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Wajsberg algebras arising from binary block codes

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Abstract

In this paper, we presented some connections between BCK commutative bounded algebras, MV-algebras, Wajsberg algebras and binary block codes. Using connections between these three algebras, we will associate to each of them a binary block code and, in some circumstances, we will prove that the converse is also true.

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References

  • Abujabal HAS, Aslam M, Thaheem AB (1996) A representation of bounded commutative BCK-algebras. Intern J Math Math Sci 19(4):733–736

    Article  MathSciNet  Google Scholar 

  • Buşneag D (2006) Categories of algebraic logic. Editura Academiei Române, Bucuresti

    MATH  Google Scholar 

  • Chang CC (1958) Algebraic analysis of many-valued logic. Trans Am Math Soc 88:467–490

    Article  MathSciNet  Google Scholar 

  • Cignoli RLO, Ottaviano IMLD, Mundici D (2000) Algebraic foundations of many-valued reasoning. Trends in logic, studia logica library. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  • Cignoli R, Torell AT (1996) Boolean products of MV-algebras: hypernormal MV-algebras. J Math Anal Appl 199:637–653

    Article  MathSciNet  Google Scholar 

  • Flaut C (2015) BCK-algebras arising from block codes. J Intell Fuzzy Syst 28(4):1829–1833

    Article  MathSciNet  Google Scholar 

  • Flaut C (2017) Some connections between binary blockcodes and hilbert algebras. In: Maturo A et al (eds) Recent trends in social systems: quantitative theories and quantitative models. Springer, Berlin, pp 249–256

    Chapter  Google Scholar 

  • Font JM, Rodriguez AJ, Torrens A (1984) Wajsberg Algebras. Stochastica 8(1):5–30

    MathSciNet  MATH  Google Scholar 

  • Gaitan H (1990) About quasivarieties of p-algebras and Wajsberg algebras. Retrospective Theses and Dissertations, 9440. https://lib.dr.iastate.edu/rtd/9440

  • Höhle U, Rodabaugh SE (1999) Mathematics of fuzzy sets: logic, topology and measure theory. Springer, Berlin

    Book  Google Scholar 

  • Imai Y, Iseki K (1966) On axiom systems of propositional calculi. Proc Jpn Acad 42:19–22

    Article  MathSciNet  Google Scholar 

  • Iorgulescu A (2008) Algebras of logic as BCK algebras. Editura ASE, Bucureşti

    MATH  Google Scholar 

  • Jun YB (2003) Satisfactory filters of BCK-algebras. Scientiae Mathematicae Japonicae 9:1–7

    Google Scholar 

  • Jun YB, Song SZ (2011) Codes based on BCK-algebras. Inf Sci 181:5102–5109

    Article  MathSciNet  Google Scholar 

  • Meng J, Jun YB (1994) BCK-algebras. Kyung Moon Sa Co., Seoul

    MATH  Google Scholar 

  • Mundici D (2007) MV-algebras-a short tutorial. University of Florence, Department of Mathematics Ulisse Dini

  • Piciu D (2007) Algebras of fuzzy logic. Editura Universitaria, Craiova

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, Ovidius University of Constanţa, Constanţa, Romania

    Cristina Flaut

  2. Doctoral School of Mathematics, Ovidius University of Constanţa, Constanţa, Romania

    Radu Vasile

Authors
  1. Cristina Flaut
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  2. Radu Vasile
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Correspondence to Cristina Flaut.

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Communicated by A. Di Nola.

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Flaut, C., Vasile, R. Wajsberg algebras arising from binary block codes. Soft Comput 24, 6047–6058 (2020). https://doi.org/10.1007/s00500-019-04653-5

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  • DOI: https://doi.org/10.1007/s00500-019-04653-5

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