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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimir: 1064-2315
ISSN On-line: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i10.40
pages 47-59

Clustering of Composite Fuzzy Numbers Aggregate Based on Sets of Scalar and Vector Levels

Evgeniy V. Ivokhin
Kiev National Taras Shevchenko University, Kiev
Dmitriy V. Apanasenko
Kiev National Taras Shevchenko University, Kiev


A new method for formalizing fuzziness in the form of composite fuzzy numbers is proposed. The axiomatics of such representation is considered, the notion of sets of scalar and vector levels is introduced, procedures for calculating distances between data are formulated. Based on developed models and methods the problems of grouping the states of the fuzzy system described by a set of composite fuzzy numbers using sets of scalar and vector levels are considered and solved. The main idea of the developed clustering algorithms is to calculate and use the distance values between the elements of the corresponding sets of a given scalar or vector level taking into account the error value determined on a rectangular grid covering a set of initial data. The proposed algorithms allow us to formalize the search for cluster centers of a set of composite fuzzy numbers and to implement the procedures for data grouping within a predetermined or automatically generated number of clusters during the course of the algorithm. Conditions for constructive use of clustering algorithms are considered. The proposed approach is a modification of existing clustering methods adapted to processing of fuzzy data of a special kind. Examples of this approach application to solving practical problems are given and the results of numerical experiments are analyzed.


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