Source code for neurokit2.complexity.entropy_fuzzy

# -*- coding: utf-8 -*-
from .entropy_approximate import entropy_approximate
from .entropy_sample import entropy_sample




def entropy_fuzzy(signal, delay=1, dimension=2, tolerance="sd", approximate=False, **kwargs):
    """**Fuzzy Entropy (FuzzyEn)**

    Fuzzy entropy (FuzzyEn) of a signal stems from the combination between information theory and
    fuzzy set theory (Zadeh, 1965). A fuzzy set is a set containing elements with varying degrees of
    membership.

    This function can be called either via ``entropy_fuzzy()`` or ``complexity_fuzzyen()``, or
    ``complexity_fuzzyapen()`` for its approximate version. Note that the fuzzy corrected
    approximate entropy (cApEn) can also be computed via setting ``corrected=True`` (see examples).

    Parameters
    ----------
    signal : Union[list, np.array, pd.Series]
        The signal (i.e., a time series) in the form of a vector of values.
    delay : int
        Time delay (often denoted *Tau* :math:`\\tau`, sometimes referred to as *lag*) in samples.
        See :func:`complexity_delay` to estimate the optimal value for this parameter.
    dimension : int
        Embedding Dimension (*m*, sometimes referred to as *d* or *order*). See
        :func:`complexity_dimension` to estimate the optimal value for this parameter.
    tolerance : float
        Tolerance (often denoted as *r*), distance to consider two data points as similar. If
        ``"sd"`` (default), will be set to :math:`0.2 * SD_{signal}`. See
        :func:`complexity_tolerance` to estimate the optimal value for this parameter.
    approximate : bool
        If ``True``, will compute the fuzzy approximate entropy (FuzzyApEn).
    **kwargs
        Other arguments.

    Returns
    ----------
    fuzzyen : float
        The fuzzy entropy of the single time series.
    info : dict
        A dictionary containing additional information regarding the parameters used
        to compute fuzzy entropy.

    See Also
    --------
    entropy_sample

    Examples
    ----------
    ..ipython:: python

      import neurokit2 as nk

      signal = nk.signal_simulate(duration=2, frequency=5)

      fuzzyen, parameters = nk.entropy_fuzzy(signal)
      fuzzyen

      fuzzyapen, parameters = nk.entropy_fuzzy(signal, approximate=True)
      fuzzyapen

      fuzzycapen, parameters = nk.entropy_fuzzy(signal, approximate=True, corrected=True)
      fuzzycapen


    References
    ----------
    * Ishikawa, A., & Mieno, H. (1979). The fuzzy entropy concept and its application. Fuzzy Sets
      and systems, 2(2), 113-123.
    * Zadeh, L. A. (1996). Fuzzy sets. In Fuzzy sets, fuzzy logic, and fuzzy systems: selected
      papers by Lotfi A Zadeh (pp. 394-432).

    """
    if approximate is False:
        out = entropy_sample(
            signal,
            delay=delay,
            dimension=dimension,
            tolerance=tolerance,
            fuzzy=True,
            **kwargs,
        )
    else:
        out = entropy_approximate(
            signal,
            delay=delay,
            dimension=dimension,
            tolerance=tolerance,
            fuzzy=True,
            **kwargs,
        )
    return out