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

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 within which the sought clustering constitution of the set of items is predicated 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 strategy can be utilized for fixing various category difficulties. right here, a few suggestions that will be worthy at this function are defined, together with a strategy for developing a collection of classified gadgets for a semi-supervised clustering set of rules, a strategy for decreasing analyzed characteristic area dimensionality and a equipment for uneven info processing. additionally, a strategy for developing a subset of the main acceptable choices for a suite of susceptible fuzzy choice family members, that are outlined on a universe of possible choices, is defined intimately, and a mode for swiftly 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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Additional resources for A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications

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The membership function of the Gaussian fuzzy number V = (m, σ ) G is defined as 2  ( x − m) 2  , − ∞ < x < ∞ . 2. The triangular fuzzy numbers can be considered as a special kind of the trapezoidal fuzzy intervals. Moreover, the trapezoidal fuzzy intervals are often called the trapezoidal fuzzy numbers. 24 1 Introductioon Fig. 2 Basic Methods of Fuzzy Clustering Objective function-based fuzzy clustering algorithms are considered in the firrst subsection which also deals with the problems of cluster validity annd interpretation of clustering g results.

114) xi ∈A where the element u 'l 'i represents the membership grade of object xi ∈ X to the fuzzy sub-cluster Al ' , l '∈{1,, c'} and the element μT ( Al ' , Aa ' ) corresponds to the similarity value between the fuzzy sub-clusters Al ' and Aa' , l ' , a'∈ {1,, c'} . Thus, the matrix Tc '×c ' = [ μT ( Al ' , A a ' )] of a fuzzy tolerance is obtained and it defines a fuzzy proximity graph in which the vertices represent the fuzzy sub-clusters and the arcs represent the links. Moreover, it is possible to define a remoteness matrix.

So, the concept of an LR -type fuzzy interval and the concept of an LR -type fuzzy number should be defined in the first place. These concepts were considered, for example, by Yang and Ko in [164]. Let L or R be decreasing, shape functions from ℜ + to [0,1] with L (0) = 1 and ∀x > 0 , L ( x) < 1 , ∀x < 1 , L( x) > 0 ; L (1) = 0 or L( x) > 0 , ∀x and 22 1 Introduction L(+∞) = 0 . 62) where m is called the lower mean value of V and m is called the upper mean value of V . The parameters a and b are called the left and right spreads, respectively.

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

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