Apanasenko D. Methods of clustering fuzzy data of a special kind and their application

he thesis is devoted to the development and practical application of models, methods and algorithms for solving tasks of clustering of a set of data presented in the form of composite fuzzy triangular numbers were carried out. The paper proposes a new method for the use of composite fuzzy numbers to formalize uncertainty, formalizes clustering information procedures under uncertainties, investigates the dynamics of the process of cluster structures development, and improves the application of the genetic algorithm for the clusterization problem. The methods of grouping composite fuzzy numbers of a triangular type are investigated. Methods of solving the problem of clustering states of fuzzy systems are developed. The conditions of their constructive application in the problems of grouping are considered. The basic stages of the work of the genetic algorithm are analyzed, the essence of the operators of the genetic algorithm is presented. A method for coding the characters given by integers and floating point numbers using Gray codes is proposed, and the scheme of the operation of the main operators of the genetic algorithm under the proposed presentation and data encoding is presented. The scheme of grouping fuzzy triangular data based on the genetic algorithm is formulated. The paper proposes the formalization of the dynamics of cluster structures, which are formed on the basis of time-varying sets of composite fuzzy numbers. As a model of the process of changes, a totally unclear difference system is considered, the states of which at any time are composed by fuzzy numbers. The concept of the trajectory and the regular trajectory of the system are formulated. The methods of grouping composite fuzzy numbers of a triangular type are investigated. Methods of solving the problem of clustering states of fuzzy systems, which are described by a set of composite fuzzy numbers, are developed. The conditions of their constructive application in the grouping problems are considered. The method of choosing solutions under the conditions of presentation of the initial data in the form of a set of composite fuzzy numbers and in the presence of a set of criteria, the set of values of which are given in numerical intervals with linear membership functions are considered. Examples of practical problems are given, in the solution of which the uncertainty of data is taken into account. The variant of implementation of the genetic algorithm for solving the scheduling problem with the consideration of teachers' wishes regarding the time of conducting training sessions is offered. The process of distribution of network resources in a two-level system of Internet access is formalized based on the use of a continuous-discrete model and the description of data in the form of composite fuzzy numbers. A mathematical model for determining the optimal distribution of capacities of data transmission channels in a local network is constructed, algorithms are proposed for solving the problem of distribution of channel capacities. The solution of the task of grouping users by the levels of consumption of network capacities and the corresponding task of efficient allocation of resources of channels of data transmission among the user groups served.