreakers: The story of secret writing, Macmillan, 1967.
  • B. Schneier, Applied cryptography: Protocols, algorithms, and source code in C, 2nd Edition, John Wiley & Sons, 1996.
  • N. Çağman, Integer theory and applications (in Turkish: Tamsayılar teorisi ve uygulamaları), Kutlu Yayinevi, 2025.
  • A. Sinkov, Elementary cryptanalysis – A mathematical approach, Vol 22, 2nd Edition, The Mathematical Association of America, 1966.
  • C. Paar, J. Pelzl, Understanding cryptography: A textbook for students and practitioners, 1st Edition, Springer, 2010.
  • J. H. Silverman, J. Pipher, J. Hoffstein, An introduction to mathematical cryptography, 1st Edition, Springer, 2008.
  • W. Stallings, Cryptography and network security: Principles and practice, Global Edition, 8th Edition, Pearson, 2024.
  • F. Çifçi, Decomposed soft sets and soft encryption, Master’s Thesis Gaziosmanpaşa University (2024) Tokat.
  • N. Çağman, Contributions to the theory of soft sets, Journal of New Results in Science 3 (4) (2014) 33–41.
  • S. J. John, Soft sets, Soft Sets: Theory and Applications, Vol. 400 of Studies in Fuzziness and Soft Computing, Springer, 2021, pp. 3–36.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (4-5) (2003) 555–562.
  • N. Polat, Soft set theory applications: Time series as soft sets and ratio based similarity measure on soft sets, AIMS Mathematics 10 (9) (2025) 21994–22022.
  • N. Demirta¸s, O. Dalkılı¸c, Bipolar fuzzy soft set theory applied to medical diagnosis, Turkish Journal of Mathematics and Computer Science 16 (2) (2024) 314–324.

Partitioned Soft Sets and Their Application to Cryptology

Year 2026, Volume: 15 Issue: 1 , 15 - 28 , 30.04.2026
https://izlik.org/JA83LY47TG

Abstract

Soft set theory, introduced by Molodtsov in 1999, is a mathematical tool for dealing with uncertainty and vagueness in a parameterized way. Cryptology is a method of protecting information and communications so that only those for whom the information is intended can read and process it. In this article, we defined partitioned soft sets, which represent a new concept in soft set theory. Using these partitioned soft sets, we then constructed a new type of cipher method called a soft cipher. It is a variation of a cipher method. Finally, we developed a computer program with examples for the soft cipher method.

References

  • D. Molodstov, Soft set theory-first results, Computers and Mathematics with Applications 37 (4-5) (1999) 19–31.
  • H. Aktaş, N. Çağman, Soft sets and soft groups, Information Science 177 (13) (2007) 2726–2735.
  • U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Computers and Mathematics with Applications 59 (11) (2010) 3458–3463.
  • D. Singh, I. A. Onyeozili, On the ring structure of soft set theory, International Journal of Scientific and Technology Research 2 (3) (2013) 96–101.
  • Y. Yang, X. Xin, P. He, Applications of soft union sets in the ring theory, Journal of Applied Mathematics 2013 (1) (2013) 474890.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Computers Mathematics with Applications 44 (8-9) (2002) 1077–1083.
  • F. Fatimah, D. Rosadi, R. F. Hakim, J. C. R. Alcantud, Probabilistic soft sets and dual probabilistic soft sets in decision-making, Neural Computing and Applications 31 (1) (2019) 397–407.
  • Y. Liu, K. Qin, L. Mart´ınez, Improving decision making approaches based on fuzzy soft sets and rough soft sets, Applied Soft Computing 65 (2018) 320–332.
  • Y. B. Jun, C. H. Park, Applications of soft sets in Hilbert algebras, Iranian Journal of Fuzzy Systems 6 (2) (2009) 75–86.
  • P. Yadav, R. Singh, El-Algebra in soft sets, Journal of Algebraic Statistics 13 (2) (2022) 1455–1462.
  • J. Zhan, Y. B. Jun, Soft BL-algebras based on fuzzy sets, Computers and Mathematics with Applications 59 (6) (2010) 2037–2046.
  • N. Çağman, S. Karataş, S. Enginoglu, Soft topology, Computers and Mathematics with Applications 62 (1) (2011) 351–358.
  • S. Enginoğlu, N. Çağman, S. Karataş, T. Aydın, On soft topology, El-Cezeri Journal of Science and Engineering 2 (3) (2015) 23–38.
  • Z. Li, T. Xie, The relationship among soft sets, soft rough sets and topologies, Soft Computing 18 (4) (2014) 717–728.
  • S. Singh, The code book: The science of secrecy from ancient Egypt to quantum cryptography, Doubleday, 1999.
  • D. Kahn, The codebreakers: The story of secret writing, Macmillan, 1967.
  • B. Schneier, Applied cryptography: Protocols, algorithms, and source code in C, 2nd Edition, John Wiley & Sons, 1996.
  • N. Çağman, Integer theory and applications (in Turkish: Tamsayılar teorisi ve uygulamaları), Kutlu Yayinevi, 2025.
  • A. Sinkov, Elementary cryptanalysis – A mathematical approach, Vol 22, 2nd Edition, The Mathematical Association of America, 1966.
  • C. Paar, J. Pelzl, Understanding cryptography: A textbook for students and practitioners, 1st Edition, Springer, 2010.
  • J. H. Silverman, J. Pipher, J. Hoffstein, An introduction to mathematical cryptography, 1st Edition, Springer, 2008.
  • W. Stallings, Cryptography and network security: Principles and practice, Global Edition, 8th Edition, Pearson, 2024.
  • F. Çifçi, Decomposed soft sets and soft encryption, Master’s Thesis Gaziosmanpaşa University (2024) Tokat.
  • N. Çağman, Contributions to the theory of soft sets, Journal of New Results in Science 3 (4) (2014) 33–41.
  • S. J. John, Soft sets, Soft Sets: Theory and Applications, Vol. 400 of Studies in Fuzziness and Soft Computing, Springer, 2021, pp. 3–36.
  • P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (4-5) (2003) 555–562.
  • N. Polat, Soft set theory applications: Time series as soft sets and ratio based similarity measure on soft sets, AIMS Mathematics 10 (9) (2025) 21994–22022.
  • N. Demirta¸s, O. Dalkılı¸c, Bipolar fuzzy soft set theory applied to medical diagnosis, Turkish Journal of Mathematics and Computer Science 16 (2) (2024) 314–324.
There are 28 citations in total.

Details

Primary Language English
Subjects Symbolic Calculation, Mathematical Logic, Set Theory, Lattices and Universal Algebra
Journal Section Research Article
Authors

Naim Çağman 0000-0003-3037-1868

Fikret Çifçi 0009-0001-3661-3779

İbrahim Halil Kanat 0009-0000-6906-9020

Submission Date June 4, 2025
Acceptance Date February 10, 2026
Publication Date April 30, 2026
IZ https://izlik.org/JA83LY47TG
Published in Issue Year 2026 Volume: 15 Issue: 1

Cite

APA Çağman, N., Çifçi, F., & Kanat, İ. H. (2026). Partitioned Soft Sets and Their Application to Cryptology. Journal of New Results in Science, 15(1), 15-28. https://izlik.org/JA83LY47TG
AMA 1.Çağman N, Çifçi F, Kanat İH. Partitioned Soft Sets and Their Application to Cryptology. JNRS. 2026;15(1):15-28. https://izlik.org/JA83LY47TG
Chicago Çağman, Naim, Fikret Çifçi, and İbrahim Halil Kanat. 2026. “Partitioned Soft Sets and Their Application to Cryptology”. Journal of New Results in Science 15 (1): 15-28. https://izlik.org/JA83LY47TG.
EndNote Çağman N, Çifçi F, Kanat İH (April 1, 2026) Partitioned Soft Sets and Their Application to Cryptology. Journal of New Results in Science 15 1 15–28.
IEEE [1]N. Çağman, F. Çifçi, and İ. H. Kanat, “Partitioned Soft Sets and Their Application to Cryptology”, JNRS, vol. 15, no. 1, pp. 15–28, Apr. 2026, [Online]. Available: https://izlik.org/JA83LY47TG
ISNAD Çağman, Naim - Çifçi, Fikret - Kanat, İbrahim Halil. “Partitioned Soft Sets and Their Application to Cryptology”. Journal of New Results in Science 15/1 (April 1, 2026): 15-28. https://izlik.org/JA83LY47TG.
JAMA 1.Çağman N, Çifçi F, Kanat İH. Partitioned Soft Sets and Their Application to Cryptology. JNRS. 2026;15:15–28.
MLA Çağman, Naim, et al. “Partitioned Soft Sets and Their Application to Cryptology”. Journal of New Results in Science, vol. 15, no. 1, Apr. 2026, pp. 15-28, https://izlik.org/JA83LY47TG.
Vancouver 1.Naim Çağman, Fikret Çifçi, İbrahim Halil Kanat. Partitioned Soft Sets and Their Application to Cryptology. JNRS [Internet]. 2026 Apr. 1;15(1):15-28. Available from: https://izlik.org/JA83LY47TG

 

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