Construction of Membership Functions in Fuzzy Modeling Tasks using the Analytic Hierarchy Process

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. © 2020, World Academy of Research in Science and Engineering. All rights reserved.