Data Quality Enhancement Technology to Improve Decision Support - Efficient Decision Support Systems: Practice and Challenges from Current to Future - page 76

If O is the actual observation for time period t and P is the forecast for the same period, then
the error is defined as:

Error: eOP   (5)

t t t

Since there are observations and predictions for n time periods, then there will be n error
terms, and the following standard statistical measures can be defined:

n

1

  Mean Absolute Error: MAE e (6)

t

n 

t 1

n

1

 

2

Root Mean Square Error (RMSE): RMSE e (7)

t

n 

t 1

The MAE is defined by first making each error positive by taking its absolute value and then
averaging the results. The RMSE is a quadratic scoring rule which measures the average
magnitude of the error. The equation for the RMSE is given in both of the references.
Expressing the formula in words, the difference between forecast and corresponding
observed values are each squared and then averaged over the sample. Finally, the square
root of the average is taken. Since the errors are squared before they are averaged, the RMSE
gives a relatively high weight to large errors. This means the RMSE is most useful when
large errors are particularly undesirable.
The MAE and the RMSE can be used together to diagnose the variation in the errors in a set
of forecasts. The RMSE will always be larger or equal to the MAE; the greater difference
between them, the greater the variance in the individual errors in the sample. If the
RMSE=MAE, then all the errors are of the same magnitude. Both the MAE and RMSE can
range from 0 to ∞. They are negatively-oriented scores: Lower values are better. Each of
these statistics deals with measures of accuracy whose size depends on the scale of the data
[25].

Dataset: Italy
(Temperature)

Before Contribution After Contribution

Measurement metrics/methods Type-1 FLS Proposed Method

MAE 7.0321 1.3994

RMSE 10.5019 1.6590

Table 3. Accuracy Measurements of Italy Dataset
In such circumstances, Table 3 shows results of error value for type-1 FLS before and after
contribution .For MAE measurement is 7.0321 and 1.3994 using type-1 FLS before and after
clustering respectively. These values in RMSE measurement are 10.5019 and 1.6590. The
result shows the method after contribution achieve minimum error rate in both MAE and
RMSE. RMSE
These effective results are due to the mechanism of Type-1 FLS* with FCM* method. Type-1
FLS + improves the quality of data by detecting outliers, removing noisy data and tuning
MFs parameters by training algorithm is called Gradient Descent algorithm. Thus this
method is a significant technique that can improve the accuracy of weather situation.