Linear and non-linear fuzzy regression: Evolutionary algorithm solutions

Authors:
James J. Buckley;Thomas Feuring
Affiliations:
School of Natural Science and Mathematics, Department of Mathematics, University of Alabama at Birmingham, 452 Campbell Hall, 1300, University Boulevard, Birmingham, AL 35294-1170, USA;Institut für Informatik, Westfälische Wilhelms-Universität Münster, Einsteinstraíe 62, 48149 Münster, Germany
Venue:
Fuzzy Sets and Systems
Year:
2000

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Abstract

Given some data, which consists of pairs of fuzzy numbers, our evolutionary algorithm searches our library of fuzzy functions (which includes linear, polynomial, exponential and logarithmic) for a fuzzy function which best fits the data. Tests of our fuzzy regression package are given for each of the four cases: linear, polynomial, exponential and logarithmic. For the linear model we also consider multiple independent variables. In all cases we use data generated with and without ''noise''. We prove that fuzzy polynomial regression can model the extension principle extension of continuous real-valued functions.