4 üldist teemat:
1. Fuzzy AHP (2-4 nädalat)
2. Fuzzy ANP
3. XMCDA standardi abil hägusate AHP (ja ANP) mudelite esitamine (2-4 nädalat)
4. Teenustepõhine arhitektuur mis toetab AHP (ja ANP) mudelite kasutamist, sh tundlikkuse analüüsi hägustamise abil.

AHP mudeli hägustamise erinevad lähenemised:
1. AHP võrdlusmaatriksi võrdlushinnangute esitamine hägusal kujul (kysitlus_sektorid hägustamise näide Excelis).
2. AHP võrdlusmaatriksi hinnangute vigade alusel Monte Carlo tundlikkuse analüüs (Oliver Oidekivi) - AHP mudeli hägustamine, mingis mõttes tulemuseks on hägus AHP mudel.
3. üle AHP mitme võrdlusmaatriksi Monte Carlo
3b. üle AHP mitme võrdlusmaatriksi Monte Carlo, arvestades Saaty skaala nivoosid (kui on piisavalt palju veakordajaid).
4. AHP mudeli struktuuri hägusus
5. Fuzzy Tradeoff Analysis (risttundlikkuse hägusus)
6. Grupiotsustuse hägususus
7. Kombinatsioon lähenemistest 1-6

Lähenemised 2-6 on automaatselt arvutatavad. See on analoogne automaatsele tundlikkuse analüüsile.
Lähenemised 1 ja 5 on sisulise tundlikkuse analüüsi osad.

NB. siinses failis kirjeldatakse varianti 2 (AHP võrdlusmaatriksi hinnangute vigade alusel Monte Carlo tundlikkuse analüüs)
NB. otsige faili keskelt järgmist rida: "NB. Siit algab Loeng 1."

   ts =: 6!:2, 7!:2@]
9!:3(5)	NB. set system for linear display of verbs

bdiag =: ([: i. ]) >/ [: i. ]
adiag =: [: |: bdiag
mp =: +/ .*		NB. mp on matrix product ehk maatrikskorrutis
product =: */
geomean =: # %: product	NB. geomeetriline keskmine
NB. geomean_log =: 13 : '^ am ^. y'

am =: +/ % #		NB. aritmeetiline keskmine (Arithmetic Mean - am)

NB. juhusliku saaty maatriksi genereerimine
saaty_rand =: (] , ]) $ (1"_ + [: ? ([: *: ]) # 9:) ^ _1: + 2: * [: ? ([: *: ]) # 2:
str =: 13 : '( =/~ i.#y) + (y*bd ) + |: (bd=.bdiag #y) * %y'
st =: 13 : 'str saaty_rand y'

re =: 13 : '(>: ? n#9) ^ <: +: ?(n=. 0.5 * y * (y - 1))#2'
rst =: 13 : '(% |:)~ (y , y)$ ( re y) } 1#~ *:y'	NB. Random Saaty Table (juhuslik saaty tabel). On verbist 'st' umbes 20% kiirem, aga 30% mälumahukam.

saaty_skaala =: }. (,%)~ >:i.9		NB. skaala o*(9 8 7 6 5 4 3 2 1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111)
saaty_rand_o =: 13 : '(y , y) $ saaty_skaala {~ ? 17 #~ *: y'
st1 =: 13 : 'str saaty_rand_o y'
st2 =: 13 : 'str (y , y) $ ((,%)~ >:i.9) {~ ? 17 #~ *: y'

kaalu =: 13 : '(% +/)~ geomean"1 y'			NB. saaty kaalude esimese lähendi arvutamine
NB. kaalu =: (% +/)~ geomean"1			NB. verb tacit kujul

log_kaalu =: 13 : '(% +/)~ ^ am"1 ^. y'	NB. saaty kaalude esimese lähendi arvutamine logaritmimise kaudu, seetõttu tuleb geomeetriline keskmine asendada aritmeetilisega. Suurte maatriksite korral ja kaalude iteratiivsel arvutamisel hädavajalik.
NB. log_kaalu =: (% +/)~ ^ am"1 ^.		NB. verb tacit kujul

iter_kaalu =: 13 : 'log_kaalu"2 mp~ ^: (y) x'	NB. saaty täpsete kaalude iteratiivne arvutamine

omavaartus =: 13 : '+/ (+/y) * log_kaalu y'		NB. Saaty maatriksi suurim omaväärtus
aci =: 13 : '((omavaartus y)-#y) % (_1 + #y)'	NB. Saaty maatriksi abs. kooskõlaindeks

juhaci =: 13 : 'am aci"2 st"0 (x # y)'	NB. verb skaalal o(9 8 7 6 5 4 3 2 1 1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111) juhuslike maatriksite abs.kooskõlaindeksite keskmise arvutamiseks
juhaci1 =: 13 : 'am aci"2 st1"0 (x # y)'	NB. skaalal o*(9 8 7 6 5 4 3 2 1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111)
juhaci2 =: 13 : 'am aci"2 st2"0 (x # y)'	NB. skaalal o*(9 8 7 6 5 4 3 2 1 0.5 0.333333 0.25 0.2 0.166667 0.142857 0.125 0.111111)

errw =: 13 : '(%/~ log_kaalu y) % y'				NB. elemendi veakordajate maatriks lähendkaalude põhjal
iter_errw =: 13 : '(%/~ log_kaalu "2 mp~ ^: (y) x) % x'	NB. elemendi veakordajate maatriks täpsete kaalude põhjal

errt =: 13 : '^ ((y * n) + ys +/ (- ys=. +/ y=. ^. y)) % (2 - n=. #y)'	NB. veakordajate tabel hinnangu kolmikute geom.keskmise vea alusel
errt_auto =: 13 : 'y * x %: errt y'	NB. hinnangute automaatne kooskõlastamine üksiku hinnangu koondvea valemi järgi (hinnangu kolmikute geom.keskmise vea alusel), tulemuseks on kooskõlaline võrdlusmaatriks
NB. ruutjuurega veaparandus: 2 errt_auto tabel
NB. ruutjuurega iteratiivne veaparandus: 2 errt_auto ^:_ tabel
NB. kuupjuurega veaparandus on: 3 errt_auto tabel
NB. kuupjuurega iteratiivne veaparandus: 3 errt_auto ^:_ tabel


NB. errt_auto2 tabel
NB. astendajaks on (n-2) % n, n on Saaty tabeli järk (n =. #tabel). Üks hinnang osaleb n-2 kolmikus.
NB. Tulemuseks on kooskõlalised hinnangud,
NB. praktikas on piisavalt täpne, iteratiivselt ei ole vaja arvutadagi.
errt_auto2 =: 13 : 'y * ( (#y) % _2 + #y) %: errt y'	

errcorr2 =: 13 : 'y * (%: errt y) ^ x'	NB. puuduvate väärtuste automaatne ruutjuurega veaparandus, 'nullid =. 0 = y' NB. nullid errcorr2 ^:_ nt
NB. kõigi hinnangute koooskõlastamiseks (sama mis: errt_auto2 tabel): 1 errcorr2 tabel
NB. nulliga tähistatud puuduvate hinnangute kooskõlastamiseks: (nullid =. 0 = tabel) errcorr2 tabel

errcorr3 =: 13 : 'y * (3%: errt y) ^ x'	NB. puuduvate väärtuste kuupjuurega veaparandus , 'nullid =. 0 = y' , nullid errcorr3 ^:_ nt

vigasemad_hinnangud =: 13 : 'lt =/ >./ >./ lt=. | ^.  errt y'	NB. tulemuseks on rea ja veeruindeks, kui vigasemaid hinnanguid on üle 1, siis kõigi nende vigaste hinnangute rea- ja veeruindeksid
kaared =: 13 : '4 $. $. y'	NB. tulemuseks on rea ja veeruindeks, kui vigasemaid hinnanguid on üle 1, siis kõigi nende vigaste hinnangute rea- ja veeruindeksid
maxerrcorr =. (errcorr2 ^:_ ~ vigasemad_hinnangud)~	NB. maxerrcorr t	NB. nõuab ainult parempoolset argumenti, vasakpoolse argumendiga on tulemus vale

errcorr0 =: 13 : 'nullid errcorr2 ^:_ y =. y + nullid =. 0 = y'	NB. 'errcorr0 tabel', tabel peab sisaldama puuduvaid võrdlusi, mis on kodeeritud 0-ga (kui nulle ei ole, siis on väljundiks algtabel)

saaty_tour =: 13 : '1 < y'			NB. saaty tabeli teisendamine turniiritabeliks
tour_saaty =: 13 : '(% |:)~ >: (<:x) * y'	NB. turniiritabeli teisendamine saaty tabeliks, vasak argument x määrab ära võidu hinnangu, kaotuseks on võidu pöördväärtus

mpnorm =: 13 : 'mp~ (% omavaartus)~ y'	
tapselt_kaalu =: log_kaalu mpnorm ^: _		NB. praktikas parem verb kui iter_kaalu, sest ei ole vaja teada kui mitmendal iteratsioonil kaalud koonduvad

tapne_omavaartus =: 13 : '+/ (+/y) * tapselt_kaalu y'		NB. Saaty maatriksi suurim omaväärtus
tapne_aci=: 13 : '((tapne_omavaartus y)-#y) % (_1 + #y)'
tapne_juhaci1 =: 13 : 'am tapne_aci"2 st1"0 (x # y)'
tapne_juhaci2 =: 13 : 'am tapne_aci"2 st2"0 (x # y)'

mrci =: 13 : '|: y ,. (x tapne_juhaci1"0 (y))'	NB. Saaty juh.maatriksite abs.kooskõlaindeksi tabel: 10000 mrci 3+i.8
mrci2 =: 13 : '|: y ,. (x tapne_juhaci2"0 (y))'	NB. 10000 mrci2 3+i.8

   
   x: +t =: st 4
  1 1r3 1r6   6
  3   1   8 1r8
  6 1r8   1 1r5
1r6   8   5   1
   
   NB. A program to apply Saaty's method in an interactive fashion.
NB. according to the link in http://actifeld.com/A%20Possible%20Method.doc

NB. 2006-03-02
NB. John Randall developed the basic algorithm on the J Programming Forum
NB. Raul Miller, Tarmo Veskioja, Devon McCormick, and Roger Hui contributed to the dialog
NB. Bill Harris put a few other pieces on.

NB. The steps:
NB. Define the Client Preference Matrix as described on p. 6 of that article
NB. Run (%+/)power on that matrix to find the principle eigenvector.
NB. Run cr to calculate the Consistency Ratio; if it is much in excess of
NB.   0.1, the judgments used to create the CPM are probably too random.
NB. Create preference matrices for each of the alternatives on each of 
NB.   the dimensions used in the CPM.  Calculate the principal eigenvectors
NB.   and consistency ratio for each.
NB. Create the Option Performance Matrix by assembling all the principal 
NB.   eigenvectors for the preference matrices.
NB. Multiply OPM time CVV to get the Value For Money vector.  

NB. Calculate principal eigenvectors of the matrix cpm by
NB.   (%+/) power cpm

NB. Calculate the principal eigenvalue of the matrix cpm by
NB.   ev cpm

NB. Calculate the relative consistency ratio of the matrix cpm by
NB.   cr cpm 

NB. The VFM shows in each position the relative preference the decision-maker
NB.   has shown for that alternative: OPM * CVV = VFM

NB. If the Option Performance Matrix is
NB. opm=: |:a,b,c,:d  
NB. where a, b, c, and d are the principal eigenvectors of each option matrix

NB. then 
NB. (%/+)opm mp cpm 
NB. is the Value For Money (VFM) matrix, giving the relative 
NB. values of each alternative

NB. The power method for calculating the principal eigenvector
mp=:+/ . *
normalize=:%(>./@:|)
iterate=:normalize@:mp
init=:[: ? # # 0:
power=:13 : 'y&iterate^:_ init y'


NB. Calculate the principal eigenvalue
NB. Postmultiply the current principal eigenvector by the matrix
NB. Divide that vector (unnormalized) by the principal eigenvector
NB. See p. 258 of Kincaid and Cheney's Numerical Analysis 3rd edition
cureigenvec =: (%+/) @: power
neweigenvec =: mp cureigenvec
ev=: [: {. neweigenvec % cureigenvec

NB. Calculate the absolute consistency index
ci =: (ev - #) % <: @: #

NB. Calculate the consistency ratio
NB. MACI is the mean absolute consistency index of random matrices
am=: +/%#
maci =: 13 : 'am ci"2 st1"0 (x # y)'
NB. maci_precomputed =: 1000 maci"0 (3+i.8)   NB. Tarmo claims it's exactly 0.5245 for 3
index =: <:^:3 & #
maciv =: 13 : '(index y) { maci_precomputed' NB. Get the value of 
cr=: ci % maciv

NB. .........................................................................
NB. Random Saaty matrices for testing
NB. st is Tarmo Veskioja's verb (e.g., st 4)
NB. st1 is Roger Hui's faster but more space-intensive equivalent
saaty_scale =: \:~ }. (,%)~ >:i.9
str =: 13 : '( =/~ i.#y) + (y*bd ) + |: (bd=. >/~ i.#y) * %y'
saaty_rand =: 13 : '(y , y) $ saaty_scale {~ ? (#saaty_scale) #~ *: y'
st =: 13 : 'str saaty_rand y'        NB. st 4
st1=: 3 : 0
 i=. 1+(,~y) ?@$ #saaty_scale
 b=. >/~i.y
 ((b*i) + |:b*i+#saaty_scale) { 1,(,%) saaty_scale
)

NB. Test matrices from Geoff Coyle's paper referenced above:
NB. peigen s/b 0.232,0.402,0.061,0.305, cr of 0.055
cpm=: >(1,(%3),5, 1);(3,1,5,1);((%5),(%5),1,(%5));(1,1,5,1)

NB. peigen s/b 0.751,0.178,0.071 w/ cr of 0.072
exp=: >(1,5,9);((%5),1,3);((%9),(%3),1) NB. Expenses

NB. peigen s/b 0.480,0.406,0.114 w/ cr of 0.026
und=: >(1,1,5);(1,1,3);((%5),(%3),1) NB. "Understandability

NB. peigen s/b 0.077,0.231,0.692 w/ cr of 0
rod=: >(1,(%3),%9);(3,1,%3);9 3 1 NB. "Replication of detail", p. 7

NB. peigen s/b 0.066,0.615,0.319 w/ cr of 0
pod=: >(1,(%9),(%5));(9,1,2);(5,(%2),1) NB. Prediction of dynamics




scan =: 3 : 0
 for_j. i.#x do.
	sum =. sum + (x matrices"0 y) % (i.17^x)
 end.
)

   
   (%+/) power x: +t =: st 4
0.591633 0.145296 0.217743 0.0453272
   
   x: +t =: st 4
  1 1r4 6 1r5
  4   1 9 1r9
1r6 1r9 1 1r7
  5   9 7   1
   
   (%+/) power t
0.100575 0.202725 0.0345109 0.662189
   
   %/~ (%+/) power t
       1 0.496117 2.91431  0.151883
 2.01565        1 5.87423  0.306144
0.343135 0.170235       1 0.0521164
 6.58401  3.26644 19.1878         1
   
   t% %/~ (%+/) power t	NB. veakordajad
       1 0.503913  2.05881   1.3168
 1.98447        1  1.53212 0.362938
0.485718 0.652692        1  2.74111
0.759416  2.75529 0.364815        1
   
   t% t% %/~ (%+/) power t
       1 0.496117 2.91431  0.151883
 2.01565        1 5.87423  0.306144
0.343135 0.170235       1 0.0521164
 6.58401  3.26644 19.1878         1
   
   ^.t% %/~ (%+/) power t	NB. logaritmitud veakordajad
        0 _0.685352 0.722128 0.275206
 0.685352         0  0.42665 _1.01352
_0.722128  _0.42665        0  1.00836
_0.275206   1.01352 _1.00836        0
   
   load 'stats'
   stddev
%:@var
   
   stddev ,^.t% %/~ (%+/) power t	NB. standardhälve logaritmitud veakordajatest
0.662618
   
   
   stddev ,^.tt% %/~ (%+/) power +tt =: st 4
0.781141
   stddev ,^.tt% %/~ (%+/) power +tt =: st 4
0.981145
   stddev ,^.tt% %/~ (%+/) power +tt =: st 4
1.12122
   
   NORMAL
|value error: NORMAL
   load 'stats/distribs'
   0 0.662618 tomusigma 1 2 3 4
0.662618 1.32524 1.98785 2.65047
   
   normalrand 5
0.15516 _0.165083 _1.13402 1.35691 _0.239741
   
   -. =/~ i.4
0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0
   4 $. $. -. =/~ i.4
0 1
0 2
0 3
1 0
1 2
1 3
2 0
2 1
2 3
3 0
3 1
3 2
   13 : '4 $. $. -. =/~ i.y'
4 $. [: $. [: -. [: =/~ i.
   reverse_identity_matrix =: 13 : '-. =/~ i.y'
   reverse_identity_matrix 4
0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0
   <"1 (4 $. $. reverse_identity_matrix 4)
┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
│0 1│0 2│0 3│1 0│1 2│1 3│2 0│2 1│2 3│3 0│3 1│3 2│
└───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┴───┘
   (<"1 (4 $. $. reverse_identity_matrix 4)) { t
0.25 6 0.2 4 9 0.111111 0.166667 0.111111 0.142857 5 9 7
   t
       1     0.25 6      0.2
       4        1 9 0.111111
0.166667 0.111111 1 0.142857
       5        9 7        1
   stddev (<"1 (4 $. $. reverse_identity_matrix 4)) { ^.t% %/~ (%+/) power t	NB. standardhälve logaritmitud veakordajatest, peadiagonaal väljaarvatud
0.773772
   
   + stddeviation =: stddev (<"1 (4 $. $. reverse_identity_matrix 4)) { ^.t% %/~ (%+/) power t	NB. standardhälve logaritmitud veakordajatest, peadiagonaal väljaarvatud
0.773772
   (#t) * <:#t
12
   (<"1 (4 $. $. reverse_identity_matrix 4)) ((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) } reverse_identity_matrix 4
0.825259 0.673318 _1.88877 0.624064 0.0350052 0.0831294 _0.202341 0.0209793 1.09252 _0.224805 1.49291 0.222825
   ^((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
       1  1.39766 0.309185  2.19784
0.682956        1  1.97291 0.168955
  1.4444 0.532161        1 0.966974
0.874857 0.421892   1.5429        1
   
   t* ^((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
       1 0.275188 3.36066  0.302383
 5.38877        1 8.96914 0.0412156
0.270433 0.100154       1  0.248234
 1.67516  21.5408  1.9653         1
   
   (%+/) power t* ^((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
0.0388793 0.148571 0.0258098 0.78674
   (%+/) power t* ^((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
0.0809316 0.16549 0.0250721 0.728506
   (%+/) power t* ^((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
0.0570977 0.217048 0.0343349 0.69152
   (%+/) power t* ^((0 ,stddeviation) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
0.156546 0.208166 0.050371 0.584917
   
   ^((0 , stddev (<"1 (4 $. $. reverse_identity_matrix #t)) { ^.t% %/~ (%+/) power t ) tomusigma normalrand (#t) * <:#t) (<"1 (4 $. $. reverse_identity_matrix #t)) } reverse_identity_matrix #t
       1  3.81711 0.183127 0.531152
0.935384        1 0.566418 0.339004
 2.03201  2.64248        1  2.80847
0.540579 0.673538  0.70532        1
   
   monte_carlo_error_factor =: 13 : '^((0 , stddev (<"1 (4 $. $. reverse_identity_matrix #y)) { ^. y % %/~ (%+/) power y ) tomusigma normalrand (#y) * <:#y) (<"1 (4 $. $. reverse_identity_matrix #y)) } reverse_identity_matrix #y'
   monte_carlo_error_factor t
      1 0.144492 0.589238  2.39264
1.35269        1 0.663721  1.11152
1.03719  1.46932        1 0.748591
1.11159  3.05932 0.188892        1
   t* monte_carlo_error_factor t
        1  0.28542 2.65428 0.184232
   12.215        1 5.50308 0.227414
0.0892592 0.272591       1 0.211094
  1.76654   9.7339 7.84091        1
   
   upper_triangle =: 13 : '</~ i.y'
   upper_triangle 4
0 1 1 1
0 0 1 1
0 0 0 1
0 0 0 0
   
   <"1 (4 $. $. upper_triangle 4)
┌───┬───┬───┬───┬───┬───┐
│0 1│0 2│0 3│1 2│1 3│2 3│
└───┴───┴───┴───┴───┴───┘
   monte_carlo_error_factor =: 13 : '^((0 , stddev (<"1 (4 $. $. upper_triangle #y)) { ^. y % %/~ (%+/) power y ) tomusigma normalrand (#y) * <:#y) (<"1 (4 $. $. upper_triangle #y)) } upper_triangle #y'
   ^(+|:)~ ((0, stddev (<"1 (4 $. $. upper_triangle #t)) { ^. t % %/~ (%+/) power t) tomusigma normalrand(+/ ,upper_triangle #t)) (<"1 (4 $. $. upper_triangle #t)) } upper_triangle #t
      1  1.10373   2.1526  1.03256
1.10373        1 0.890765 0.729677
 2.1526 0.890765        1 0.361969
1.03256 0.729677 0.361969        1
   monte_carlo_error_factor =: 13 : '^(+|:)~ ((0, stddev (uti) { ^. y % %/~ (%+/) power y) tomusigma normalrand(+/ ,ut)) (uti =. <"1 (4 $. $. ut)) } ut =. upper_triangle #y'
   monte_carlo_error_factor t
       1  2.88198 0.90409 0.971323
 2.88198        1 1.89537 0.220267
 0.90409  1.89537       1  0.58946
0.971323 0.220267 0.58946        1
   t* monte_carlo_error_factor t
       1  0.123146 4.77024  0.123288
 1.97034         1  6.8053 0.0320912
0.132507 0.0840161       1  0.173633
 3.08221   2.59939 8.50803         1
   t
       1     0.25 6      0.2
       4        1 9 0.111111
0.166667 0.111111 1 0.142857
       5        9 7        1
   
   (%+/) power t* monte_carlo_error_factor t
0.130584 0.133144 0.0153946 0.720877
   (2, #t)$ t
       1     0.25 6      0.2
       4        1 9 0.111111
0.166667 0.111111 1 0.142857
       5        9 7        1

       1     0.25 6      0.2
       4        1 9 0.111111
0.166667 0.111111 1 0.142857
       5        9 7        1
   monte_carlo_error_factor"2 ((2, #t)$ t)
       1  1.38219 0.429269  1.04275
 1.38219        1 0.784692 0.947911
0.429269 0.784692        1 0.504057
 1.04275 0.947911 0.504057        1

       1 0.853777 0.943976  1.52523
0.853777        1  1.27463 0.507077
0.943976  1.27463        1  1.50017
 1.52523 0.507077  1.50017        1
   (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       1  0.433943 3.98547  0.163932
 6.94309         1 13.8081  0.152621
0.110707  0.170471       1  0.107785
 4.09831   12.3623 5.28146         1

       1  0.171276 16.5817  0.142095
 2.74042         1 4.95961 0.0807486
0.460603 0.0612298       1  0.321086
 3.55236   6.54063 15.7332         1
   $ (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
2 4 4
   (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
0.0497705 0.157313 0.0251139 0.767803
0.0685681 0.245165 0.0261178 0.660149
   
   (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((3, #t)$ t))
0.0718784 0.400952 0.0544337 0.472736
0.0984765 0.234001 0.0358821  0.63164
0.0549167 0.265892 0.0284535 0.650738
   (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((4, #t)$ t))
 0.110367   0.4071 0.0176637  0.46487
0.0984903 0.131783 0.0266773 0.743049
  0.12489  0.43934  0.020262 0.415508
0.0836392 0.237199 0.0264369 0.652725
   NB. from Monte Carlo weights of alternatives -> to pairwise stochastic domination probabilities (or as z-scores of those probabilities)
   
   |: (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
 0.158385  0.135904
 0.182406  0.230939
0.0542439 0.0264175
 0.604965   0.60674
   |:"1 (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
0.119655 0.271521 0.0287073 0.580116
0.109664 0.260286 0.0308555 0.599195
   %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       1 0.0878645 0.768369   0.11412
 11.3812         1  8.74493   1.29882
 1.30146  0.114352        1  0.148523
  8.7627   0.76993  6.73298         1

       1  0.349945  4.26012  0.125826
 2.85759         1  12.1737  0.359559
0.234735 0.0821444        1 0.0295357
 7.94749   2.78119  33.8573         1
   %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       1 0.384057 1.81645 0.0797335
 2.60378        1 4.72963  0.207609
0.550526 0.211433       1 0.0438953
 12.5418  4.81675 22.7815         1

       1 0.364469 3.37744  0.169385
 2.74372        1 9.26675  0.464743
0.296082 0.107913       1 0.0501517
 5.90372  2.15172 19.9395         1
   geomean
# %: product
   
   ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 _0.677074 _0.430282 _2.79589
0.677074         0  0.246792 _2.11882
0.430282 _0.246792         0 _2.36561
 2.79589   2.11882   2.36561        0

       0 _0.532702   1.38192 _2.31123
0.532702         0   1.91462 _1.77852
_1.38192  _1.91462         0 _3.69315
 2.31123   1.77852   3.69315        0
   stddev ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 0.855707 0.356611 0.636231
0.855707        0 0.499096 0.219476
0.356611 0.499096        0  0.27962
0.636231 0.219476  0.27962        0
   stddev ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 0.197691   0.7788 0.604328
0.197691        0 0.581108 0.406637
  0.7788 0.581108        0 0.174471
0.604328 0.406637 0.174471        0
   mean ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 _0.534258 1.41023 _1.80967
0.534258         0 1.94449 _1.27541
_1.41023  _1.94449       0  _3.2199
 1.80967   1.27541  3.2199        0
   t
       1     0.25 6      0.2
       4        1 9 0.111111
0.166667 0.111111 1 0.142857
       5        9 7        1
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 _1.53005 1.01371 _9.71937
 1.53005        0 1.31867 _6.07822
_1.01371 _1.31867       0 _4.58278
 9.71937  6.07822 4.58278        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 _1.56445 10.6164 _87.2836
 1.56445        0 3.18758 _1.83479
_10.6164 _3.18758       0 _22.0112
 87.2836  1.83479 22.0112        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((2, #t)$ t))
       0 _0.316758 2.16102 _54.0074
0.316758         0 38.4076 _2.13536
_2.16102  _38.4076       0 _4.55516
 54.0074   2.13536 4.55516        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((200, #t)$ t))
       0 _1.23056 1.88248 _3.01156
 1.23056        0 3.23988 _2.01458
_1.88248 _3.23988       0 _4.71694
 3.01156  2.01458 4.71694        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((200, #t)$ t))
       0 _1.30988 1.86672 _3.57365
 1.30988        0 3.08665 _2.09042
_1.86672 _3.08665       0 _5.62711
 3.57365  2.09042 5.62711        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((100, #t)$ t))
       0 _1.14942 2.37082 _3.62477
 1.14942        0 3.54092 _2.26891
_2.37082 _3.54092       0  _6.1477
 3.62477  2.26891  6.1477        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((10000, #t)$ t))
      0 _1.22775   1.864 _3.23678
1.22775        0 3.12144  _2.0326
 _1.864 _3.12144       0 _5.13796
3.23678   2.0326 5.13796        0
   (mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((10000, #t)$ t))
       0 _1.20796 1.86048 _3.21104
 1.20796        0 3.11496 _2.07301
_1.86048 _3.11496       0 _5.12671
 3.21104  2.07301 5.12671        0
   t
       1     0.25 6      0.2
       4        1 9 0.111111
0.166667 0.111111 1 0.142857
       5        9 7        1
   (%+/) power t
0.100575 0.202725 0.0345109 0.662189
   
   monte_carlo_domination_matrix =: 13 : '(mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   t monte_carlo_domination_matrix 10000	NB. results on z-scale, ie. those are pairwise domination z-scores, based on Monte Carlo results based on standard deviations of pairwise comparison inconsistencies with respect to the eigenvector weights of the original pairwise comparison matrix
       0 _1.23424 1.88247 _3.25392
 1.23424        0 3.16264 _2.06875
_1.88247 _3.16264       0 _5.18863
 3.25392  2.06875 5.18863        0
   
   pnorm_f _2
0.0227501
   pnorm_f _3
0.00134997
   pnorm_f _1
0.158655
   pnorm_f _1*|t monte_carlo_domination_matrix 10000	NB. probabilities of results on z-scale, ie. those are pairwise domination z-scores, based on Monte Carlo results based on standard deviations of pairwise comparison inconsistencies with respect to the eigenvector weights of the original pairwise comparison matrix
        0.5    0.112781   0.0311042 0.000659287
   0.112781         0.5 0.000973289   0.0196713
  0.0311042 0.000973289         0.5  1.49961e_7
0.000659287   0.0196713  1.49961e_7         0.5
   
   i.#t
0 1 2 3
   =/~ i.#t
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
   <"1 (4 $. $. =/~ i.#t)
┌───┬───┬───┬───┐
│0 0│1 1│2 2│3 3│
└───┴───┴───┴───┘
   (1) (<"1 (4 $. $. =/~ i.#t)) } pnorm_f _1*|t monte_carlo_domination_matrix 10000
          1   0.114446  0.0324735 0.000764838
   0.114446          1 0.00091031   0.0197757
  0.0324735 0.00091031          1  1.61271e_7
0.000764838  0.0197757 1.61271e_7           1
   (1) (<"1 (4 $. $. =/~ i.#t)) } pnorm_f _1*|t monte_carlo_domination_matrix 100000
         1    0.110195   0.0312041 0.00070246
  0.110195           1 0.000865114  0.0204631
 0.0312041 0.000865114           1 1.54138e_7
0.00070246   0.0204631  1.54138e_7          1
   (1) (<"1 (4 $. $. =/~ i.#t)) } pnorm_f _1*|t monte_carlo_domination_matrix 100000
          1    0.110876   0.0308965 0.000696462
   0.110876           1 0.000935254    0.020134
  0.0308965 0.000935254           1  1.39608e_7
0.000696462    0.020134  1.39608e_7           1
   (1) (<"1 (4 $. $. =/~ i.#t)) } pnorm_f _1*|t monte_carlo_domination_matrix 1000000	NB. probabilities of results on z-scale
          1    0.111355   0.0306399 0.000721007
   0.111355           1 0.000910692   0.0199328
  0.0306399 0.000910692           1  1.36079e_7
0.000721007   0.0199328  1.36079e_7           1
   
   (%+/) power t
0.100575 0.202725 0.0345109 0.662189
   
   (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((3, #t)$ t))
0.0933734 0.227554 0.0311296 0.647943
 0.159619 0.205461 0.0308552 0.604065
0.0431886 0.204929 0.0332564 0.718626
   
   + abi =: (%"2 +/"1) power"2 (t*"2 monte_carlo_error_factor"2 ((3, #t)$ t))
  0.11726 0.190265 0.0195988 0.672876
 0.124357  0.15765 0.0256969 0.692297
0.0892888 0.255517 0.0278544  0.62734
   
   >/"1~ abi
0 0 1 0
1 0 1 0
0 0 0 0
1 1 1 0

0 0 1 0
1 0 1 0
0 0 0 0
1 1 1 0

0 0 1 0
1 0 1 0
0 0 0 0
1 1 1 0
   +/ >/"1~ abi
0 0 3 0
3 0 3 0
0 0 0 0
3 3 3 0
   
   monte_carlo_votes_from_weights =: 13 : '+/ >/"1~ (%"2 +/"1) power"2 (x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   t monte_carlo_votes_from_weights 10000
   0 1128 9585  33
8872    0 9963 286
 415   37    0   1
9967 9714 9999   0
   t monte_carlo_votes_from_weights 100000
    0 11232 95904  319
88768     0 99597 3001
 4096   403     0    1
99681 96999 99999    0
   t monte_carlo_votes_from_weights 1000
  0 117  960  1
883   0  996 25
 40   4    0  0
999 975 1000  0
   0.5 1000 0,"(1 0) (,t monte_carlo_votes_from_weights 1000)
0.5 1000 0    0
0.5 1000 0  109
0.5 1000 0  955
0.5 1000 0    2
0.5 1000 0  891
0.5 1000 0    0
0.5 1000 0  997
0.5 1000 0   44
0.5 1000 0   45
0.5 1000 0    3
0.5 1000 0    0
0.5 1000 0    0
0.5 1000 0  998
0.5 1000 0  956
0.5 1000 0 1000
0.5 1000 0    0
   binomialprob"1 (0.5 1000 0,"(1 0) (,tvotes =: t monte_carlo_votes_from_weights 1000))
9.33264e_302 1.06345e_151 1 4.67099e_296 1 9.33264e_302 1 1.85764e_238 2.99663e_223 4.67099e_296 9.33264e_302 9.33264e_302 1 1 1 9.33264e_302
   binomialprob"1 (0.5 1000 1000,"(1 0) (,tvotes =: t monte_carlo_votes_from_weights 1000))
0 0 0 0 0 0 0 0 0 0 0 0 0 0 9.33264e_302 0
   
   NB. Siit algab Loeng 1.
   NB. Iversoni notatsioon võimaldab enamasti vältida muutujate indekseid ja koodi tsükleid.
   
   NB. Let S be a pairwise comparison matrix using comparisons on a Saaty ratio scale.
   NB. Let st be the function that generates such a random pairwise comparison matrix.
   NB. x: +S =: st 4
   x: +S =: st 4
1 1r8 1r5 1r8
8   1 1r6   8
5   6   1   3
8 1r8 1r3   1
   
   NB. Let power be the function that computes the first eigenvector of S by using the Power method.
   NB. Let normalise_to_1 be the function for the AHP weights normalisation (the sum of weights to 1) .
   normalise_to_1 =: 13 : '(%+/) y'
   normalise_to_1 power S	NB. extract weights from comparison matrix S as the 1st eigenvector; normalize to 1
0.0368928 0.304092 0.541317 0.117698
   
   NB. Weights eigenvector can be used to reproduce consistent comparisons by pairwise ratios between weights. Let the function of reproducing consistent comparisons matrix be rccm. Let those consistent comparisons form a comparison matric cS
   rccm =: 13 : '%/~ y'
   + cS =: rccm normalise_to_1 power S		NB. reproduced consistent comparisons
      1 0.121321 0.0681539 0.313453
8.24258        1  0.561764  2.58366
14.6727  1.78011         1  4.59919
3.19027 0.387048   0.21743        1
   
   NB. Let E be the the error matrix that results when the original comparison matrix S is divided by the reproduced consistent matrix cS.
   + E =: cS % S	NB. error matrix E.
       1  0.97057  0.34077  2.50762
 1.03032        1  3.37058 0.322957
 2.93453 0.296685        1  1.53306
0.398784  3.09639 0.652289        1
   
   NB. Such an error matrix E consists of error coefficients on a ratio scale.
   NB. Let us transform the values on a ratio scale onto a logarithmic scale to be able to measure standard deviation. Lets use the natural logarithm.
   ln =: ^.
   
   + lnE =: ln E
         0 _0.0298714  _1.07655 0.919335
0.0298714          0   1.21509 _1.13024
  1.07655   _1.21509         0 0.427268
_0.919335    1.13024 _0.427268        0
   
   NB. Now it is possible to measure the standard deviation of pairwise comparison errors (inconsistencies, to be more precise).
   NB. But one should leave aside the main diagonal values (errors of comparisons with itself) and take the values only from above the diagonal or only from below the diagonal, because the matrix S is reciprocal, thus also E and lnE are reciprocal.
   NB. Let upper_indices be the function to provide the desired indices to extract the upper triangle values (above the main diagonal).
   upper_triangle =: 13 : '</~ i.y'
   upper_triangle 4
0 1 1 1
0 0 1 1
0 0 0 1
0 0 0 0
   <"1 (4 $. $. upper_triangle 4)
┌───┬───┬───┬───┬───┬───┐
│0 1│0 2│0 3│1 2│1 3│2 3│
└───┴───┴───┴───┴───┴───┘
   monte_carlo_error_factor =: 13 : '^(+|:)~ ((0, stddev (uti) { ^. y % %/~ (%+/) power y) tomusigma normalrand(+/ ,ut)) (uti =. <"1 (4 $. $. ut)) } ut =. upper_triangle #y'
   
   upper_indices =: 13 : '<"1 (4 $. $. upper_triangle#y)'
   upper_indices S
┌───┬───┬───┬───┬───┬───┐
│0 1│0 2│0 3│1 2│1 3│2 3│
└───┴───┴───┴───┴───┴───┘
   
   NB. Now the relevant matrix values can be selected.
   (upper_indices S) { lnE
_0.0298714 _1.07655 0.919335 1.21509 _1.13024 0.427268
   
   NB. Let stddev be the function to compute the standard deviation of pairwise comparison errors on the logarithmic scale.
   + stddev_lnE =: stddev (upper_indices S) { lnE
0.992355
   
   NB. This standard deviation can be used to generate random values for random disturbancies (inconsistencies) on the original comparison matrix S for the Monte Carlo approach.
   (0, stddev_lnE) tomusigma normalrand +/ ,upper_triangle #S
_0.104234 _0.126767 1.63646 0.154813 0.107062 0.451059
   NB. Let rand_values_from_stddev be the function to generate as many random values as there were cells in the upper triangle by using the computed standard deviation.
   rand_values_from_stddev =: 13 : '(0, y) tomusigma normalrand +/ ,upper_triangle #x'
   
   + lnErand =: lnE rand_values_from_stddev stddev_lnE
_0.813282 _0.473706 0.432572 1.23414 _1.45497 _1.22697
   
   NB. Those generated random values should be placed into an upper triangle empty matrix to corresponding cells and the upper triangle matrix should be mirrored into the lower triangle as well.
   NB. And the values on the natural logarithm scale should be reversed back by e^x
   NB. and don't forget that the lower triangle values should be multiplied by -1 with respect to the upper triangle values.
   (+ _1*|:)~ lnErand (upper_indices S) } upper_triangle #S
      
       0 _0.813282 _0.473706 0.432572
 0.813282         0   1.23414 _1.45497
 0.473706  _1.23414         0 _1.22697
_0.432572   1.45497   1.22697        0
   
   place_upper_mirror_lower =: 13 : '^(+ _1*|:)~ y (upper_indices x) } upper_triangle #x'
   S place_upper_mirror_lower lnErand
       1 2.91762 0.840225 6.42945
 2.91762       1  6.10382  5.7591
0.840225 6.10382        1 1.03849
 6.42945  5.7591  1.03849       1
   
   NB. Let all the prior steps together (besides the 1st one) be defined as a function named as monte_carlo_error_factor
   monte_carlo_error_factor =: 13 : '^(+ _1*|:)~ ((0, stddev (uti) { ^. y % %/~ (%+/) power y) tomusigma normalrand(+/ ,ut)) (uti =. <"1 (4 $. $. ut)) } ut =. upper_triangle #y'
   monte_carlo_error_factor S
       1  1.14521 0.409888  3.24524
0.873203        1  0.89768  5.56753
 2.43969  1.11398        1 0.709766
0.308144 0.179613  1.40891        1
   
   NB. Any time that function is called, it will generate another set of error factors for Monte Carlo analysis.
   NB. If the original comparison matrix S is multiplied with the error factor matrix, it will give a perturbed comparison matrix, from which the perturbed eigenvector can be computed.
   S* monte_carlo_error_factor S
      1  0.36763  0.256456 0.110734
23.5283        1 0.0337449  13.5714
6.41141  1.21482         1  2.08629
  7.087 0.212053   0.23181        1
   
   normalise_to_1 power S* monte_carlo_error_factor S
0.0533954 0.337412 0.507268 0.101924
   
   NB. Multiple perturbation matrices can be generated and from them eigenvectors computed.
   (%"2 +/"1) power"2 (S*"2 monte_carlo_error_factor"2 ((3, #S)$ S))
0.0396175 0.442519 0.399766 0.118097
0.0495589 0.380845 0.467032 0.102565
0.0320612 0.483632 0.339766 0.144541
   
   NB. Those eigenvector weights of perturbation matrices are the basis for gathering statistics.
   NB. The idea is to compare the ratios of pairwise weights of alternatives of the comparison matrix.
   NB. For that, one can use individual eigenvectors to recreate individual comparison matrices, analogous to step (xxx).
   NB. And then compare values (transformed to the logarithmic scale) from the same cell position from different comparison matrices.
   
   NB. For each cell position over different perturbed comparison matrices a ratio of an arithmetic mean and standard deviation can be computed.
   NB. If the weights of two alternatives are equal, then the mean of perturbed weights of those two alternatives should be around zero.
   
   monte_carlo_domination_matrix =: 13 : '(mean % stddev) ^. %/"1~ (%"2 +/"1) power"2 (x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   + pairwiseDom_10000 =: S monte_carlo_domination_matrix 10000	NB. results on z-scale (Standard score), ie. those are pairwise domination z-scores, based on Monte Carlo results based on standard deviations of pairwise comparison inconsistencies with respect to the eigenvector weights of the original pairwise comparison matrix
      0 _2.77181  _3.53659 _1.54419
2.77181        0 _0.746461  1.23904
3.53659 0.746461         0  1.96161
1.54419 _1.23904  _1.96161        0
   
   NB. The ratio between the mean and standard deviation is a z-score - it measures how far probabilistically the weights of those two alternatives are from each other on a z-scale.
   NB. Those z-scores can be transformed into direct probabilities - the probability that the weight of one alternative stochastically dominates over the weight of another alternative.
   + Zscore_probs_10000 =: pnorm_f _1* | pairwiseDom_10000	NB. probabilities of results on z-scale, ie. those are pairwise domination z-scores, based on Monte Carlo results based on standard deviations of pairwise comparison inconsistencies with respect to the eigenvector weights of the original pairwise comparison matrix
        0.5 0.00278731 0.000202703 0.0612709
 0.00278731        0.5    0.227694  0.107665
0.000202703   0.227694         0.5  0.024904
  0.0612709   0.107665    0.024904       0.5
   
   NB. small probabilities may vary from run to run, even if 10000 Monte Carlo instances are used only 2 significant digits have converged.
   NB. One could generate 100 x 10000 runs to assess the variability.
      pnorm_f _1* | S monte_carlo_domination_matrix 10000
        0.5 0.00333692 0.000272496 0.0611648
 0.00333692        0.5    0.231864  0.104073
0.000272496   0.231864         0.5 0.0261009
  0.0611648   0.104073   0.0261009       0.5
   
   pnorm_f _1* | S monte_carlo_domination_matrix 10000
        0.5 0.00271866 0.000184834 0.0560598
 0.00271866        0.5    0.233777  0.101264
0.000184834   0.233777         0.5 0.0245882
  0.0560598   0.101264   0.0245882       0.5
   
   pnorm_f _1* | S monte_carlo_domination_matrix 10000
        0.5 0.00281555 0.000211742 0.0585169
 0.00281555        0.5    0.235259  0.104284
0.000211742   0.235259         0.5 0.0269903
  0.0585169   0.104284   0.0269903       0.5
   
   
   NB. But this approach assumes normal distribution of values. If the values at a cell position over different perturbed comparison matrices are not normally distributed, then another option would be to use voting and binary distribution calculations to assess stochastic dominance of one alternative weight over the weight of another alternative.
   NB. The steps with voting and binary distribution calculation are described next.
   
   NB. Instead of pairwise ratios (as in step xx2), one would compute pairwise dominance votes.
   NB. Let monte_carlo_votes_from_weights be the function to compute the voting table from the eigenvectors of perturbed comparison matrices.
   monte_carlo_votes_from_weights =: 13 : '+/ >/"1~ (%"2 +/"1) power"2 (x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   
   + dom_votes_monte_carlo_10000 =: S monte_carlo_votes_from_weights 10000
   0   72   14  696
9928    0 2144 8912
9986 7856    0 9722
9304 1088  278    0
   
   
   dom_votes_monte_carlo_10000 < -:10000
1 1 1 1
0 1 1 0
0 0 1 0
0 1 1 1
   
   (upper_indices S) { dom_votes_monte_carlo_10000
72 14 696 2144 8912 9722
   
   dom_votes_monte_carlo_10000 > -:10000
0 0 0 0
1 0 0 1
1 1 0 1
1 0 0 0
   10000* dom_votes_monte_carlo_10000 > -:10000
    0     0 0     0
10000     0 0 10000
10000 10000 0 10000
10000     0 0     0
   10000* (upper_indices S) { dom_votes_monte_carlo_10000 > -:10000
0 0 0 0 10000 10000
   
   (0.5 10000),"(1 1) /:~"1 ((upper_indices S) { dom_votes_monte_carlo_10000) ,. (10000* (upper_indices S) { dom_votes_monte_carlo_10000 > -:10000)
0.5 10000    0    72
0.5 10000    0    14
0.5 10000    0   696
0.5 10000    0  2144
0.5 10000 8912 10000
0.5 10000 9722 10000
   binomialprob"1 (0.5 10000),"(1 1) /:~"1 ((upper_indices S) { dom_votes_monte_carlo_10000) ,. (10000* (upper_indices S) { dom_votes_monte_carlo_10000 > -:10000)
0 0 0 0 0 0
   
   S
1 0.125      0.2 0.125
8     1 0.166667     8
5     6        1     3
8 0.125 0.333333     1
   
   */ S
320 0.09375 0.0111111 3
   */"1 S
0.003125 10.6667 90 0.333333
   S*S*S
  1 0.00195313      0.008 0.00195313
512          1 0.00462963        512
125        216          1         27
512 0.00195313   0.037037          1
   
   S^(_1* #S)
          1        4096  625        4096
0.000244141           1 1296 0.000244141
     0.0016 0.000771605    1   0.0123457
0.000244141        4096   81           1
   
   (*/ S) */ (*/"1 S)
          1  3413.33  28800   106.667
0.000292969        1 8.4375   0.03125
 3.47222e_5 0.118519      1 0.0037037
   0.009375       32    270         1
   (S^(_1* #S))* (*/ S) */ (*/"1 S)
         1   1.3981e7 1.8e7     436907
7.15256e_8          1 10935 7.62939e_6
5.55556e_8 9.14495e_5     1 4.57247e_5
2.28882e_6     131072 21870          1
   %2- ~ #S
0.5
   %S^#S
          1        4096  625        4096
0.000244141           1 1296 0.000244141
     0.0016 0.000771605    1   0.0123457
0.000244141        4096   81           1
   
   (%S ^ #S)* (*/ S) */ (*/"1 S)
         1   1.3981e7 1.8e7     436907
7.15256e_8          1 10935 7.62939e_6
5.55556e_8 9.14495e_5     1 4.57247e_5
2.28882e_6     131072 21870          1
   ((%S ^ #S)* (*/ S) */ (*/"1 S)) ^ (%2- ~ #S)
          1    3739.12 4242.64    660.989
0.000267443          1 104.571 0.00276214
0.000235702 0.00956292       1 0.00676201
 0.00151288    362.039 147.885          1
   
   (S ^ #S)* (*/ S) */ (*/"1 S)
        1  0.833333      46.08 0.0260417
      1.2         1 0.00651042       128
0.0217014     153.6          1       0.3
     38.4 0.0078125    3.33333         1
   %2- #S
_0.5
   ((S ^ #S)* (*/ S) */ (*/"1 S)) ^ (%2- #S)	NB. see peaks olema õige, ehkki astendajat tuleb veel modida
       1   1.09545 0.147314   6.19677
0.912871         1  12.3935 0.0883883
 6.78823 0.0806872        1   1.82574
0.161374   11.3137 0.547723         1
   
   S
1 0.125      0.2 0.125
8     1 0.166667     8
5     6        1     3
8 0.125 0.333333     1
   
   + E =: cS % S	NB. error matrix E
       1  0.97057  0.34077  2.50762
 1.03032        1  3.37058 0.322957
 2.93453 0.296685        1  1.53306
0.398784  3.09639 0.652289        1
   
   S*E
      1 0.121321 0.0681539 0.313453
8.24258        1  0.561764  2.58366
14.6727  1.78011         1  4.59919
3.19027 0.387048   0.21743        1
   cS
      1 0.121321 0.0681539 0.313453
8.24258        1  0.561764  2.58366
14.6727  1.78011         1  4.59919
3.19027 0.387048   0.21743        1
   cS -: S*E
1
   
   + kriteeriumid =: 3 3 $ 1 5 7, 1r5 1 1r3, 1r7 3 1
  1 5   7
1r5 1 1r3
1r7 3   1
   
   + kvaliteet =: 4 4 $ 1 3 7 3, 1r3 1 4 2, 1r7 1r4 1 1r2, 1r3 1r2 2 1
  1   3 7   3
1r3   1 4   2
1r7 1r4 1 1r2
1r3 1r2 2   1
   
   + kulutused =: 4 4 $ 1 1r4 1r7 1r3, 4 1 1r3 1r2, 7 3 1 1r2, 3 2 2 1
1 1r4 1r7 1r3
4   1 1r3 1r2
7   3   1 1r2
3   2   2   1
   
   + kaugus =: 4 4 $ 1 1r7 1r5 1r2, 7 1 1r2 5, 5 2 1 7, 2 1r5 1r7 1
1 1r7 1r5 1r2
7   1 1r2   5
5   2   1   7
2 1r5 1r7   1
   
   NB. Multiple perturbation matrices can be generated and from them eigenvectors computed.
   (%"2 +/"1) power"2 (S*"2 monte_carlo_error_factor"2 ((3, #S)$ S))
 0.015571 0.191469 0.614371 0.178589
 0.101675 0.248761 0.571632 0.077932
0.0211424 0.413645 0.468878 0.096334
   
   mc_vectors =: 13 : '(%"2 +/"1) power"2 (x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   S mc_vectors 3
0.0162444 0.249217 0.661743 0.0727954
0.0383866 0.318945  0.50146  0.141209
0.0545937 0.343472 0.482931  0.119004
   
   $ krit_10000 =: kriteeriumid mc_vectors 10000	NB. 10 000 Monte Carlo abil häiritud kriteeriumite osakaalude vektorit
10000 3
   
   $ kvaliteet_10000 =: kvaliteet mc_vectors 10000	NB. 10 000 Monte Carlo abil häiritud kvaliteedi alusel alternatiivide osakaalude vektorit
10000 4
   
   $ kulutused_10000 =: kulutused mc_vectors 10000	NB. 10 000 Monte Carlo abil häiritud kulude alusel alternatiivide osakaalude vektorit
10000 4
   
   $ kaugus_10000 =: kaugus mc_vectors 10000	NB. 10 000 Monte Carlo abil häiritud kauguse alusel alternatiivide osakaalude vektorit
10000 4
   NB. algse AHP mudeli lõpptulemuse arvutamise sammud, samm 1. arvuta kriteeriumite osakaalud:
   normalise_to_1 power kriteeriumid	NB. extract weights from comparison matrix S as the 1st eigenvector; normalize to 1
0.738307 0.0915203 0.170172
   
   NB. samm 2, arvuta alternatiivide osakaalud iga üksiku kriteeriumi suhtes
   normalise_to_1 power kvaliteet
0.541566 0.244679 0.0691291 0.144626
   
   normalise_to_1 power kulutused
0.0683294 0.177959 0.364361 0.38935
   
   normalise_to_1 power kaugus
0.0612357 0.349414 0.5054 0.083951
   
   kvaliteet; kulutused; kaugus
┌─────────────┬─────────────┬─────────────┐
│  1   3 7   3│1 1r4 1r7 1r3│1 1r7 1r5 1r2│
│1r3   1 4   2│4   1 1r3 1r2│7   1 1r2   5│
│1r7 1r4 1 1r2│7   3   1 1r2│5   2   1   7│
│1r3 1r2 2   1│3   2   2   1│2 1r5 1r7   1│
└─────────────┴─────────────┴─────────────┘
   normalise_to_1 each power each kvaliteet; kulutused; kaugus
┌────────────────────────────────────┬───────────────────────────────────┬──────────────────────────────────┐
│0.541566 0.244679 0.0691291 0.144626│0.0683294 0.177959 0.364361 0.38935│0.0612357 0.349414 0.5054 0.083951│
└────────────────────────────────────┴───────────────────────────────────┴──────────────────────────────────┘
   
   NB. ja nüüd korruta alternatiivide osakaalud kriteeriumi suhtes läbi kriteeriumi enda osakaaluga ja siis summeeri korrutised.
   
   normalise_to_1 power kriteeriumid
0.738307 0.0915203 0.170172
   
   > (normalise_to_1 power kriteeriumid) */ each (normalise_to_1 each power each kvaliteet; kulutused; kaugus)
  0.399842  0.180648 0.0510386  0.106778
0.00625353 0.0162869 0.0333464 0.0356335
 0.0104206 0.0594605  0.086005 0.0142861
   
   NB. 3-kihilise AHP mudeli lõppkaalude arvutamine võrdlusmaatriksite pealt:
   +/ > (normalise_to_1 power kriteeriumid) */ each (normalise_to_1 each power each kvaliteet; kulutused; kaugus)
0.416516 0.256396 0.17039 0.156698
   
   NB. võrdlusmaatriksi piires Monte Carlo häiritusega osakaalude hulgast saab võtta ühe neist häiritud omavektoritest juhuslikult välja.
   NB. samamoodi saab iga võrdlusmaatriksi MC häiritud vektorite seast võtta ühe vektori juhuslikult välja.
   NB. Ja nende juhuslikult väljavalitud Monte Carlo häiritud omavektorite komplekti alusel saab arvutada AHP häiritud lõppkaalud.
   
   $ krit_10000
10000 3
   
   ?10000		NB. juhusliku arvu (järjeindeksi) genereerimine vahemikust [0; 10000]
8141
   
   (?10000) { krit_10000	NB. kriteeriumite Monte Carlo häiritud omavektoritest ühe juhuslik väljavalimine
0.776119 0.0894553 0.134426
   
   ((?10000) { kvaliteet_10000); ((?10000) { kulutused_10000); ((?10000) { kaugus_10000)
┌────────────────────────────────────┬──────────────────────────────────┬─────────────────────────────────────┐
│0.500272 0.271934 0.0755431 0.152251│0.058889 0.158884 0.349496 0.43273│0.0579002 0.339461 0.530394 0.0722451│
└────────────────────────────────────┴──────────────────────────────────┴─────────────────────────────────────┘
   NB. juhusliku valiku põhjal AHP Monte Carlo häiritud lõppkaalud
   +/ > ((?10000) { krit_10000) */ each ((?10000) { kvaliteet_10000); ((?10000) { kulutused_10000); ((?10000) { kaugus_10000)
0.385577 0.281087 0.167683 0.165653
   
   #krit_10000
10000
   
   $ krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
4
   $ {. krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000

   # each $ {. krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000

   ># each {. krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
10000
   
   4?10000
7115 4194 4305 5741
   #>{. krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
10000
   $ krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
4
   #>{. krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
10000
   (4?10000) { each krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
┌──────────────────────────┬──────────────────────────────────┬───────────────────────────────────┬─────────────────────────────────────┐
│0.771263 0.0625073 0.16623│0.537951 0.242772 0.06681 0.152467│0.0808955 0.32564 0.232058 0.361406│0.0479556 0.347623 0.524975 0.0794466│
└──────────────────────────┴──────────────────────────────────┴───────────────────────────────────┴─────────────────────────────────────┘
   + juhuvalik =: 4?10000
3602 3573 8372 7366
   juhuvalik { each krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
┌───────────────────────────┬────────────────────────────────────┬──────────────────────────────────┬───────────────────────────────────┐
│0.684567 0.0964539 0.218979│0.553514 0.228884 0.0635161 0.154085│0.05927 0.137378 0.337584 0.465767│0.0667297 0.31903 0.534517 0.079723│
└───────────────────────────┴────────────────────────────────────┴──────────────────────────────────┴───────────────────────────────────┘
   3602 { krit_10000
0.684567 0.0964539 0.218979
   3573 { kvaliteet_10000
0.553514 0.228884 0.0635161 0.154085
   
   {. (( $yy ) ? ( #>{. yy ))
6105 2098 7026 6509
   AHP3_MC_juhu =: 13 : '({. ( $y ) ? ( #>{. y )) { each y'
   AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
┌───────────────────────────┬────────────────────────────────────┬───────────────────────────────────┬─────────────────────────────────────┐
│0.681569 0.0854619 0.232969│0.570059 0.254255 0.0670337 0.108652│0.0526388 0.136507 0.36434 0.446515│0.0631979 0.375355 0.480493 0.0809541│
└───────────────────────────┴────────────────────────────────────┴───────────────────────────────────┴─────────────────────────────────────┘
   
   }. AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
┌────────────────────────────────────┬────────────────────────────────────┬─────────────────────────────────────┐
│0.529551 0.251367 0.0661342 0.152948│0.0732661 0.193686 0.397403 0.335645│0.0613392 0.321044 0.522824 0.0947931│
└────────────────────────────────────┴────────────────────────────────────┴─────────────────────────────────────┘
   >{. AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.744832 0.0833157 0.171852
   }. AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
┌────────────────────────────────────┬────────────────────────────────────┬─────────────────────────────────────┐
│0.541303 0.259414 0.0659776 0.133305│0.0984535 0.244991 0.236979 0.419576│0.0485136 0.410281 0.458305 0.0828997│
└────────────────────────────────────┴────────────────────────────────────┴─────────────────────────────────────┘
   ( >{. sisend ) */ each }. sisend =: AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
┌───────────────────────────────────┬────────────────────────────────────────┬─────────────────────────────────────┐
│0.405255 0.189037 0.0593536 0.11064│0.00613301 0.0180251 0.0326405 0.0305734│0.00940078 0.0559478 0.0691939 0.0138│
└───────────────────────────────────┴────────────────────────────────────────┴─────────────────────────────────────┘
   > ( >{. sisend ) */ each }. sisend =: AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
  0.464639   0.186129 0.0579653  0.108548
0.00325689 0.00673614 0.0153358 0.0170005
0.00843612  0.0430191 0.0760653 0.0128688
   +/ > ( >{. sisend ) */ each }. sisend =: AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.442312 0.225699 0.1703 0.161689
   
   +/ > ( >{. sisend ) */ each }. sisend =: AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.43942 0.231166 0.166597 0.162816
   +/ > ( >{. sisend ) */ each }. sisend =: AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.422675 0.244251 0.17343 0.159644
   AHP3_loppkaalud =: 13 : '+/ > ( >{. y ) */ each }. y'
   AHP3_loppkaalud AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.428408 0.225858 0.190996 0.154738
   
   AHP3_loppkaalud AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.419417 0.27476 0.156355 0.149468
   AHP3_loppkaalud AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.455653 0.240366 0.156694 0.147288
   AHP3_loppkaalud AHP3_MC_juhu krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000
0.407407 0.273272 0.152101 0.16722
   
   + juhuvalik =: 5 4 $ (5 * 4)?10000
7321 2462 1240 2985
7444 8938 5821  660
9226 5660 4961 6260
3826 2263 1832 7894
7422 3742 2494  909
   
   # juhuvalik
5
   AHP3_MC_juhud =: 13 : 'y { each x'
   ( krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000 ) AHP3_MC_juhud"(1 1) juhuvalik =: 5 4 $ (5 * 4)?10000
┌───────────────────────────┬────────────────────────────────────┬────────────────────────────────────┬─────────────────────────────────────┐
│0.696837 0.100917 0.202246 │0.564586 0.239963 0.0720827 0.123368│0.0622102 0.171496 0.336786 0.429508│0.0683579 0.411018 0.44197 0.0786539 │
├───────────────────────────┼────────────────────────────────────┼────────────────────────────────────┼─────────────────────────────────────┤
│0.808962 0.0562828 0.134756│0.514806 0.238346 0.0803917 0.166456│0.0573034 0.157369 0.342235 0.443092│0.0633014 0.381262 0.478471 0.0769652│
├───────────────────────────┼────────────────────────────────────┼────────────────────────────────────┼─────────────────────────────────────┤
│0.816514 0.0522513 0.131235│0.531784 0.254117 0.0700017 0.144098│0.0726573 0.165822 0.334718 0.426804│0.0583178 0.354719 0.509377 0.0775855│
├───────────────────────────┼────────────────────────────────────┼────────────────────────────────────┼─────────────────────────────────────┤
│0.743005 0.102758 0.154237 │0.519285 0.259721 0.0730938 0.1479  │0.062059 0.171616 0.365257 0.401068 │0.0679203 0.339194 0.51615 0.0767355 │
├───────────────────────────┼────────────────────────────────────┼────────────────────────────────────┼─────────────────────────────────────┤
│0.713523 0.0737127 0.212764│0.520646 0.261708 0.0657888 0.151857│0.0613668 0.150431 0.379716 0.408486│0.0514903 0.343852 0.541049 0.0636095│
└───────────────────────────┴────────────────────────────────────┴────────────────────────────────────┴─────────────────────────────────────┘
   
   NB. lõppkaalude arvutamine iga AHP Monte Carlo häiritud osakaalude komplekti korral. Näites 5 komplekti osakaalusid.
   
   + kool_MC_loppkaalud =: AHP3_loppkaalud"1 ( krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000 ) AHP3_MC_juhud"(1 1) juhuvalik =: 5 4 $ (5 * 4)?10000
0.382119 0.267274 0.178331 0.172275
0.420596 0.244429 0.163514 0.171462
0.399593 0.276683 0.171759 0.151965
0.378461  0.26431  0.19849 0.158739
0.368737  0.25672 0.209441 0.165102
   
   monte_carlo_domination_matrix2 =: 13 : '(mean % stddev) ^. %/"1~ y'
   
   monte_carlo_domination_matrix2 kool_MC_loppkaalud 
       0  4.90259    4.9644  12.2987
_4.90259        0   3.26668  5.13304
 _4.9644 _3.26668         0 0.933931
_12.2987 _5.13304 _0.933931        0
   
   NB. The ratio between the mean and standard deviation is a z-score - it measures how far probabilistically the weights of those two alternatives are from each other on a z-scale.
   NB. Those z-scores can be transformed into direct probabilities - the probability that the weight of one alternative stochastically dominates over the weight of another alternative.
   + Zscore_probs_10000 =: pnorm_f _1 * |  monte_carlo_domination_matrix2 kool_MC_loppkaalud	NB. probabilities of results on z-scale, ie. those are pairwise domination z-scores, based on Monte Carlo results based on standard deviations of pairwise comparison inconsistencies with respect to the eigenvector weights of the original pairwise comparison matrix
        0.5  4.73585e_7  3.45091e_7 4.75082e_35
 4.73585e_7         0.5 0.000544145  1.42808e_7
 3.45091e_7 0.000544145         0.5     0.17517
4.75082e_35  1.42808e_7     0.17517         0.5
   
   NB. samad viimased sammud läbi tehtuna 10000 komplekti osakaaludega, 10000 kordust (kordusi võiks võtta vähem, näiteks 100, võtab vähem aega).
   
rand_deal_1 =: 13 : 'y?y'
   $ |: rand_deal_1"0 (4#10000)
10000 4
   
   monte_carlo_domination_matrix_probs =: 13 : 'pnorm_f _1 * |  monte_carlo_domination_matrix2 AHP3_loppkaalud"1 ( x ) AHP3_MC_juhud"(1 1) juhuvalik =: |: rand_deal_1"0 (4# #>{.x)'
   
   NB. 10000 komplekti osakaalude stohhastilise domineerimise tõenäosused (paremuse erinevus algsete lõppkaalude paremusest), 10000 korduse pealt aritmeetiline keskmine ja standardhälve (ehkki siingi peaks tõenäosuste maatriksid enne viima logaritmskaalale, aga kui eeldada et tõenäosused palju ei kõigu siis võib jätta ka logaritmimata)
   NB. väljundi esimeses kastis on tõenäosuste aritmeetilised keskmised, teises kastis on tõenäosuste standardhälbed.
   (mean; stddev) ( krit_10000; kvaliteet_10000; kulutused_10000; kaugus_10000 ) monte_carlo_domination_matrix_probs"(1 0) 10000#1
┌─────────────────────────────────────────────┬───────────────────────────────────────────────┐
│        0.5 7.04643e_5 2.43192e_5 1.08689e_15│2.57585e_14  5.61501e_6  1.41327e_6 3.82864e_16│
│ 7.04643e_5        0.5 0.00325172  4.88791e_7│ 5.61501e_6 2.57585e_14 0.000152322  7.10498e_8│
│ 2.43192e_5 0.00325172        0.5    0.294529│ 1.41327e_6 0.000152322 2.57585e_14  0.00100174│
│1.08689e_15 4.88791e_7   0.294529         0.5│3.82864e_16  7.10498e_8  0.00100174 2.57585e_14│
└─────────────────────────────────────────────┴───────────────────────────────────────────────┘
   
   NB. meeldetuletuseks algse tavalise AHP mudeli lõppkaalud (ilma hägustamiseta)
   +/ > (normalise_to_1 power kriteeriumid) */ each (normalise_to_1 each power each kvaliteet; kulutused; kaugus)
0.416516 0.256396 0.17039 0.156698
   
   NB. Näiteks Alternatiiv 3 on algses mudelis veidi parem kui alternatiiv 4.
   NB. Aga läbi tehtud Monte Carlo analüüs näitab, et alternatiiv 4 võib siiski osutuda 3ndast paremaks keskmise tõenäosusega 29,45%.
   NB. Ja alternatiiv 3 võib osutuda paremaks alternatiivist 2 tõenäosusega keskmise tõenäosusega 0,325% ...
   NB. ...ja selle tõenäosuse 2-sigma kõikumispiirid on umbes 0,295% - 0,355%.
   NB. Ja alternatiiv 2 (kool B) võib osutuda paremaks alternatiivist 1 (kool A) keskmise tõenäosusega 0,007%.
   
   NB. Tuleb siiski meeles pidada, et läbi on tehtud vaid hägustamise lähenemise variant 2 (vt. faili alguses lähenemiste loendit), ülejäänud hägustamise lähenemised (ja nende kombineerimine) võivad lõppkaalude hajuvust suurendada.
   
     NB. kui jätta kõrvale need häiritud võrdlusmaatriksid mille suhtelise kooskõlaindeks on üle 0,2:
   NB. aluseks võtkem häiritud kaalude verb, kaalude arvutamist kohe ei tee. Vaja on häiritud võrdlusmaatrikseid.
   mc_vectors =: 13 : '(%"2 +/"1) power"2 (x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   
   mc_matrices =: 13 : '(x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   
   $ krit_10000m =: kriteeriumid mc_matrices 10000
10000 3 3
   
   maci_precomputed =: 10000 maci"0 (3+i.8)
   
   $ krit_cr_10000 =: cr"2 krit_10000m
10000
   
   5000{ \:~ krit_cr_10000
0.23338
   5450{ \:~ krit_cr_10000	NB. umbes 54,5% häiritud (kriteeriumite-) võrdlusmaatriksitest on kooskõlaindeksiga üle 0,2
0.200176
   
   $ krit_10000_consistent =: (%"2 +/"1) power"2  (I. krit_cr_10000 < 0.2) { krit_10000m
4547 3
   
   $ kvaliteet_10000m =: kvaliteet mc_matrices 10000
10000 4 4
   
   $ kulutused_10000m =: kulutused mc_matrices 10000
10000 4 4
   
   $ kulutused_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kulutused_10000m) < 0.2) { kulutused_10000m
6203 4
   
   $ kvaliteet_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kvaliteet_10000m) < 0.2) { kvaliteet_10000m
10000 4
   
   $ kaugus_10000m =: kaugus mc_matrices 10000
10000 4 4
   
   $ kaugus_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kaugus_10000m) < 0.2) { kaugus_10000m
9406 4
   
   juhuv6tt_kastist =: 13 : '(?># each valjavotukast) { each valjavotukast =. y{ x'
   
   ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) juhuv6tt_kastist"(1 0) i.4
┌───────────────────────────┬────────────────────────────────────┬────────────────────────────────────┬────────────────────────────────────┐
│0.754355 0.0711033 0.174541│0.474811 0.287264 0.0698144 0.168111│0.0782411 0.257866 0.363042 0.300851│0.0723261 0.35331 0.501218 0.0731458│
└───────────────────────────┴────────────────────────────────────┴────────────────────────────────────┴────────────────────────────────────┘
   
   juhuv6tte_kastist =: 13 : 'x juhuv6tt_kastist"(1 0) i.$x'
   $ ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) juhuv6tte_kastist"(1 0) i.10000
10000 4
   + kool_MC_loppkaalud =: AHP3_loppkaalud"1 ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) juhuv6tte_kastist"(1 0) i.5
0.427257 0.278075 0.144214 0.150454
0.381123  0.25993 0.160267  0.19868
0.414339 0.257744 0.173652 0.154265
0.428964 0.256363 0.167021 0.147652
0.402057 0.257163 0.178411 0.162369
   
   mc_dom_matrix2 =: 13 : 'pnorm_f _1 * |  monte_carlo_domination_matrix2 mc_loppkaalud =: AHP3_loppkaalud"1 x juhuv6tte_kastist"(1 0) i.y'
   
   pnorm_f _1 * |  monte_carlo_domination_matrix2 mc_loppkaalud =: AHP3_loppkaalud"1 ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) juhuv6tte_kastist"(1 0) i.10000
       0.5  0.00172513 0.00101174  3.15088e_9
0.00172513         0.5    0.01998 0.000119473
0.00101174     0.01998        0.5    0.336776
3.15088e_9 0.000119473   0.336776         0.5
   
   ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) mc_dom_matrix2"(1 0) 10000
       0.5 0.00183559 0.00109285 2.24238e_9
0.00183559        0.5  0.0213659 9.87569e_5
0.00109285  0.0213659        0.5   0.330268
2.24238e_9 9.87569e_5   0.330268        0.5
   
  NB. 3 korda 10000 juhuvõtuga Monte Carlo kooli näite peal. Häiritus on lisatud algsele võrdlusmaatriksile. 
   ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) mc_dom_matrix2"(1 0) 3#10000
        0.5  0.00180699 0.000986859  1.89296e_9
 0.00180699         0.5   0.0198642 0.000108347
0.000986859   0.0198642         0.5    0.324898
 1.89296e_9 0.000108347    0.324898         0.5

        0.5  0.00166334   0.0010204  1.90436e_9
 0.00166334         0.5    0.020477 0.000106618
  0.0010204    0.020477         0.5    0.328629
 1.90436e_9 0.000106618    0.328629         0.5

        0.5  0.00178842  0.00100767   2.1975e_9
 0.00178842         0.5   0.0193155 0.000116681
 0.00100767   0.0193155         0.5    0.329872
  2.1975e_9 0.000116681    0.329872         0.5
   
   NB. parem oleks häiritus lisada algse võrdlusmaatriksi ja lõppkaaludest taastatud kooskõlalise võrdlusmaatriksi geomeetrilisele keskmisele. Ja standardhälvet vähendada 2x.
   
      mc_matrices =: 13 : '(x*"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
	  
	  NB. seda verbi peaks muutma. Korrutise esimeseks teguriks peaks olema algse võrdlusmaatriksi ja kooskõlalise võrdlusmaatriksi geomeetriline keskmine.
   
   normalise_to_1 power S
0.0780047 0.456815 0.167932 0.297249
   (%/~) normalise_to_1 power S
      1 0.170758 0.464503 0.262422
5.85625        1  2.72024  1.53681
2.15284 0.367614        1 0.564953
3.81065 0.650698  1.77006        1
   
   S
1      0.5 0.2   0.5
2        1   1     7
5        1   1 0.125
2 0.142857   8     1
   
   cr S
0.848041
   
   S; (%/~) normalise_to_1 power S
┌────────────────────┬──────────────────────────────────┐
│1      0.5 0.2   0.5│      1 0.170758 0.464503 0.262422│
│2        1   1     7│5.85625        1  2.72024  1.53681│
│5        1   1 0.125│2.15284 0.367614        1 0.564953│
│2 0.142857   8     1│3.81065 0.650698  1.77006        1│
└────────────────────┴──────────────────────────────────┘
   geomean > S; (%/~) normalise_to_1 power S
      1 0.292197 0.304796 0.362231
3.42235        1  1.64932  3.27989
3.28088 0.606312        1 0.265743
2.76067 0.304888  3.76304        1
   
   comp_matrix_consistent_geomean =: 13 : 'geomean > y; (%/~) normalise_to_1 power y'
   mc_matrices =: 13 : '( (comp_matrix_consistent_geomean x) *"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   
   $ krit_10000m =: kriteeriumid mc_matrices 10000
10000 3 3
   
   $ krit_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 krit_10000m) < 0.2) { krit_10000m
7375 3
   
   $ kvaliteet_10000m =: kvaliteet mc_matrices 10000
10000 4 4
   $ kvaliteet_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kvaliteet_10000m) < 0.2) { kvaliteet_10000m
10000 4
   
   $ kulutused_10000m =: kulutused mc_matrices 10000
10000 4 4
   $ kulutused_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kulutused_10000m) < 0.2) { kulutused_10000m
9172 4
   
   $ kaugus_10000m =: kaugus mc_matrices 10000
10000 4 4
   $ kaugus_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kaugus_10000m) < 0.2) { kaugus_10000m
9951 4
   
   ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) mc_dom_matrix2"(1 0) 3#10000
        0.5  0.00201107  0.00097266  4.63463e_9
 0.00201107         0.5   0.0182752 0.000120223
 0.00097266   0.0182752         0.5    0.331963
 4.63463e_9 0.000120223    0.331963         0.5

        0.5   0.0018743 0.000982556  2.50061e_9
  0.0018743         0.5   0.0193016 0.000103592
0.000982556   0.0193016         0.5    0.330163
 2.50061e_9 0.000103592    0.330163         0.5

        0.5  0.00192654   0.0011217  3.38186e_9
 0.00192654         0.5   0.0205115 0.000125201
  0.0011217   0.0205115         0.5    0.335105
 3.38186e_9 0.000125201    0.335105         0.5
   
   NB. leidkem 100x10000 Monte Carlo domineerimise tulemused, esimeses maatriksis on aritmeetiline keskmine üle 100 simulatsiooni, teises tabelis on standardhälve.
   NB. Kuna domineerimise maatriks näitab tõenäosusi, siis teoreetiliselt oleks muidugi õigem leida aritmeetilise keskmise asemel geomeetriline keskmine ja standardhälve arvutada logaritmskaalal.
   NB. Aga kui arvujada sisaldab ka nulle, siis geomeetriline keskmine tuleks null.
   
   > (mean; stddev) ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) mc_dom_matrix2"(1 0) 100#10000
        0.5  0.00186021   0.0011202 3.79994e_9
 0.00186021         0.5   0.0203833 0.00011975
  0.0011202   0.0203833         0.5   0.335008
 3.79994e_9  0.00011975    0.335008        0.5

 1.2274e_15 0.000145331  9.72345e_5 1.07774e_9
0.000145331  1.2274e_15 0.000898482 1.29302e_5
 9.72345e_5 0.000898482  1.2274e_15 0.00385209
 1.07774e_9  1.29302e_5  0.00385209 1.2274e_15
   
   NB. Tulemuste tõlgendamine:
   NB. kool D on nõrgem koolist C, aga tõenäosusega 33,5% võib kool D siiski edestada kooli C.
   NB. Selle tõenäosuse esindusviga (st. kõikumispiirid mille vahele jääb 95%) on umbes 2x standardhälvet, ehk 0,77%
   NB. Nii on domineerimise tõenäosusvahemikuks [32,73% ; 34,27% ]
   NB. Kool C võib domineerida kooli B üle keskmise tõenäosusega 2,04%.
   NB. Selle tõenäosuse esindusviga on 0,18%.
   NB. Domineerimise tõenäosusvahemik on [ 1,86% ; 2,22% ]
   NB. Kool B võib domineerida kooli A üle keskmise tõenäosusega 0,19%.
   NB. Selle tõenäosusvahemik on [ 0,161% ; 0,219% ]
   
   NB. nüüd peaks standardhälvet 2x vähendama.
   NB. Algne verb
   
         NB. Let all the prior steps together (besides the 1st one) be defined as a function named as monte_carlo_error_factor
   monte_carlo_error_factor =: 13 : '^(+ _1*|:)~ ((0, stddev (uti) { ^. y % %/~ (%+/) power y) tomusigma normalrand(+/ ,ut)) (uti =. <"1 (4 $. $. ut)) } ut =. upper_triangle #y'
   monte_carlo_error_factor S
      1 0.917674 0.545202 0.209063
1.08971        1  2.00593 0.242934
1.83418 0.498523        1  2.94156
4.78325  4.11635 0.339955        1
      
   NB. muudetud verb
   
   monte_carlo_error_factor =: 13 : '^(+ _1*|:)~ ((0, 0.5*stddev (uti) { ^. y % %/~ (%+/) power y) tomusigma normalrand(+/ ,ut)) (uti =. <"1 (4 $. $. ut)) } ut =. upper_triangle #y'
   
   monte_carlo_error_factor S
       1 0.511431 0.991751  1.38725
  1.9553        1 0.601837 0.797119
 1.00832  1.66158        1  2.91022
0.720851  1.25452 0.343617        1
   
   NB. ja arvutused uuesti teha
   
   mc_matrices =: 13 : '( (comp_matrix_consistent_geomean x) *"2 monte_carlo_error_factor"2 ((y, #x)$ x))'
   
   $ krit_10000m =: kriteeriumid mc_matrices 10000
10000 3 3
   $ krit_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 krit_10000m) < 0.2) { krit_10000m
9114 3
   
   $ kvaliteet_10000m =: kvaliteet mc_matrices 10000
10000 4 4
   $ kvaliteet_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kvaliteet_10000m) < 0.2) { kvaliteet_10000m
10000 4
   
   $ kulutused_10000m =: kulutused mc_matrices 10000
10000 4 4
   $ kulutused_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kulutused_10000m) < 0.2) { kulutused_10000m
10000 4
   
   $ kaugus_10000m =: kaugus mc_matrices 10000
10000 4 4
   $ kaugus_10000_consistent =: (%"2 +/"1) power"2  (I. (cr"2 kaugus_10000m) < 0.2) { kaugus_10000m
10000 4
   
   ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) mc_dom_matrix2"(1 0) 3#10000
        0.5  4.7911e_10 1.22085e_10 2.99954e_34
 4.7911e_10         0.5   1.6111e_5  2.0446e_14
1.22085e_10   1.6111e_5         0.5    0.207245
2.99954e_34  2.0446e_14    0.207245         0.5

        0.5 4.65458e_10 1.24953e_10 1.17754e_34
4.65458e_10         0.5  1.65616e_5 2.57938e_14
1.24953e_10  1.65616e_5         0.5    0.208223
1.17754e_34 2.57938e_14    0.208223         0.5

        0.5 4.32532e_10 1.58114e_10 5.45296e_34
4.32532e_10         0.5  2.03516e_5 6.26846e_14
1.58114e_10  2.03516e_5         0.5    0.209359
5.45296e_34 6.26846e_14    0.209359         0.5
   
   > (mean; stddev) ( krit_10000_consistent; kvaliteet_10000_consistent; kulutused_10000_consistent; kaugus_10000_consistent ) mc_dom_matrix2"(1 0) 100#10000
        0.5 5.33666e_10 2.12333e_10 1.53985e_33
5.33666e_10         0.5  2.07443e_5 3.14236e_14
2.12333e_10  2.07443e_5         0.5    0.209515
1.53985e_33 3.14236e_14    0.209515         0.5

 1.2274e_15 1.75486e_10 6.48519e_11 1.53585e_33
1.75486e_10  1.2274e_15   2.6999e_6 1.43894e_14
6.48519e_11   2.6999e_6  1.2274e_15   0.0033272
1.53585e_33 1.43894e_14   0.0033272  1.2274e_15
   
   NB. Nagu näha, on kooli B tõenäosus domineerida kooli A üle kahanenud kõvasti.