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The Concept of Entropy on D-Posets

Yıl 2013, Cilt: 10 Sayı: 1, - , 01.05.2013

Öz

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.

Kaynakça

  • [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.
Yıl 2013, Cilt: 10 Sayı: 1, - , 01.05.2013

Öz

Kaynakça

  • [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.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Mohamad Ebrahimi Bu kişi benim

Batool Mosapour Bu kişi benim

Yayımlanma Tarihi 1 Mayıs 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 10 Sayı: 1

Kaynak Göster

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. Mayıs 2013;10(1).
Chicago Ebrahimi, Mohamad, ve Batool Mosapour. “The Concept of Entropy on D-Posets”. Cankaya University Journal of Science and Engineering 10, sy. 1 (Mayıs 2013).
EndNote Ebrahimi M, Mosapour B (01 Mayıs 2013) The Concept of Entropy on D-Posets. Cankaya University Journal of Science and Engineering 10 1
IEEE M. Ebrahimi ve B. Mosapour, “The Concept of Entropy on D-Posets”, CUJSE, c. 10, sy. 1, 2013.
ISNAD Ebrahimi, Mohamad - Mosapour, Batool. “The Concept of Entropy on D-Posets”. Cankaya University Journal of Science and Engineering 10/1 (Mayıs 2013).
JAMA Ebrahimi M, Mosapour B. The Concept of Entropy on D-Posets. CUJSE. 2013;10.
MLA Ebrahimi, Mohamad ve Batool Mosapour. “The Concept of Entropy on D-Posets”. Cankaya University Journal of Science and Engineering, c. 10, sy. 1, 2013.
Vancouver Ebrahimi M, Mosapour B. The Concept of Entropy on D-Posets. CUJSE. 2013;10(1).