Fuzzy Optimization and Decision Making

, Volume 9, Issue 4, pp 383–412 | Cite as

A mixture of fuzzy filters applied to the analysis of heartbeat intervals

  • Mohit Kumar
  • Matthias Weippert
  • Norbert Stoll
  • Regina Stoll


This study provides a stochastic modeling of the heartbeat intervals using a mixture of Takagi–Sugeno type fuzzy filters. The model parameters are inferred under variational Bayes (VB) framework. The model of the heartbeat intervals is in the form of a history-dependent probability density. The parameters, characterizing the heartbeat intervals probability density, include the estimated parameters of different fuzzy filters and may serve as the features of the heartbeat interval series. The features of the heartbeat intervals provide a description of the physiological state of an individual. A novelty of our analysis method is that the physiological state is predicted as a part of the features extraction procedure. This is done via deriving, using VB paradigm, an analytical expression for the posterior distribution that the observed heartbeat intervals have been generated by the stochastic model of the physiological state. The method is illustrated with the data of 40 healthy subjects studied in a tilt-table experiment.


Fuzzy filtering R–R interval Heart rate variability Variational Bayes Probability distribution 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Mohit Kumar
    • 1
  • Matthias Weippert
    • 2
  • Norbert Stoll
    • 3
  • Regina Stoll
    • 2
  1. 1.Center for Life Science AutomationRostockGermany
  2. 2.Institute of Preventive MedicineRostockGermany
  3. 3.Institute of AutomationRostockGermany

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