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The Concept of Entropy on D-Posets

Year 2013, Volume: 10 Issue: 1, - , 01.05.2013

Abstract

In this paper, partition and entropy of partitions in a D-poset are introduced
and their properties are investigated. Also we introduce the conditional entropy and then
we study some their results. At the end we define the entropy of a dynamical system, we
prove some results on that, and we show its invariance.

References

  • [1] D. Dubois and H. Prade, A review of fuzzy set aggregation connectives, Information Science 36 (1985), 85–121.
  • [2] A. Dvurecenskij and S. Pulmannova, Difference posets, effects, and quantum measurements, International Journal of Theoretical Physics 33 (1994), 819–850.
  • [3] D. Dumitrescu, Fuzzy partitions with the connectives T∞, S∞, Fuzzy Sets and Systems 47 (1992), 193–195.
  • [4] M. Ebrahimi and U. Mohamadi, m-Generators of fuzzy dynamical systems, C¸ ankaya University Journal of Science and Engineering 9 (2012), 167–182.
  • [5] D. J. Foulis and M. K. Bennett, Effect algebras and unsharp quantum logics, Foundations of Physics 24 (1994), 1331–1352.
  • [6] M. Khare and S. Roy, Conditional entropy and the Rokhlin metric on an orthomodular lattice with Bayessian state, International Journal of Theoretical Physics 47 (2008), 1386–1396.
  • [7] M. Khare and S. Roy, Entropy of quantum dynamical systems and sufficient families in orthomodular lattices with Bayessian state, Communications in Theoretical Physics 50 (2008), 551–556.
  • [8] F. Kopka and F. Chovanec, D-posets, Mathematica Slovaca 44 (1994), 21–34.
  • [9] G. Kalmbach, Orthomodular Lattices, Academic Press, London, 1983.
  • [10] M. Kalina, V. Olejcek and J. Paseka, Sharply dominating MV -effect algebras, International Journal of Theoretical Physics 50 (2011), 1152–1159.
  • [11] D. Markechova, The entropy of complete fuzzy partitions, Mathematica Slovaca 43 (1993), 1–10.
  • [12] T. Neubrunn and B. Riecan, Miera a integral, Veda, Bratislava 1981 (in Slovak).
  • [13] J. Petrovicova, On the entropy of partitions in product MV algebra, Soft Computing 4 (2000), 41–44.
  • [14] J. Petrovicova, On the entropy of dynamical systems in product MV algebras, Fuzzy Sets and Systems 121 (2001), 347–351.
  • [15] P. Ptak and S. Pulmannova, Orthomodular Structures as Quantum Logics, VEDA and Kluwer Acad. Publ., Bratislava and Dordrecht 1991.
  • [16] B. Riecan, Kolmogorov-Sinaj entropy on MV -algebras, International Journal of Theoretical Physics 44 (2005), 1041–1052.
  • [17] B. Riecan and D. Markechova, The entropy of fuzzy dynamical systems, general scheme and generators, Fuzzy Sets and Systems 96 (1998), 191–199.
  • [18] J. Rybarik, The entropy of partitions on MV -algebras, International Journal of Theoretical Physics 39 (2000), 885–892.
  • [19] P. Walters, An Introduction to Ergodic Theory, Springer, New York, Berlin 1982.
  • [20] J. Wang, J. Wu and M. Cho, Entropy of partitions on sequential effect algebras, Communications in Theoretical Physics 53 (2010), 399–402.
  • [21] H. Yuan, Entropy of partitions on quantum logic, Communications in Theoretical Physics 43 (2005), 437–439.
  • [22] Y. Zhao and Z. Ma, Conditional entropy of partitions on quantum logic, Communications in Theoretical Physics 48 (2007), 11–13.
Year 2013, Volume: 10 Issue: 1, - , 01.05.2013

Abstract

References

  • [1] D. Dubois and H. Prade, A review of fuzzy set aggregation connectives, Information Science 36 (1985), 85–121.
  • [2] A. Dvurecenskij and S. Pulmannova, Difference posets, effects, and quantum measurements, International Journal of Theoretical Physics 33 (1994), 819–850.
  • [3] D. Dumitrescu, Fuzzy partitions with the connectives T∞, S∞, Fuzzy Sets and Systems 47 (1992), 193–195.
  • [4] M. Ebrahimi and U. Mohamadi, m-Generators of fuzzy dynamical systems, C¸ ankaya University Journal of Science and Engineering 9 (2012), 167–182.
  • [5] D. J. Foulis and M. K. Bennett, Effect algebras and unsharp quantum logics, Foundations of Physics 24 (1994), 1331–1352.
  • [6] M. Khare and S. Roy, Conditional entropy and the Rokhlin metric on an orthomodular lattice with Bayessian state, International Journal of Theoretical Physics 47 (2008), 1386–1396.
  • [7] M. Khare and S. Roy, Entropy of quantum dynamical systems and sufficient families in orthomodular lattices with Bayessian state, Communications in Theoretical Physics 50 (2008), 551–556.
  • [8] F. Kopka and F. Chovanec, D-posets, Mathematica Slovaca 44 (1994), 21–34.
  • [9] G. Kalmbach, Orthomodular Lattices, Academic Press, London, 1983.
  • [10] M. Kalina, V. Olejcek and J. Paseka, Sharply dominating MV -effect algebras, International Journal of Theoretical Physics 50 (2011), 1152–1159.
  • [11] D. Markechova, The entropy of complete fuzzy partitions, Mathematica Slovaca 43 (1993), 1–10.
  • [12] T. Neubrunn and B. Riecan, Miera a integral, Veda, Bratislava 1981 (in Slovak).
  • [13] J. Petrovicova, On the entropy of partitions in product MV algebra, Soft Computing 4 (2000), 41–44.
  • [14] J. Petrovicova, On the entropy of dynamical systems in product MV algebras, Fuzzy Sets and Systems 121 (2001), 347–351.
  • [15] P. Ptak and S. Pulmannova, Orthomodular Structures as Quantum Logics, VEDA and Kluwer Acad. Publ., Bratislava and Dordrecht 1991.
  • [16] B. Riecan, Kolmogorov-Sinaj entropy on MV -algebras, International Journal of Theoretical Physics 44 (2005), 1041–1052.
  • [17] B. Riecan and D. Markechova, The entropy of fuzzy dynamical systems, general scheme and generators, Fuzzy Sets and Systems 96 (1998), 191–199.
  • [18] J. Rybarik, The entropy of partitions on MV -algebras, International Journal of Theoretical Physics 39 (2000), 885–892.
  • [19] P. Walters, An Introduction to Ergodic Theory, Springer, New York, Berlin 1982.
  • [20] J. Wang, J. Wu and M. Cho, Entropy of partitions on sequential effect algebras, Communications in Theoretical Physics 53 (2010), 399–402.
  • [21] H. Yuan, Entropy of partitions on quantum logic, Communications in Theoretical Physics 43 (2005), 437–439.
  • [22] Y. Zhao and Z. Ma, Conditional entropy of partitions on quantum logic, Communications in Theoretical Physics 48 (2007), 11–13.
There are 22 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Mohamad Ebrahimi This is me

Batool Mosapour This is me

Publication Date May 1, 2013
Published in Issue Year 2013 Volume: 10 Issue: 1

Cite

APA Ebrahimi, M., & Mosapour, B. (2013). The Concept of Entropy on D-Posets. Cankaya University Journal of Science and Engineering, 10(1).
AMA Ebrahimi M, Mosapour B. The Concept of Entropy on D-Posets. CUJSE. May 2013;10(1).
Chicago Ebrahimi, Mohamad, and Batool Mosapour. “The Concept of Entropy on D-Posets”. Cankaya University Journal of Science and Engineering 10, no. 1 (May 2013).
EndNote Ebrahimi M, Mosapour B (May 1, 2013) The Concept of Entropy on D-Posets. Cankaya University Journal of Science and Engineering 10 1
IEEE M. Ebrahimi and B. Mosapour, “The Concept of Entropy on D-Posets”, CUJSE, vol. 10, no. 1, 2013.
ISNAD Ebrahimi, Mohamad - Mosapour, Batool. “The Concept of Entropy on D-Posets”. Cankaya University Journal of Science and Engineering 10/1 (May 2013).
JAMA Ebrahimi M, Mosapour B. The Concept of Entropy on D-Posets. CUJSE. 2013;10.
MLA Ebrahimi, Mohamad and Batool Mosapour. “The Concept of Entropy on D-Posets”. Cankaya University Journal of Science and Engineering, vol. 10, no. 1, 2013.
Vancouver Ebrahimi M, Mosapour B. The Concept of Entropy on D-Posets. CUJSE. 2013;10(1).