| Title:
|
On the entropy and generators of dynamical systems (English) |
| Author:
|
Riečan, Beloslav |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
161-168 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Recently D. Dumitrescu ([4], [5]) introduced a new kind of entropy of dynamical systems using fuzzy partitions ([1], [6]) instead of usual partitions (see also [7], [11], [12]). In this article a representation theorem is proved expressing the entropy of the dynamical system by the entropy of a generating partition. (English) |
| Keyword:
|
entropy of dynamical systems |
| Keyword:
|
fuzzy partitions |
| Keyword:
|
entropy of generating partition |
| MSC:
|
28D20 |
| idZBL:
|
Zbl 0863.28014 |
| idMR:
|
MR1382463 |
| DOI:
|
10.21136/AM.1996.134319 |
| . |
| Date available:
|
2009-09-22T17:50:55Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134319 |
| . |
| Reference:
|
[1] J. L. Bezdek: Pattern Recognition with Fuzzy Objective Function Algorithms.Plenum Press, New York, 1981. Zbl 0503.68069, MR 0631231 |
| Reference:
|
[2] P. Billingsley: Ergodic Theory and Information.Willey, New York, 1965. Zbl 0141.16702, MR 0192027 |
| Reference:
|
[3] D. Butnariu, E. P. Klement: Triangular norm-based measures and their Markov kernel representation.J. Math. Anal. Appl. 169 (1991), 111–143. MR 1135265, 10.1016/0022-247X(91)90181-X |
| Reference:
|
[4] D. Dumitrescu: Measure preserving transformation and the entropy of fuzzy partition.13th Linz seminar on fuzzy set theory (Linz 1991), 25–27. |
| Reference:
|
[5] D. Dumitrescu: Fuzzy measures and the entropy of fuzzy partitions.J. Math. Anal. Appl. 176 (1993), 359–373. Zbl 0782.28012, MR 1224152, 10.1006/jmaa.1993.1220 |
| Reference:
|
[6] K. Kuriyama: Entropy of a finite partition of fuzzy sets.J. Math. Anal. Appl. 94 (1983), 38–43. Zbl 0511.94030, MR 0701448, 10.1016/0022-247X(83)90004-5 |
| Reference:
|
[7] P. Maličký, B. Riečan: On the entropy of dynamical systems.Proc. Ergodic theory and related topics II (Georgenthal 1986), Teubner, Berlin, 1987, 135–138. MR 0931138 |
| Reference:
|
[8] D. Markechová: The entropy of $F$-quantum spaces.Math. Slovaca 40 (1990), 177–190. MR 1094772 |
| Reference:
|
[9] D. Markechová: The entropy of fuzzy dynamical systems and generators.Fuzzy Sets and Systems 48 (1992), 351–363. MR 1178175, 10.1016/0165-0114(92)90350-D |
| Reference:
|
[10] R. Mesiar: The Bayes formula and the entropy of fuzzy probability spaces.Int. J. General Systems 20 (1990), 67–71. 10.1080/03081079108945015 |
| Reference:
|
[11] B. Riečan: On a type of entropy of dynamical systems.Tatra Mountains Math. Publications. |
| Reference:
|
[12] D. J. Rudolph: Fundamentals of Measurable Dynamics.Claredon Press, Oxford, 1990. Zbl 0718.28008, MR 1086631 |
| Reference:
|
[13] J. Rybárik: The entropy of $Q$-$F$-dynamical systems.Busefal 48 (1991), 24–26. |
| . |
