Download e-book for iPad: A Heuristic Approach to Possibilistic Clustering: Algorithms by Dmitri A. Viattchenin

By Dmitri A. Viattchenin

The current e-book outlines a brand new method of possibilistic clustering during which the sought clustering constitution of the set of items relies at once at the formal definition of fuzzy cluster and the possibilistic memberships are decided without delay from the values of the pairwise similarity of gadgets. The proposed strategy can be utilized for fixing diverse type difficulties. the following, a few innovations that would be helpful at this function are defined, together with a technique for developing a suite of categorized items for a semi-supervised clustering set of rules, a technique for lowering analyzed characteristic house dimensionality and a tools for uneven info processing. additionally, a method for developing a subset of the main acceptable choices for a suite of vulnerable fuzzy choice kinfolk, that are outlined on a universe of possible choices, is defined intimately, and a style for quickly prototyping the Mamdani’s fuzzy inference structures is brought. This publication 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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An ordered sequence 0 < α 0 <  < α  <  < α Z ≤ 1 of the threshold values α  ∈ (0,1] must be constructed for solving the problem of decomposition of the fuzzy relations. The method of constructing the sequence 0 < α 0 <  < α  <  < α Z ≤ 1 was proposed in [118]. 57) where α q ∈ (0,1] is the current value of α , and the last value α Z in the sequence 0 < α 0 ≤ α1 ≤  ≤ α  ≤  ≤ α Z ≤ 1 is determined as follows: α Z = Proj( R ) . 58) and the corresponding fast algorithm is presented in [118].

So, the validity criteria are used sequentially as follows: 34 1 Introduction 1. 2. 3. Compute different fuzzy c -partitions for c = 2,  , c max ; Compute the value of a validity criterion; Seek for the extreme value of validity criterion and set the optimal number of clusters to its correspondent c value. On the other hand, some fuzzy clustering algorithms were proposed that do not require the pre-definition of the number of clusters. The CA-algorithm which was proposed by Frigui and Krishnapuram [37] and the E-FCM-algorithm which was developed by Kaymak and Setnes [62] are good examples of such clustering procedures.

Let X = {x1 ,  , x n } be the finite universe and R be a fuzzy relation on X with μ R ( x i , x j ) being its membership function. 54) for all α  ∈ (0, Proj( R)] . Proof. 23) can be rewritten as Proj( R) = max μ R ( xi , x j ) , xi , x j ∀xi , x j ∈ X . If the fuzzy relation R is the subnormal fuzzy relation, then Proj( R ) < 1 . So, the values of the membership function μ R ( x i , x j ) are absent on the interval (Proj( R ),1] and α  ∉ (Proj( R),1] . On the other hand, if the fuzzy R is the α  ∈ (0, Proj( R) = 1] .

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