By Dmitri A. Viattchenin

ISBN-10: 3642355358

ISBN-13: 9783642355356

ISBN-10: 3642355366

ISBN-13: 9783642355363

The current publication outlines a brand new method of possibilistic clustering during 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 method can be utilized for fixing diversified class difficulties. right here, a few thoughts that may be priceless at this goal are defined, together with a strategy for developing a collection of classified items for a semi-supervised clustering set of rules, a technique for lowering analyzed characteristic area dimensionality and a equipment for uneven info processing. furthermore, a strategy for developing a subset of the main applicable choices for a collection of susceptible fuzzy choice family, that are outlined on a universe of possible choices, is defined intimately, and a mode for speedily prototyping the Mamdani’s fuzzy inference structures is brought. This ebook addresses engineers, scientists, professors, scholars and post-graduate scholars, who're drawn to and paintings with fuzzy clustering and its applications

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**Example text**

90) can be used for validation in these cases. On the other hand, the indirect indices can be modified for the relational clustering algorithms in each concrete case. 89) was modified by Roubens [95] as follows: m c n c u li2 − n . 95) should be maximized. Some other validity measures for the FNM-algorithm were proposed by Libert and Roubens [72] and [73]. 91) is appropriate for the ARCA-algorithm, because the ARCA-algorithm, though being a relational clustering algorithm, generates prototypes.

120) with the number of fuzzy clusters c = 2 and the weighting exponent value ψ = 2 . The PCM-algorithm was performed with the initialization of cluster centers: τ 1 = (60, 150) and τ 2 = (145, 150) . Thus, the objects x1 and x9 were selected as the initialization of cluster centres. 8 and the values which equal to zero are not shown in the figure. The membership values of the first class are represented by ○ and the membership values of the second class are represented by ■. 3 Methods of Possibilistiic Clustering 551 Fig.

2 Basic Methods of Fuzzy Clustering 25 Xˆ n×m1 = [ xˆ it1 ] , i = 1, , n , t1 = 1, , m1 and the data are called sometimes the two-way data [102]. , xn } is the set of objects. So, the two-way data matrix can be represented as follows: Xˆ n×m1 xˆ11 xˆ 2 = 2 xˆ 1 n xˆ12 xˆ1m1 xˆ 22 xˆ 2m1 . 69) Therefore, the two-way data matrix can be represented as Xˆ = ( xˆ 1 , , xˆ m1 ) using n -dimensional column vectors xˆ 1 , t1 = 1, , m1 , composed of the t elements of the t1 -th column of Xˆ .

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