Let us introuduce you the features provided by the Smart Picker Pro.
software
when facing a ranking problem. These will help you to gain a better
insight in your problem and eventually making your decision...
Therefore, let us consider the following small
problem:
James
would
like to buy
a new car, but he has no idea which car to choose. His car retailer
proposes James to help him, and shows him therefore 6 different cars
whose evaluations are given in the Table below. After discussion, James
has been able to give some preference parameters (the weights, the
thresholds, etc.).
For
more information about the preference parameters go to:
Preference parametersJames'
preference
parameters:
James is now interested in his results. His has different tools to
analyse his results.... He can use:
-
the shortcuts
of the
toolbar (displayed left), or -
the ranking tools from
the toolbar...(displayed right)
|
|
|
|
|
|
|
|
Gives the Ranking
Scores in a table.
Gives the Ranking Charts, i.e. a graphical
represenation of the ranking
Displays the Gaia Map, i.e. a graphival
representation
of your decision problem. |
|
|
|
|
|
Let us now analyse every possible result.
1.
Using the tool
or
clicking F6 or
going to the
Menu Bar --> Ranking --> Ranking
Display:
This figure displays the scores and the ranks for
all the cars
according to the preference parameters. By right-clicking with the
mouse on the top of the
Net
Flows column, you can order
the actions in increasing
order whereas when right-clicking on the
Position
column in
decreasing order.
We
can conclude that "Action 2 - Sport" is James' best car with a score
of 0.26983, followed by "Action 1 - Tour. A" with a score of 0.07919.
2.
Using the tool
or
clicking F5
or going to the
Menu Bar --> Ranking --> Ranking Charts
Display:
|
By clicking right on the chart graph
or by clicking on the Paramter
button:
|
So this figure, displays the scores of all the actions. The
actions
with a global positive score (i.e. a positive net score), are displyaed
in blue whereas the actions with a negative score are displayed in red.
This figure might be saved easily in any picture format (.png, .bmp,
.giff) and some other features are displayed on the right: criteria
descriptive, ordered, thermometer view.
You
can change the display of the previous graph and represent the
actions in increasing rank:
Ordered
graph.
When
selecting the
Criteria
Descriptive view, the
following graph is displayed:
The left figure, displays the contribution of each criterion for each
action to the final score. For instance, we know that the Sport car
has
a score of 0.27. This score is coming from a good performance on the
criteria consumption, power and in a smaller manner price. Yes, a good
performance on the consumption criteria.... check the data in Fig. .
(Do not forget this is not real data :-)). However, the Sport car
doesn't seem to perform well the comfort criterion....
this is
indicated by the negative contribution (the light blue is in the
negative part). Compensating the good poins by the weakness leads to a
score of 0.27, represented by the black bullet and doted white line. If
we consider Lux 2 car, we can see that it performs very well on comfort
and space, but is very weak on the price
and on the consumption.
So this graph permits us to understand the origin of the final score ;
i.e. the contributions on each criterion.
By moving the mouse over the graph (red cross on the right figures),
you will have access to detailed - value information.
When selecting the
Thermometer
view, the following graph is displayed:
|
The upper line displays
a ranking of the actions
according to their
strong performances, i.e.
based on the positive flows.
The
higher this score, the better.
The lower line displays a ranking of the actions
according to their weaknesses.
This
is traduced by the negative
flows. The lower their
weakness the better it
is...
The middle line displays the average of the negative and positive
flows: the net
flows
which is obtained as follows: the positive - negative flows.
So we can see for instance that
- car 1 has strong performances compared to the other cars (-->
2nd position on the positive scores) but car 1 has also certain
weaknesses (3rd position on the negative scores)... but
globally,
it is the second position
- car 3 doesn't have much strong weaknesses... (see negative ranking)
but doesn't have strong points (see positive flows) --> average
car: 3rd position.
- car 6 has lots of weaknesses and relatively some good performances
too.... on average 5th position. |
3.
The GAIA MAP: Click on the tool
or F8or going to the
Menu Bar --> Ranking -->
GAIA MAP
For the problem described in previous sections, the GAIA Map will look
as follows:
|
The map displayed on the
left is called the GAIA map
and represents the decision problem. It permits thus to
discover quickly the
weaknesses and strengths of all the actions in one plane, and thus to
compare them. Moreover, it
permits to discover quickly and easily
similarities between actions...
- The bullets in blue represent the actions or the cars amongst which
to choose (Sport, Lux.1, etc.
- The coloured arrows represent the criteria/features
describing the cars (price, power, etc.)
- The black
arrow D, also
called the decision stick, represents the direction of the
compromise of the decision maker. Its position depends on the
weigths
given to the criteria.... It represent thus the decision.... look at
the figure here below if the weight of power is 95%...
How
to understand this map ?
- The position of the actions/bullets gives you information about their
similarity/dissimilarity. For instance, Lux.1 and Lux.2. are close to
each other on the plane --> their performances are not
very
different --> they are quite similar with some small differences
though. On the other hand, we can see that Sport and Economic are far
away from each other --> very different.
- If an action lies in the direction of a criterion (arrow), it means
that it behaves very well on that criterion. For instance, Tour A and
certainly
Economic are very goods cars considering their price.
However, if the actions are in an opposite direction of a criterion,
they are weak on that criterion. For instance, Ecomomic is very weak on
the criterion space....
- The relative position of the criteria tell us which criteria are
correlated and
which are conflicting. Close criteria, i.e., wich are
pointing in the same direction are correlated, whereas criteria
pointing in oppposite directions, are conflicting: a car can not have a
good price (small price) and have lots of space. The comfort can not be
great if the car is very powerful. But the space and comfort are on
the
other hand correlated...
Let us remark that when representing this map, some information is lost
(due to the projection when going from n-dimensions to 2 dimensions).
The quality of the map is given by the Delta-value (here 80% which is a
good value).
|
|
Gaia map of the same
problem but in this case, the
weight of power is
95%. The Decision stick is very very very close to the power criterion.
The GAIA map depends thus on the preference parameters....
|
When
clicking right on the map or when
clicking in the Parameters button,
you can access to the features of this map: projections, legends,
performances and weigths.
When clicking on the
projections the following graphs may appear:
The
left figure represents the GAIA MAP with projections on the
Decision Stick. We can thus see, that Sport is in the same direction as
the stick. From this projections, we see thus that Sport is the best.
whereas Economic is the wost one. Between those two extreme, the
luxuary and touring cars are close to each other.
By
clicking left on the Consumption - green arrow, we have now the
projections on the Consumption criterion. We can easily deduce fron
this view that Sport is the best on this criterion, whereas Lux.1 and
Lux.2. are very weak because those two cars consume a lot.By choosing
Performances (in
the
display parameters) you can display, the actual values of the
performances of the car. We are now remembered that th consumption of
Sport is 7.0 and that fron Lux 2. 9.0
4.
Criterion Net Flows:
In the
Menu Bar --> Ranking --> Unicriterion Net Flows:
The scores of the actions on the different criteria are thus given. You
can order the results, by right clicking on the head of the column.
Indeed,
these values can be exported to excel by copying-pasting from
the table.
5.
All flows: the positive, negative and net flows...
In the
Menu Bar --> Ranking -->All flows:
6.
In the
Menu Bar --> Ranking -->Preference matrix
and Menu Bar --> Ranking -->Binary
Preference matrix
The preference matrix is a matrix which contains the preference
degrees between two actions. We might see in the figure below that the
decision maker, according to his preferences, prefers A2-Sport to Tour
A with a strength of 0.74714 and Tour A to Sport with only 0.1326. The
preference degrees
are values between 0 and 1, 0 means no preference at
all.... 1 a strong preference.
On the right, you can find the binary decision matrix.
If the preference degree of a over b minus the preference degree of b
over a is higher then 0.05, then we have the value 1.
If the preference degree of a over b minus the
preference degree of b
over a is lower then If -0.05, then we have the value -1.
If the preference degree of a over b minus the preference degree of b
over a is between 0.1 and -0.1, then we have the value 0.
7.
Improvement of the ranking of an action
or Performance
sensitivity/analysis
In the
Menu Bar --> Ranking -->
Improve
an action
At
left, we can notice that action Tour-A is ranked 2nd. So, the
purpose of the 'Improve the rank of an action' is to give the
possibility to change the performance of an action (choose in the list
left) on a criterion (choose in the list right) with a slider between
two values. This permits, combined with the ranking charts, to discover
when
an action will be better ranked, and maybe become the best. In the
example, we can notice that as soon as A1-Tour A gets a power of 104,
it becomes the best car.
The decision maker can change the values (e.g., 50 and 110) which by
default are the minimum and maximum values of the actions on the chosen
criterion.
You
can always save the new value or come back to the old value.