A Heuristic Approach to Possibilistic Clustering: Algorithms by Dmitri A. Viattchenin

By Dmitri A. Viattchenin

The current ebook outlines a brand new method of possibilistic clustering within which the sought clustering constitution of the set of items relies without delay at the formal definition of fuzzy cluster and the possibilistic memberships are made up our minds at once from the values of the pairwise similarity of items. The proposed process can be utilized for fixing assorted category difficulties. right here, a few options that would be worthwhile at this function are defined, together with a technique for developing a suite of categorized gadgets for a semi-supervised clustering set of rules, a strategy for lowering analyzed characteristic house dimensionality and a tools for uneven facts processing. furthermore, a method for developing a subset of the main acceptable possible choices for a collection of susceptible fuzzy choice kinfolk, that are outlined on a universe of choices, is defined intimately, and a style for quickly prototyping the Mamdani’s fuzzy inference platforms is brought. This booklet addresses engineers, scientists, professors, scholars and post-graduate scholars, who're attracted to and paintings with fuzzy clustering and its applications

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Extra info for A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

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89) is taken as the optimal number c of fuzzy clusters. The partition entropy is similar to the partition coefficient and an optimal classification provides a minimal value for the validity measure. The partition entropy is defined as follows: 1 c n V pe ( P ) = −   u li ⋅ ln u li . 90) Thus, the partition coefficient and the partition entropy are bounded in such a way that conditions 1 с ≤ V pc ( P ) ≤ 1 and 0 ≤ V pe ( P ) ≤ ln с are met. In the second place, Xie and Beni proposed in [158] a well-known validity index which measures the overall average compactness against the separation of the fuzzy c -partition.

So, the problem of classification boils down to the construction of a hierarchy of crisp clusters based  on the fuzzy relation T . Third, a fuzzy divisive hierarchical (FDH) clustering method has been proposed by Dumitrescu [34] and a multilevel fuzzy classification is obtained from the corresponding FDH-algorithm. Therefore, each fuzzy partition is a refinement of the fuzzy partition which corresponds to the previous level of classification. Since the FDH-algorithm produces a hierarchy of fuzzy clusters, the clustering procedure is essentially different from both the previously considered hierarchical clustering methods based on fuzzy relations which yield hierarchies of crisp clusters.

O On the other hand, this notiion allows to save values of the membership functioon which can be interpreteed as the degree possession of an object xi ∈ X oof properties of class which h is associated with the corresponding fuzzy cluster Al , l ∈ {1,  , c} . It is should be noted that the approach is simple and more usefu ful than oftwo previous meethods of the interpretationof fuzzy clustering resullts because the membership values v of objects are saved. The notion of α -corees of fuzzy clusters can be explained by the followinng simple example [128].

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