CLUSTERING-BASED OBJECTS STATE DIAGNOSTICS IN CONDITIONS OF FUZZY SOURCE DATA

Abstract

У The problem of distribution of a set of objects, the state of which is determined by a set of controlled parameters, into a set of subsets of objects maximally homogeneous in their properties is considered. Relevance of the problem and important advantage of the clustering procedure: when its implementing it is possible to reduce the initial difficult problem of high dimensionality objects analysing to the solution of a number of simpler problems of lower dimensionality.  This circumstance acquires additional attractiveness and importance if the initial data of the problem contain uncertainty, for example, are vaguely defined.  Research object is the procedure of partitioning a set of objects into clusters under conditions of uncertainty.  In this regard, the purpose of the study is to develop a method for solving the problem of clustering in conditions where the initial data on objects controlled parametersthe values contain uncertainty.  The method of solving the problem is based on clustering procedure mathematical model development, containing analytical expressions for the criterion of its effectiveness, written in the form of a twice fractionally quadratic function.  The impossibility of mathematical programming problem direct solution   initiated the development of a heuristic algorithm for its solution.  As a result, an iterative method was obtained and applied to solve the clustering problem under conditions of fuzzy initial data.  The developed computational procedure is based on a reasonable system of rules for performing operations on fuzzy numbers.  The situations when the belonging functions of problem fuzzy parameters are defined on infinite or compact media are considered.  The developed system of rules allows to correctly perform operations in the metric of fuzzy defined states between clustering objects.  The proposed method is easily generalised to the case when the uncertainty of the initial data is hierarchical.