Research Article
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Brief Review of Soft Sets and Its Application in Coding Theory

Year 2020, Issue: 33, 95 - 106, 31.12.2020
https://izlik.org/JA82EJ98ST

Abstract

In this paper, we will focus to one of the recent applications of PU-algebras in the coding theory, namely the construction of codes by soft sets PU-valued functions. First, we shall introduce the notion of soft sets PU-valued functions on PU-algebra and investigate some of its related properties. Moreover, the codes generated by a soft sets PU-valued function are constructed and several examples are given. Furthermore, example with graphs of binary block code constructed from a soft sets PU-valued function is constructed.

References

  • D. Molodtsov, Soft Set Theory-first Results, Computers and Mathematics with Applications 37 (1999) 19-31.
  • P. K. Maji, R. Biswas, A. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (4) (2003) 555-562.
  • P.K. Maji, R. Biswas, A.R. Roy, Fuzzy Soft Sets, Journal of Fuzzy Mathematics 9 (3) (2001) 589-602.
  • H. Aktaş, N. Çağman, Soft Sets and Soft Groups, Information Sciences 177 (2007) 2726-2735.
  • N. Çağman, S. Enginoğlu, FP-soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics 2 (2011) 219–226.
  • N. Çağman, S. Enginoğlu, Soft Set Theory and uni-int Decision Making, European Journal of Operational Research 207 (2) (2010) 848–855.
  • Y. B. Jun, C. H. Park, Applications of Soft Sets in Ideal Theory of BCK/BCI-algebras, Information Sciences 178 (2008) 2466-2475.
  • Y. B. Jun, K. J. Lee, J. Zhan, Soft p-ideals of Soft BCI-algebras, Computers and Mathematics with Applications 58 (2009) 2060-2068.
  • Y. B. Jun, K. J. Lee, C. H. Park, Fuzzy Soft Set Theory Applied to BCK/BCI-algebras, Computers and Mathematics with Applications 59 (2010) 3180-3192.
  • N. Wiberg, Codes and Decoding on General Graphs. Sweden: Department of Electrical Engineering, Linköping University (1996).
  • L. H. Encinas, Y. B. Jun, S. Z. Song, Codes Generated by R0-Algebra Valued Functions, Applied Mathematical Sciences 9(107) (2015) 5343-5352.
  • C. Flaut, Some Connections Between Binary Block Codes and Hilbert Algebras, in: Maturo A., Hošková-Mayerová Š., Soitu DT., Kacprzyk J. (eds) Recent Trends in Social Systems: Quantitative Theories and Quantitative Models. Studies in Systems, Decision and Control, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-319-40585-8_22
  • Y. B. Jun, S. Z. Song, Codes Based on BCK-algebras, Information Sciences, 181(22) (2011) 5102-5109.
  • A. B. Saeid, H. Fatemidokht, C. Flaut, M. K. Rafsanjani. On Codes based on BCK-algebras, Journal of Intelligent and Fuzzy Systems 29 (5) (2015) 2133-2137.
  • S. M. Mostafa, B. Youssef, H. A. Jad, Coding Theory Applied to KU-algebras, Journal of New Theory 6 (2015) 43-53.
  • S. M. Mostafa, B. A. B. Youssef, H. A. Jad, Efficient Algorithm for Constructing KU-algebras from Block Codes, International Journal of Engineering Science Invention 5(5) (2016) 32-43.
  • S. M. Mostafa, F. F. Kareem, H. A. Jad, Intersectional (α, A)-soft New Ideals in PU-algebras, Journal of New Theory 13 (2016) 38-48.

Year 2020, Issue: 33, 95 - 106, 31.12.2020
https://izlik.org/JA82EJ98ST

Abstract

References

  • D. Molodtsov, Soft Set Theory-first Results, Computers and Mathematics with Applications 37 (1999) 19-31.
  • P. K. Maji, R. Biswas, A. Roy, Soft Set Theory, Computers and Mathematics with Applications 45 (4) (2003) 555-562.
  • P.K. Maji, R. Biswas, A.R. Roy, Fuzzy Soft Sets, Journal of Fuzzy Mathematics 9 (3) (2001) 589-602.
  • H. Aktaş, N. Çağman, Soft Sets and Soft Groups, Information Sciences 177 (2007) 2726-2735.
  • N. Çağman, S. Enginoğlu, FP-soft Set Theory and Its Applications, Annals of Fuzzy Mathematics and Informatics 2 (2011) 219–226.
  • N. Çağman, S. Enginoğlu, Soft Set Theory and uni-int Decision Making, European Journal of Operational Research 207 (2) (2010) 848–855.
  • Y. B. Jun, C. H. Park, Applications of Soft Sets in Ideal Theory of BCK/BCI-algebras, Information Sciences 178 (2008) 2466-2475.
  • Y. B. Jun, K. J. Lee, J. Zhan, Soft p-ideals of Soft BCI-algebras, Computers and Mathematics with Applications 58 (2009) 2060-2068.
  • Y. B. Jun, K. J. Lee, C. H. Park, Fuzzy Soft Set Theory Applied to BCK/BCI-algebras, Computers and Mathematics with Applications 59 (2010) 3180-3192.
  • N. Wiberg, Codes and Decoding on General Graphs. Sweden: Department of Electrical Engineering, Linköping University (1996).
  • L. H. Encinas, Y. B. Jun, S. Z. Song, Codes Generated by R0-Algebra Valued Functions, Applied Mathematical Sciences 9(107) (2015) 5343-5352.
  • C. Flaut, Some Connections Between Binary Block Codes and Hilbert Algebras, in: Maturo A., Hošková-Mayerová Š., Soitu DT., Kacprzyk J. (eds) Recent Trends in Social Systems: Quantitative Theories and Quantitative Models. Studies in Systems, Decision and Control, vol 66. Springer, Cham. https://doi.org/10.1007/978-3-319-40585-8_22
  • Y. B. Jun, S. Z. Song, Codes Based on BCK-algebras, Information Sciences, 181(22) (2011) 5102-5109.
  • A. B. Saeid, H. Fatemidokht, C. Flaut, M. K. Rafsanjani. On Codes based on BCK-algebras, Journal of Intelligent and Fuzzy Systems 29 (5) (2015) 2133-2137.
  • S. M. Mostafa, B. Youssef, H. A. Jad, Coding Theory Applied to KU-algebras, Journal of New Theory 6 (2015) 43-53.
  • S. M. Mostafa, B. A. B. Youssef, H. A. Jad, Efficient Algorithm for Constructing KU-algebras from Block Codes, International Journal of Engineering Science Invention 5(5) (2016) 32-43.
  • S. M. Mostafa, F. F. Kareem, H. A. Jad, Intersectional (α, A)-soft New Ideals in PU-algebras, Journal of New Theory 13 (2016) 38-48.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Samy Mohammed Mostafa This is me 0000-0002-5069-2434

Fatema Faisal Kareem 0000-0002-6141-8721

Hussein Ali Jad This is me 0000-0002-3326-872X

Submission Date November 9, 2018
Publication Date December 31, 2020
IZ https://izlik.org/JA82EJ98ST
Published in Issue Year 2020 Issue: 33

Cite

APA Mostafa, S. M., Kareem, F. F., & Jad, H. A. (2020). Brief Review of Soft Sets and Its Application in Coding Theory. Journal of New Theory, 33, 95-106. https://izlik.org/JA82EJ98ST
AMA 1.Mostafa SM, Kareem FF, Jad HA. Brief Review of Soft Sets and Its Application in Coding Theory. JNT. 2020;(33):95-106. https://izlik.org/JA82EJ98ST
Chicago Mostafa, Samy Mohammed, Fatema Faisal Kareem, and Hussein Ali Jad. 2020. “Brief Review of Soft Sets and Its Application in Coding Theory”. Journal of New Theory, nos. 33: 95-106. https://izlik.org/JA82EJ98ST.
EndNote Mostafa SM, Kareem FF, Jad HA (December 1, 2020) Brief Review of Soft Sets and Its Application in Coding Theory. Journal of New Theory 33 95–106.
IEEE [1]S. M. Mostafa, F. F. Kareem, and H. A. Jad, “Brief Review of Soft Sets and Its Application in Coding Theory”, JNT, no. 33, pp. 95–106, Dec. 2020, [Online]. Available: https://izlik.org/JA82EJ98ST
ISNAD Mostafa, Samy Mohammed - Kareem, Fatema Faisal - Jad, Hussein Ali. “Brief Review of Soft Sets and Its Application in Coding Theory”. Journal of New Theory. 33 (December 1, 2020): 95-106. https://izlik.org/JA82EJ98ST.
JAMA 1.Mostafa SM, Kareem FF, Jad HA. Brief Review of Soft Sets and Its Application in Coding Theory. JNT. 2020;:95–106.
MLA Mostafa, Samy Mohammed, et al. “Brief Review of Soft Sets and Its Application in Coding Theory”. Journal of New Theory, no. 33, Dec. 2020, pp. 95-106, https://izlik.org/JA82EJ98ST.
Vancouver 1.Samy Mohammed Mostafa, Fatema Faisal Kareem, Hussein Ali Jad. Brief Review of Soft Sets and Its Application in Coding Theory. JNT [Internet]. 2020 Dec. 1;(33):95-106. Available from: https://izlik.org/JA82EJ98ST


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