文档介绍：Fuzzy Sets and Systems 112 (2000) 381–394
ate/fss
Linear and non-linear fuzzy regression: Evolutionary algorithm
solutions
James J. Buckleya;∗, Thomas Feuring b;1
a 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
b Institut fur Informatik, Westfalische Wilhelms-Universitat Munster, Einsteinstrae 62, 48149 Munster, Germany
Received August 1997; received in revised form April 1998
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 ÿts 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.
c 2000 Elsevier Science . All rights reserved.
Keywords: Fuzzy regression; Evolutionary algorithms
1. Introduction The last section contains our conclusions, a brief sum-
mary and directions for further research.
In this section we ÿrst present the notation we will We place a bar over a capital letter to denote a
use in this paper and then we discuss the fuzzy regres- fuzzy subset of the real numbers. So A, B, C, X,
sion problem. In the next section we look at the type of etc. are all fuzzy subsets of the real numbers. We
fuzzy functions (models) we will use including linear, write A(x), a number in [0; 1], for the membership
polynomial, exponential and logarithmic. Our evolu- function of A evaluated as -cut of A, written
tionary algorithm is discussed in Appendix B and the as