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This article solves the problem of modelling a fuzzy neural network to generate fuzzy rules and to use them for determining the state of objects in conditions of uncertainty. Traditional methods of mathematical statistics do not allow constructing adequate models of objects under the specified conditions. Therefore, at present, the solution of many problems is based on the use of data mining technologies using the methods of fuzzy logic. The traditional approach to the construction of fuzzy systems is associated with the need to involve an expert to formulate fuzzy rules. To eliminate this drawback, the automation of generating fuzzy rules based on machine learning methods is relevant. One of the approaches to solving this problem is to build a fuzzy neural network and instruction in it based on the data characterizing the object under study. The implementation of this approach required the choice of the type of fuzzy rules, taking into account the peculiarities of the processed data. In addition, the development of an algorithm of logic rule-based inference was required. The stages of the algorithm determine the number of layers in a fuzzy neural network and their functionality. An algorithm for learning a fuzzy neural network has been developed, as a result of which a system of fuzzy-production rules is built. In order to assess the effectiveness of the developed model of a fuzzy neural network, a software package has been implemented. On its basis, the studies on assessment of the classifying ability of the generated rules using the example of data analysis from the UCI Machine Learning Repository have been conducted. The research results show that the classifying ability of fuzzy rules is not inferior to other classification methods in accuracy. In addition, the inferencing algorithm based on the rules makes it possible to successfully perform the classification in the absence of some of the source data. This proves the significance of the obtained results and the effectiveness of the proposed approach for solving the problem of instance state estimate in conditions of fuzziness, heterogeneity and the lack of a part of the analyzed data.
Currently, in various application domains there is a need to solve practical problems associated with modeling and assessing the state of objects, characterized by the following features: – the presence of a large number of inputs, outputs and states; – different types of parameters; – uncertainty, fuzziness and incompleteness of data at the input of the object; – fuzzy severity of the structure. Traditional approaches based on mathematical statistics [1,2] or simulation modeling [3,4] do not allow building adequate models of objects in the indicated conditions. Therefore, at present, artificial intelligence methods are used when solving many problems related to the assessment of the state of objects [5-10]. The theory of fuzzy sets [11-15], as one of the directions of artificial intelligence, enables to construct fuzzy models of objects. Methods of fuzzy logic are widely used to solve problems of diagnostics, control, support for decision-making in various subject areas [16-19]. However, in spite of the advantages of fuzzy systems, they have a drawback connected with the need to involve a person in order to form the rules of the knowledge base and a task of the membership functions used in them. The most difficult step in building a fuzzy system is the choice of the form and parameters of the membership functions due to the subjectivity of a person’s opinion. Moreover, this process requires considerable time and considerable analytical work, which significantly complicates the development of a fuzzy system. There are adaptive fuzzy models in which the parameters of the membership functions are adjusted automatically in the learning process based on experimental data . This class of fuzzy models is called “soft systems” . Soft approach to the generation of fuzzy rules is based on the use of data of the methods and data mining algorithms. However, when constructing knowledge bases of soft systems and solving specific problems of assessing the state of objects, it becomes necessary to take into account the features of the analyzed data which impose restrictions on the knowledge representation model and the inferencing algorithm. Therefore, to form adequate fuzzy models for assessing the state of objects in uncertainty, the development of a new approach to the generation of fuzzy rules that adequately describe the patterns in the analyzed data is relevant.
Thus, the developed model of a fuzzy neural network is an effective tool for generating fuzzy rules for assessing the state of objects in uncertainty. In the future, in order to develop the proposed methods for generating fuzzy rules, it is advisable to improve the developed software, as well as to develop and to put into practice intelligent systems for assessing the state of objects in various fields 
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