Page 222 - Contributed Paper Session (CPS) - Volume 3

CPS1999 Pranesh K. et al.
| −|
1 − , − ≤ ≤ + ; = 1,2, … , ,
() = { (2)

0, ℎ,

where is the central value and is the width. The membership function of

the fuzzy output can be described as

| −|
1 − , − ≤ ≤ + ; = 1,2, … , ,
() = { (3)

0, ℎ.

The degree of fitting of the fuzzy regression model to the given data =

( , ) is measured by an index min [ℎ ], where
̅

| − |
̅
ℎ = 1 − . (4)

∑ | |−

The vagueness of the fuzzy regression model is defined by = ∑ . The fuzzy

coefficient parameter is obtained so as to minimize subject to ℎ ≥ ,
̅
̃

where is chosen as the degree of fitting the model by the experimenter.

The basic idea is to minimize the fuzziness of the model by minimizing the
total support of the fuzzy coefficients subject to including all the given data.
As a result, we can obtain the best fitted model for the given data by solving
the conventional linear programming problem.

min = 0 +∑ =1 ∑ =1 , such that

≥∑ −(1−) ∑ +(1−) , (5)
=1 =1
≤∑ +(1−) ∑ −(1−) ,
=1 =1
≥0,=0,1,…,.

We have prepared Matlab 2018 programming codes for fitting the model
which are not included for saving the space, however, can be requested.

3. Result
For illustration of the fuzzy regression model, we have adapted the data of
global sea ice extent and ocean heat content from 1979 to 2015 [Source:
National Snow and Ice Data Center (NSIDC)]. Global climate data indicate that
in 2018, a new record was set for the total amount of warmth stored in the
seas known as the ocean heat content (OHC). Measured OHC was warmer than
any other year since observations began in the early 1940s. Sea ice was at
record or near-record lows in the Arctic, noted to be only the 6th lowest since
records began in the late 1970s. There is also currently a near-record low level
of multi-year sea ice in the Arctic, with around 80% of sea ice only one to two

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