The Concept of Entropy on D-Posets
Year 2013,
Volume: 10 Issue: 1, - , 01.05.2013
Mohamad Ebrahimi
Batool Mosapour
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
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- [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
Mohamad Ebrahimi
Batool Mosapour
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.