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Fuzzy membership value for Markov states.
Generally, the degree of membership value for each fuzzy variable is decided based on experimentation.
And if X falls in the high region the membership values for high region would be: Δ 1 = X − High − Point 1 N P ; Δ 2 = High − Point 2 N P − X. and slope S 1 = 1 ( High − Point 3 N P − High − Point 1 N P ). if ((Δ1 ≤ 0) or (Δ2 ≤ 0)) then the membership value for high region would be High − Me m N P = 0. else High − Me m N P = min ( Δ 1 × S 1, Max ).
The resulting fuzzy segmentation can be converted to a hard or crisp segmentation by assigning each pixel solely to the class that has the highest membership value for that pixel.
As shown in Additional file 1: Appendix 3, Figure A3.3, most observations in the test set have relatively low prediction residuals from HC-PLSR, and the mean prediction error (taken over the 200 time steps) decreases as the distance from the nearest cluster centre decreases (increasing membership value for most probable cluster).
To accomplish this, we had to choose from a collection of analytical curves to fit the points in the most accurate way possible (MATLAB Software, The MathWorks, Inc .. Our discrete set gives rise to a continuous domain, thus letting us get a membership value for "any" value of the variable (see all of them in Figure 1).
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These rules will be maintained by Boolean value either 0 or 1 and the corresponding membership values for each rule is calculated from the decision module by using max − min product form.
Membership values for each gene in the corresponding cluster can be found in Table S2.
Moreover, the membership values for the clusters can be used to determine the level of coregulation under consideration.
c-means clustering computes membership values for each tile towards all the clusters and all the membership values add up to 1.
In contrast to crisp clustering methods, such as K-means clustering, which allocate each observation to a unique cluster, fuzzy clustering returns membership values for the different clusters for each observation [ 45].
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