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Kolmogorov–Sinaj Entropy on MV-Algebras

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Abstract

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov–Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličký modification of the Kolmogorov–Sinaj entropy for fuzzy sets (Maličký and Riečan, 1986; Riečan and Mundici, 2002; Riečan and Neubrunn, 1997).

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References

  • Butnariu, D. and Klement, E. P. (1993). Triangular Norm/based Measures and Games with Fuzzy Conditions, Kluwer, Dordrecht.

    Google Scholar 

  • Dvurečenskij, A. (2000). Loomis–Sikorski theorem for σ-complete MV-algebras and l-groups. Journal of the Australian Mathematical Society Series A 68, 261–277.

    Google Scholar 

  • Dvurečenskij, A. and Pulmannová, S. (2000). New Trends in Quantum Structures, Kluwer, Dordrecht.

    Google Scholar 

  • Dvurečenskij, A. and Riečan, B. (1999). Weakly divisible MV-algebras and product. Journal of Mathematical Analysis and Applications 234, 208–222.

    MathSciNet  Google Scholar 

  • Goodearl, K. (1986). Partially Ordered Abelian Groups with Interpolation. Math, Surveys and Monographs No. 20, American Mathematical Society, Providence, Rhode Island.

    Google Scholar 

  • Maličký, P. and Riečan, B. (1986). On the entropy of dynamical systems. In Proc. Conf. Ergodic Theory and Related Topics II, H. Michel, ed., Teubner, Leipzig, pp. 135–138.

  • Marra, V. (2000). Every Abelian l-group is ultrasimplicial. Journal of Algebra 225, 872–884.

    Article  MATH  ISI  MathSciNet  Google Scholar 

  • Montagna, F. (2000). An algebraic approach to propositional fuzzy logic. Journal of Logic, Language and Information 9, 91–124.

    Article  MATH  MathSciNet  Google Scholar 

  • Mundici, D. (1986). Interpretation of AFC*-algebras in Lukasiewicz sentential calculus. Journal of Functional Analysis 65, 15–63.

    Article  MATH  ISI  MathSciNet  Google Scholar 

  • Mundici, D. (1999). Tensor products and the Loomis–Sikorski theorem for MV-algebras. Advanced Applied Mathematics 22, 227–248.

    MATH  MathSciNet  Google Scholar 

  • Petrovičová, J. (2000). On the entropy of partitions in product MV-algebras. Soft Computing 4, 41–44.

    Google Scholar 

  • Petrovičová, J. (2001). On the entropy of dynamical systems in product MV-algebras. Fuzzy Sets and Systems 121, 347–351.

    MathSciNet  Google Scholar 

  • Riečan, B. (1999). On the Product MV Algebras, Vol. 16, Tatra Mountains Mathematical Publications, pp. 143–149.

  • Riečan, B. and Mundici, D. (2002). Probability on MV-algebras. In Handbook of Measure Theory, E. Pap, ed., North Holland, Amsterdam, pp. 869–909.

  • Riečan, B. and Neubrunn, T. (1997). Integral, Measure, and Ordering, Kluwer, Dordrecht.

    Google Scholar 

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Correspondence to Beloslav Riečan.

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Riečan, B. Kolmogorov–Sinaj Entropy on MV-Algebras. Int J Theor Phys 44, 1041–1052 (2005). https://doi.org/10.1007/s10773-005-7080-9

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