**2.8 The transmission potential modeling by using the logistic regression and artificial neural network and similarity weighted instance-based learning (SIM weight)**

In this study, by using the forest cover maps of 1984 and 2012, the calibration period is considered, and the transfer potential is modeled by using six variables, and by using the driver variables of the digital model, height, slope, distance from the road, distance from agricultural land, the distance from the edge of the forest and the distance from the village in 1984, the relationship between the change of use from forest to nonforest is determined by using cramer's correlation coefficient.

The probability of changing each user to another user is calculated by using the Markov chain [38]. In this study, changes are predicted for the year 2015 using the hard forecasting model and the calibration period of 1984–2012.

### **2.9 Validation of the model**

For evaluating the accuracy of the modeling, the forest cover map of 2015 and statistics such as the relative performance characteristic curve (ROC), figure of merit [39], and ratio Hits/False Alarms [40] are used. From the ROC/AUC statistic, the range is 0–1 based on the percentage of false positives and true positives. It is used to compare a continuous image of merit with a Boolean image, where a value of 1 indicates complete spatial agreement and a value of 0.5 indicates random agreement. The merit number statistic has a value between zero and one hundred, where the value of one hundred indicates the complete agreement of the predicted map with the ground reality, and the value of zero indicates noncompliance [41]. The closer the figure of merit is to 100. It means that the predicted map has higher accuracy [39]. The figure of merit is obtained from Eq. (9):

$$\text{Figureof merit} = \left(\frac{B}{A+B+C}\right) \tag{9}$$

A: The number of pixels that have changed in reality but remained constant in the prediction (Miss).

B: The number of pixels that have changed in the ground reality, and these changes were correctly predicted by the model (Hits).

C: The number of pixels that have remained constant in the ground reality, but these pixels have changed in the model prediction (False Alarm).

If the ratio of success to error warning in the used model is more than 25%, it can be said that the model has good accuracy in predicting the considered changes [29].

At this stage, according to the relevant statistics, for evaluating the accuracy, the best model with the highest accuracy was selected to continue the research process.
