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Brief Review of Soft Sets and Its Application in Coding Theory

Year 2020, Issue: 33, 95 - 106, 31.12.2020

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

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 This is me 0000-0002-6141-8721

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

Publication Date December 31, 2020
Submission Date November 9, 2018
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.
AMA Mostafa SM, Kareem FF, Jad HA. Brief Review of Soft Sets and Its Application in Coding Theory. JNT. December 2020;(33):95-106.
Chicago Mostafa, Samy Mohammed, Fatema Faisal Kareem, and Hussein Ali Jad. “Brief Review of Soft Sets and Its Application in Coding Theory”. Journal of New Theory, no. 33 (December 2020): 95-106.
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 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, December 2020.
ISNAD Mostafa, Samy Mohammed et al. “Brief Review of Soft Sets and Its Application in Coding Theory”. Journal of New Theory 33 (December 2020), 95-106.
JAMA 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, 2020, pp. 95-106.
Vancouver Mostafa SM, Kareem FF, Jad HA. Brief Review of Soft Sets and Its Application in Coding Theory. JNT. 2020(33):95-106.


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