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To this aim, we perform a threshold sensitivity analysis, as well as evaluate the homogeneity of clusters using the graph compactness and Adjusted Rand Index as metrics.
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The graph compactness (C p ) is a cluster validity index that indicates how 'compact' (or homogeneous) the clusters are, based on their intra-connectivity characteristics.
Then, using the concentration compactness principle, we get the compactness of { u n }.
Using the Aubin compactness lemma, we complete the proof.
Graphs were drawn using the yEd Graph Editor [ 57].
The measurement of spatial patterns is accomplished by using the indicators of compactness index and entropy.
Using the resulting graphs, Bentzen sequences the visual action.
MFA uses the intrinsic graph and the penalty graph to characterize the local structure in discriminant analysis and thus increases the intraclass compactness and interclass separability.
We use the concentration compactness principle (see [17, 18]) to overcome those difficulties.
We use the sequentially compactness of the set G we will define further.
By using the Hausdorff measure of non-compactness and under compactness type conditions, authors proved the existence of solution of fuzzy fractional integral equation.
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