Oleksii Shushura et al., International Journal of Advanced Trends in Computer Science and Engineering, 9(3), May – June 2020, 2702 – 2707 2702 ABSTRACT The paper presents an overview of existing approaches to the problem of fuzzy set membership functions and suggests a method of constructing the membership functions with many arguments for the linguistic variables terms in fuzzy modeling and control problems, which combines statistical data analysis and expert evaluation based on the analytic hierarchy process. The method involves fuzzy clustering of the linguistic variables universal set and the formation of the set of its terms and tabular membership functions. The paper presents an approach to the formation of a set of analytical functions types for each term and their expert evaluation based on the advantages for the conditions of the modeling. To calculate the parameters of the analytic term membership functions it is suggested to use the coordinate centers of the respective clusters and optimization methods for the paired criteria for the accuracy of approximation, as shown in the example of the cone-shape membership function. The criterion for selecting an analytic type of membership function is formalized based on the analytic hierarchy process, using the criteria of approximation accuracy and expert evaluation of the advantages for the modeling object conditions. We suggest to set the priority of selection criteria separately for each modeling object, taking into account the quality of statistics, the level of experts’ expertise, the requirements for the accuracy of modeling. In general, the developed method can be applied to construct the membership function of many arguments in the development of information systems based on fuzzy logic. Key words: analytic hierarchy process, fuzzy clustering, fuzzy modeling, information system, membership function. 1. INTRODUCTION Fuzzy logic is widely used in the construction of intelligent information systems of various applications. It is applied in tasks of modeling, data analysis [1], control and decision-making support [2]. Fundamentals of the application of fuzzy logic in practical problems are laid in the works of L. Zadeh [3]. One of the most responsible steps in fuzzy modeling, which determines the quality of the problem solution and the accuracy of the results obtained, is the construction of membership functions for fuzzy sets or linguistic variables terms. 1.1 Problem analysis Defining the membership function is a stage that allows to start using a fuzzy set. As a rule, the membership function is constructed on the basis of statistical information or with the participation of an expert (expert group). In the first case, the membership function must have a frequency interpretation, in the second case, the degree of membership is approximately equal to the intensity of the manifestation of some property. Expert methods of constructing the membership function are divided into direct and indirect. In direct methods, the degree of membership is assigned directly in a table, graph or formula. Direct group methods are a variety of direct methods. A group of experts is presented with a specific object and everyone has to answer: does this object belong to a given set? The value of the object's belonging function to the fuzzy set is defined as the number of positive responses divided by the total number of experts [4], [5]. After selecting the membership function type, experts are involved in determining its parameters [6]. The values of the membership function parameters can be calculated based on statistics, for Construction of Membership Functions in Fuzzy Modeling Tasks using the Analytic Hierarchy Process Oleksii Shushura 1 , Liudmyla Asieieva 2 , Iryna Husyeva 3 , Mykhailo Stepanov 4 , Oksana Datsiuk 5 1 Doctor of Technical Sciences, Professor, Department of design automation for energy processes and systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, shushura.oleksiy@gmail.com 2 PhD student, State University of Telecommunications, Ukraine, aseewal@i.ua 3 Candidate of Economic Sciences, Associate Professor, Department of design automation for energy processes and systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, iguseva@yahoo.com 4 Doctor of Technical Sciences, Professor of the Department of information systems and technologies Taras Shevchenko National University of Kyiv, Ukraine, 2m.stepanov@gmail.com 5 Senior Lecturer, Department of design automation for energy processes and systems, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, doka70@ukr.net ISSN 2278-3091 Volume 9, No.3, May - June 2020 International Journal of Advanced Trends in Computer Science and Engineering Available Online at http://www.warse.org/IJATCSE/static/pdf/file/ijatcse33932020.pdf https://doi.org/10.30534/ijatcse/2020/33932020