Tuning a model

Following the structuring of the model and the construction of the multi-criteria layer, the next step involves the construction of the decision map. The decision map transforms the multi-criteria layer by assigning each element within it to one category out of a set of ordered categories. The step of tuning a model corresponds to defining these categories and determining the model parameters that will be used in the construction of the decision map.

Therefore, we first decide on the number of ordered categories that will be represented in the decision map and their corresponding labels. This is achieved in the Tune Model panel of a model, under the Categories tab.

Then we either fix the model parameters or infer them using a supervised learning approach.

Fixing the model parameters

The model parameters are divided in two:

The first set of parameters are related to the relative importance of the criteria and the coalitions that are sufficient in order to validate whether one area characterised by multiple criteria is at least as good as another or not. At the core, these parameters are the criteria weights and the majority threshold, however an approach for extracting these parameters that is less focused on their exact value is to define a set of majority and minority coalitions. The first contains the sets of criteria for which the sum of their weights surpasses the majority threshold, while the second the sets of criteria for which this sum does not.

These parameters are fixed in the Tune Model panel of a model, under the Criteria Coalitions tab.

Only the criteria coalitions may be input inside MODEL, although the actual values of the majority threshold and the criteria weights can also be seen. These values are updated either after learning the parameters (see corresponding section), or after constructing the decision map.

The second set of parameters consists of a set of delimiting profiles for the categories. These profiles correspond to the minimum levels on each criterion that an area needs to surpass over a majority coalition of criteria in order to be placed in the category above the profile.

The values of the profiles may be edited directly in the Tune Model panel of a model, under the Category Profiles tab.

Learning the model parameters

The model parameters may be extracted via a supervised learning approach which takes input from the user in the form of assignments of a subset of areas from the multi-criteria layer to the set of ordered categories.

This process is accessed by clicking the Learn Model Parameters button at the top of the Tune Model panel.

Inside the Learn Parameters panel there are three tabs corresponding to the contraints that may be placed on the criteria coalitions, the categories profiles and the assignment examples.

Inside the first tab, the Criteria Coalitions tab, we can edit the set of majority and minority criteria coalitions that we wish to enforce (left side) and view the set of criteria coalitions that are present in the set of parameters found by the learning algorithm (right side).

Following an execution of the learning algorithm, the criteria coalitions on the left side of the Criteria Coalitions tab that are invalidated are highlighted in gray.

Inside the second tab, the Category Profiles tab, we may place constraints on the maximum and minimum values that each category profile is allowed to take. In this way certain profiles may be fixed, while other are left to be changed by the learning algorithm.

Inside the last tab, the Assignment Examples tab, a subset of areas from the multi-criteria layer are listed, along with the values they hold on each criterion.

The comboboxes inside the first column are used by the user to place the desired objects inside one category although it is not mandatory to do this for all objects. Objects that are not placed in any category are not used by the learning algorithm.

The second column will display the categories in which the objects have been placed by the learning algorithm. Conflicts between the category selected by the user and the category found by the algorithm are highlighted in red.

Initially 10 objects are selected randomly, although this list may be expanded using the 5 obj. button. The number of objects to be added may be changed using the up and down arrows to the right of the button.

The list of objects may be reset by pressing the Restart button, which empties the list and adds 10 randomly selected objects.

At the bottom of the Learn Parameters panel we may select whether to learn the criteria coalitions, the category profiles or both using two checkboxes.

The learning algorithm is launched using the Learn button.

Any changes made to the parameters as a result of the learning algorithm are only saved into the model if the OK button is pressed, bringing us back to the Tune Model panel. Pressing the Cancel button, or pressing any other button leading away from the Learn Parameters panel will not make any change to the parameters of the model.

Constructing the decision map

Once all the parameters have been validated, we may construct the decision map using the Build Decision Map button at the bottom of the MODEL interface.