Page 220 - Contributed Paper Session (CPS) - Volume 3

CPS1999 Pranesh K. et al.

Effect of the ocean heat content on the global
sea ice extent using Fuzzy Logic Approach
2
1
Pranesh Kumar , Jiefei Yang
1 University of Northern British Columbia, Prince George, BC, Canada
2 Dalian University of Technology, Dalian, P. R. China

Abstract
Statistical linear regression has been used in almost every field of science. The
purpose of regression analysis is to explain the variation of a dependent
variable in terms of the variation of explanatory variables. The classical linear
regression has crisp coefficients and is bounded by some strict assumptions
about the observed data, that is, the unobserved error terms are mutually
independent and identically distributed. Fuzzy linear regression (FLR) was first
introduced by H. Tanaka in 1982, which includes a fuzzy output, fuzzy
coefficients and a non-fuzzy input vector. Some strict assumptions of the
classical linear regression models are relaxed. This paper describes the fuzzy
logic approach to fit the response surface model, analysis and the
implementation of chosen method by using the global sea ice extent and
ocean heat content data from 1979 to 2015. We have calculated the upper
and the lower bounds of sea ice extent and carried error analysis which clearly
indicates the comparative performance of fuzzy regression over the ordinary
least squares regression. Besides, the width of predicted intervals of fuzzy
regression model is much smaller than that of ordinary least squares model,
which indicates the superiority of fuzzy regression methodology.

Keywords
Fuzzy logic; Least squares regression; Modelling; Climate change

1. Introduction
Crisp data, also known as precise data, are very common in everyday life.
The traditional science and technology pursuit for certainty in all its
manifestations and almost all the mathematical theories are developed for
handling such kind of data. However, in many cases, data have the
characteristic of uncertainty. There are primarily two types of uncertainty. The
first is probabilistic uncertainty, which is well developed overtime. The second
is what is termed as fuzzy uncertainty. Let us start with fuzzy data, which is a
combination of fuzzy variable and random variable and can characterize both
fuzziness and randomness. Fuzzy Logic as a superset of conventional (Boolean)
logic was first introduced by Zadeh (1965) to handle the concept of partial
truth. Fuzzy Logic is considered as the most powerful tool for dealing with
imprecision and uncertainties. Zadeh proposed that fuzzy set can be applied
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