Abstract
In this paper the notion of a relative metric space, as a mathematical model compatible with a physical phenomena, is considered. The notion of relative topological entropy for relative semi-dynamical systems on a relative metric space is studied. It is proved that observational topological entropy is an invariant object up to a relative conjugate relation.
Keywords
Observer Relative structure Molecular lattice Relative topology Observational topological entropy 2000 AMS Classification: 37 B 40
References
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- Rahmat, M. R. S. and Noorani, M. S. M., Product of fuzzy metric spaces and fixed point theorems, Int. J. Contemp. Math. Sciences 3 (15), 703–712, 2008.
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- Rao, K. P. R., Babu, G. R. and Fisher, B. Common fixed point theorems in fuzzy metric spaces under implicit relations, Hacet. J. Math. Stat. 37 (2), 97–106, 2008.
- Ray, A. D. and Saha, P. K. Fixed point theorems on generalized fuzzy metric spaces, Hacet. J. Math. Stat. 39 (1), 1–9, 2010.
- Sostak, A. Two decades of fuzzy topology: Basic ideas, notions and results, Russian Math- ematical Surveys 44 (6), 125–186, 1989.
- Wang, G. J. Theory of topological molecular lattices, Fuzzy Sets and Systems 47 (3), 351– , 1992.
- Zadeh, L. A. Fuzzy sets, Inform. and Control 8, 338–353, 1965.
Abstract
References
- George, A. and Veeramani, P. On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90, 365–368, 1997.
- Liu, B. A survay of entropy of fuzzy varables, Journal of Uncertain Systems 1 (1), 4–13, Liu, B. Some research problems in uncertainty theory, Journal of Uncertain Systems, 3 (1), –10, 2009.
- Molaei, M. R. Observational modeling of topological spaces, Chaos, Solitons and Fractals 42, –619, 2009.
- Molaei, M. R. Mathematical modeling of observers in physical systems, Journal of Dynamical Systems and Geometric Theories 4 (2), 183–186, 2006.
- Molaei, M. R. Relative semi-dynamical systems, International Journal of Uncertainty, Fuzzi- ness and Knowledge-Based Systems, 12 (2), 237–243, 2004.
- Molaei, M. R. and Hoseini Anvari, M. R. Relative manifolds, Intelligent Automation and Soft Computing 14 (2), 219–226, 2008.
- Molaei, M. R., Hoseini Anvari, M. R. and Haqiri, T. On relative semi-dynamical systems, Intelligent Automation and Soft Computing, 13 (4), 405–413, 2007.
- Petr, H. Metamathematics of Fuzzy Logic (Dordrecht: Kluwer, ISBN 0792352389, 1998).
- Rahmat, M. R. S. and Noorani, M. S. M., Product of fuzzy metric spaces and fixed point theorems, Int. J. Contemp. Math. Sciences 3 (15), 703–712, 2008.
- Ramadan, A. A. and Abd El-latif, A. A. Supra fuzzy convergence of fuzzy filters, Bull. Korean Math. Soc. 45, 207–220, 2008.
- Rao, K. P. R., Babu, G. R. and Fisher, B. Common fixed point theorems in fuzzy metric spaces under implicit relations, Hacet. J. Math. Stat. 37 (2), 97–106, 2008.
- Ray, A. D. and Saha, P. K. Fixed point theorems on generalized fuzzy metric spaces, Hacet. J. Math. Stat. 39 (1), 1–9, 2010.
- Sostak, A. Two decades of fuzzy topology: Basic ideas, notions and results, Russian Math- ematical Surveys 44 (6), 125–186, 1989.
- Wang, G. J. Theory of topological molecular lattices, Fuzzy Sets and Systems 47 (3), 351– , 1992.
- Zadeh, L. A. Fuzzy sets, Inform. and Control 8, 338–353, 1965.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | May 1, 2011 |
| Published in Issue | Year 2011 Volume: 40 Issue: 5 |