1. MADMMLMADMML®®
FiltersDeviceFiltersDevice
Arithme tic Me anArithme tic Me an
Filte r of Crite rionsFilte r of Crite rions
Re turn to ROOTRe turn to ROOT
Pre se ntationPre se ntation
Pe ssimisticallyPe ssimistically
Filte r of Crite rionsFilte r of Crite rions
This section presents the software possibilities to determine the
decision-maker’s preferences, as the values of target parameters and their
address are simultaneously determined. The decision-maker chooses one
of thebuilt-up filtersaccording to themulti-criteriaproblem formulated.
These numerical filters are: a pessimistic forming decision with
values of over a given threshold for all target function; arithmetical
average with determined weight coefficients of each criterion
participation.
The limitation of the field containing the solutions is done by a
number iterationsthrough shifting the“cutting” plains.
The principle of filter functioning is presented by only two
criteria but the software allows to examine simultaneously an unlimited
number of criteriaaccording to theproblem formulated.

2. Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Thetrade-off solutions capturedinthefilterarecoloredintheThetrade-off solutions capturedinthefilterarecoloredinthe
“cutting”plain color with the higher priority.Decisions are determined“cutting”plain color with the higher priority.Decisions are determined
afteratestof non-dominationcarriedout.afteratestof non-dominationcarriedout.
InitiallytheDecision-Makerspecifies areferencevalueof oneInitiallytheDecision-Makerspecifies areferencevalueof one
the criteriabythefirst “cutting”plain. Theotherfour“cutting”plainsthe criteriabythefirst “cutting”plain. Theotherfour“cutting”plains
with the first iteration are evenlydistributed within the interval up towith the first iteration are evenlydistributed within the interval up to
100% bythedecision-maker.100% bythedecision-maker.
MADMML is capable to determine the achievable aims of theMADMML is capable to determine the achievable aims of the
multi-criteria model formulated without the decision-maker’smulti-criteria model formulated without the decision-maker’s
preferences being stated beforehand (in case that it does not havepreferences being stated beforehand (in case that it does not have
informationof its preferences).informationof its preferences).

3. Y[1] 0 .. 20 %
Y[2] 20 .. 40 %
Y[3] 40 .. 60 %
Y[4] 60 .. 80 %
Y[5] 80 .. 100 %
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filte r 1
X1
X2
Y2= X1-X2
2
Y1= X1•X2-X2
Filte r 2
X2X2
X2
X1
X1X1
Y1->max
Y2->max
Filte r 1 ∩
Y1->max
Y2->min
______________
solution
(X1, X2) =...
Filte r 2 ∩

4. Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Y[1] 0 .. 60 %
Y[2] 60 .. 70 %
Y[3] 70 .. 80 %
Y[4] 80 .. 90 %
Y[5] 90 .. 100 %
Filte r 1
X1
X2
Y2= X1-X2
2
Y1= X1•X2-X2
Filte r 2
X2X2
X2
X1
X1X1
Y1->max
Y2->max
Filte r 1 ∩
Y1->max
Y2->min
______________
solution
(X1, X2) =...
Filte r 2 ∩

5. Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Y[1] 0 .. 60 %
Y[2] 60 .. 61 %
Y[3] 61 .. 62 %
Y[4] 62 .. 63 %
Y[5] 63 .. 100 %
Filte r 1
X1 in [-1, .., 0, .., 1]
X2in[-1,..,0,..,
1]
X2in[-1,..,0,..,
1]
X2in[-1,..,0,..,
1]
X1 in [-1, .., 0, ..,
1]
X1 in [-1, .., 0, ..,
1]
Filte r 1 Filte r 1
Y[1] 0 .. 60 %
Y[2] 60 .. 70 %
Y[3] 70 .. 80 %
Y[4] 80 .. 90 %
Y[5] 90 .. 100 %
Y[1] 0 .. 60 %
Y[2] 60 .. 61 %
Y[3] 61 .. 61.2 %
Y[4] 61.2 .. 61.4 %
Y[5] 61.4 .. 100 %
Ste p 1 Ste p 2 Ste p 3

6. Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filte r 1
X2in[-1,..,0,..,1]
X1 in [-1, .., 0, .., 1]
Y[1] 0 .. 61.4 %
Y[2] 61.4 .. 61.6 %
Y[3] 61.6 .. 61.8 %
Y[4] 61.8 .. 61.9 %
Y[5] 61.9 .. 100 %
Y2= X1-X2
2
Y1= X1•X2-X2
Y1= X1•X2-X2 -> max
Y2= X1-X2
2
-> max
Filte r 1 ∩
____________________
solution
No X1 X2 Y1, % Y2, %
1 0,225 -0,6 61,62 62,17
2 0,25 -0,63 61,72 61,98
3 0,275 0,65 61,78 61,75
4 0,3 -0,67 61,81 61,48

7. The stages of reaching the solution of the four-The stages of reaching the solution of the four-
parametermulti-criteriaproblemdeterminedanddescribedparametermulti-criteriaproblemdeterminedanddescribed
by two regression models with a respective identifier areby two regression models with a respective identifier are
tracedvisuallybyanumber of slides following below. Thetracedvisuallybyanumber of slides following below. The
identifier except by the minimum or maximum can beidentifier except by the minimum or maximum can be
determined as the criterion value change within limitsdetermined as the criterion value change within limits
exactly determined. A number of cases of solutionexactly determined. A number of cases of solution
determining are examined. These cases provide 1) thedetermining are examined. These cases provide 1) the
maximumof both criteria; 2) the maximumof one of themaximumof both criteria; 2) the maximumof one of the
criteriaandthe minimumof the otherat one andthe samecriteriaandthe minimumof the otherat one andthe same
time.time.
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions

8. Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Y[1] between 0 .. 60 %
Y[2] between 60 .. 70 %
Y[3] between 70 .. 80 %
Y[4] between 80 .. 90 %
Y[5] between 90 .. 100 %
Filter1
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->max
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩

9. Y[1] between 0 .. 70 %
Y[2] between 70 .. 75 %
Y[3] between 75 .. 78 %
Y[4] between 78 .. 79 %
Y[5] between 79 .. 100 %
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filter2
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->max
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩

10. Y[1] between 0 .. 75 %
Y[2] between 75 .. 76 %
Y[3] between 76 .. 77 %
Y[4] between 77 .. 78 %
Y[5] between 78 .. 100 %
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filter3
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->max
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩

11. Y[1] between 0 .. 77 %
Y[2] between 77 .. 77.4 %
Y[3] between 77.4 .. 77.6 %
Y[4] between 77.6 .. 77.8 %
Y[5] between 77.8 .. 100 %
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filter4
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->max
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩

12. Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Y[1] between 0 .. 60 %
Y[2] between 60 .. 70 %
Y[3] between 70 .. 80 %
Y[4] between 80 .. 90 %
Y[5] between 90 .. 100 %
Filter1
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->min
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩

13. Y[1] between 0 .. 70 %
Y[2] between 70 .. 74 %
Y[3] between 74 .. 76 %
Y[4] between 76 .. 78 %
Y[5] between 78 .. 100 %
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filter2
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->min
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩

14. Y[1] between 0 .. 76 %
Y[2] between 76 .. 77 %
Y[3] between 77 .. 77.5 %
Y[4] between 77.5 .. 78.5 %
Y[5] between 78.5 .. 100 %
Pe ssimistically Filte r of Crite rionsPe ssimistically Filte r of Crite rions
Filter3
Y1= f(X1, X2, X3,
X4)
Y2= f(X1, X2, X3,
X4)
Y1->max
Y2->min
______________
solution
(X1, X2, X3, X4)
=...
Filte r i ∩