Markov chain lumpability on fuzzy partitions

IEEE International Conference on Fuzzy Systems

Volumn , Issue , 2007, Pages

  Gerontidis, Ioannis I ^a   Kontakos, Stavros P ^a  

^a TECHNOLOGICAL EDUCATIONAL INSTITUTE OF KAVALA   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

FUZZY LOGIC; FUZZY SYSTEMS; STATE SPACE METHODS;

ASYMPTOTIC BEHAVIORS; CLASSICAL THEORY; FUZZY PARTITIONING; HOMOGENOUS MARKOV CHAIN; INTERNATIONAL CONFERENCES; LUMPABILITY; MARKOV CHAINS; MARKOV PROPERTY; NECESSARY AND SUFFICIENT CONDITIONS; STATE SPACES; STOCHASTIC SYSTEMS; TRANSITION PROBABILITIES;

MARKOV PROCESSES;

EID: 50249159678     PISSN: 10987584     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/FUZZY.2007.4295387     Document Type: Conference Paper

References (14)

1. D. R. Barr and M. U. Thomas, "An eigenvector condition for Markov chain lumpability," Operations Research, vol. 25, no 6, pp. 1028-1031, 1977.
2. J. C. Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, New York, Plenum, 1981, pp. 15-28.
3. J. C. Bezdek and J. D. Harris, "Convex decompositions of fuzzy partitions," Journal of Mathematical Analysis and Applications, vol.67, pp.490-512, 1979.
4. M. Bhattacharyya, "Fuzzy Markovian decision process," Fuzzy Sets and Systems, vol.99, pp. 273-282, 1998.
5. P. Bu chholz, "Exact and ordinary lumpability in finite Markov chains," Journal of Applied Probability, vol.31, pp. 59-75, 1994.
6. C. J. Burke and M. Rosenblatt, "A Markovian function of a Markov chain," Annals of Mathematical Statistics, vol.29, pp. 1112-1122, 1958.
7. M. Iosifescu, Finite Markov Processes and Their Applications, Chichester, Wiley, 1980, pp.213-233.
8. J. G. Kemeny and J.L. Snell, Finite Markov Chains, New York, Springer-Verlag, 1976, pp. 123-140.
9. E. Raspini, "A new approach to clustering," Information and Control, vol.15, pp. 22-32, 1969.
10. R. T. Rockafellar, Convex Analysis, New Jersey, Princeton University Press, 1997, pp.153-161.
11. G. Rubino and B. Sericola, "A finite characterization of weak lumpable Markov chains, Part I: The discrete time case" Stochastic Processes and Their Applications, vol.38, pp. 195-204, 1991.
12. U. Sumita and M. Rieders, "Lumpability and time reversibility in the aggregation-disaggregation method for large Markov chains," Communications in Statistics-Stochastic Models, vol. 5, pp. 63-81, 1989.
13. L. A. Zadeh, "Fuzzy sets," Information and Control, vol.8, pp. 338-353, 1965.
14. L. A. Zadeh, "Probability measures of fuzzy events," Journal of Mathematical Analysis and Applications, vol.23, pp. 421-427, 1968.