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Step 1. Definition of fuzzy entropy.

The proposed definition evaluation based on fuzzy entropy is used to calculate the image definition value.

Moreover, in order to reduce computational cost, some authors have combined fuzzy selection mechanisms with genetic algorithms or even have introduced the concept of fuzzy entropy for selecting relevant features [ 44- 46].

Numerical stability is enhanced through semi-discrete satisfaction of global conservation properties stemming from the second law of thermodynamics and the entropy equation.

Then, two nonlinear parameters namely; K-Nearest Neighbour (K-NN) entropy estimator and Fuzzy Entropy (FzEn) are extracted from the decomposed sub-band signals.

[5], [7] The geometric structure of the unit hypercube and sets as points representation was chosen in order to develop these measures from the fuzzy subsethood theorem, and the fuzzy entropy theorem, measured in fuzzy cardinality.

From Eq. (2), we can know that the fuzzy entropy obtains the minimum value when the membership function ( {mu}_k ) is the maximum of 1 at f i, j) = k.

At the last step of the proposed method, an optimal threshold for discriminating main vessels of the retina from other parts of the tissue is achieved by employing fuzzy entropy.

Different from the Shannon entropy, which measures the randomness uncertainty (probabilistic), the fuzzy entropy contains vagueness and ambiguity uncertainties.

Fuzzy entropy is defined as a quantity measure of the fuzzy information gained from a fuzzy set or fuzzy system [17].

Fuzzy entropy is the entropy of a fuzzy set, loosely representing the information of uncertainty.

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