A fuzzy regression functions approach based on Gustafson-Kessel clustering algorithm

Abstract

Fuzzy inference systems, referring to a system that works on fuzzy sets, have been used in many areas such as classification, information order, especially in the field of forecasting. Because fuzzy inference systems are based on certain rules, determining these rules is the most important problem of many well-known fuzzy inference systems in the literature. To overcome this problem, the Type-1 fuzzy regression functions approach uses fuzzy functions instead of relations, unlike many fuzzy inference systems that operate on a rule base and establish a compound relation between the input and output of the system. One of the most important success criteria of Type-1 fuzzy regression functions is the type of clustering method. The Gustafson Kessel clustering algorithm has no limitations unlike the fuzzy clustering algorithm and can recognize ellipsoidal clusters. In this study, the Gustafson Kessel clustering algorithm is used instead of the fuzzy clustering algorithm and thus the membership values of the input set are obtained with the Gustafson Kessel clustering algorithm in the structure of the fuzzy regression functions approach. The analysis results show that the forecasting performance is increased considerably with the use of the Gustafson Kessel clustering algorithm.