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The power point presentation about decision making process with the help of AHP and ANP.
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7/18/2019 Business Decision Processes
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From Verbal Scales toNumerical Scales in
Decision Making
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The Fundamental Scale about AbsoluteNumbers
1 Equal importance two activities contribute equally to the objective
2Weak or slight3 Moderate importancee!"erience an# ju#gment slightly $avor oneactivity
over another
% Mo#erate "lus
5 Strong importancee!"erience an# ju#gment strongly $avor oneactivity over
another
& Strong "lus
7 Ver strong or demonstrated importancean activity is $avore#very
strongly over another' its #ominance #emonstrate# in"ractice
(Very very strong
! E"treme importancethe evi#ence $avoring one activity over another iso$ the
highest "ossible or#er o$ a)rmation
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Saat#s argument $or comparati%equestions
*+,n a##ition- when we think o$ an alternative we
are alrea#y conscious o$ other alternatives an#rate it silently as i$ we are thinking o$ it alone-which is rarely ever the case. ,n $act- once wehave rate# the /rst alternative- we cannot $orget itwhen we rate the ne!t one an# the one a$ter. 0ll
subsequent ratings #e"en# on what "assesthrough our min#s be$ore+1
*he conclusion is that assuming in#e"en#ence
an# rating things one at a time is a convenientan# unscienti/c way to assign numers subjectivelyto alternatives. he numbers are "ulle# out o$ ahat even when an e!"ert is involve#1
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Saat#s argument $or 1&! scale3esearch in "sychology that relates the use o$ the$un#amental scale o$ the absolute numbers 45 tore"resent ju#gments in making "airwise com"arisons o$homogeneous elements with res"ect to a common"ro"erty6
Stanislas Dehaene 6 78he number sense- 9ow the min#creates mathematics88
*+,ntros"ection suggests that we can mentally re"resentthe meaning o$ numbers $rom 4 to 5 with actual acuity.,n#ee#- these symbols seem equivalent to us+.,nsummary- the invention o$ numerical symbols shoul#have $ree# us $rom the $u::ines o$ the quantitative
re"resentation o$ numbers+1
0lso- integers $rom 45 use# in "airwise com"arisonju#gments can be #erive# $rom stimulus res"onse theory.
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The 'rst argument against the 1&!scale( irregular changings in the
corresponding priorit %ector
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;revious $ormulas gave rise to aninteresting observation
.
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So- i$ Saaty8s numerical scale is use#-
with integers $rom 4 to 5 an# theirreci"rocals-
to a change o$ one unit on the scale $unctioncorres"on#
irregular changes
in the corres"on#ing "riorityvectors.
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The second argument against the 1&! scale(the distribution o$ the corresponding priorit%ector
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,n the en# o$ this #iscussion regar#ing a #ecision matri! one "erha"s woul#want to notice the "articular convenient$orm o$ the "riority vector which
allowe# $or all this consi#erations.
When one u"gra#es to a #ecisionmatri! or it is consi#ering instea# ahierarchy- all the "revious scheme o$reasoning becomes ina""licable.
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The consistenc inde" and the randominde"
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he ran#om in#e! is a measure o$ the range
o$ the consistency in#e! $or matrices o$ thesame #imensions.
he u""er #iagonal o$ a matri! is /lle# with
ran#omly e!tracte# elements $rom the Saaty8sscale $unction A4B5-..4-+5C-
the elements below the main #iagonal arecom"lete# by taking the reci"rocals-
on the main #iagonal are onesan#
the corres"on#ent , is calculate#- $or E-trials.
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he corres"on#ent average is the
ran#om in#e! 3,.
he consistency ratio is the ratio
among consistency in#e! an# theran#om in#e!.
Saaty recommen#s that theconsistency ratio shoul# always besmaller than .4.
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Numerical scales in the literature
so $ar
his section is revising the e!istent literature
regar#ing alternative numerical scales mainlybase# on the work #oneby DongGall - Hlliot -Salo an#9amalainen .
Matching a certain numerical scale to abroa#ly acce"te# linguistic scale raises issueswhich are not currently sorte# out.
he variety o$ criterions taken intoconsi#eration when a certain numerical scaleis a#o"te# can she# a light to the im"licationso$ a certain choice over the other alternatives.
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his broa# range o$ criterions assessing the *quality o$ a certainnumerical scale1 le# to a more $ormali:e# way o$ looking at thelinguistic variables- in the attem"t to im"ose on these a minimal set o$a!ioms.
hus- $ollowing Dong G all - i$ we acce"t that
linguistic variablesare )udgments# %aguel quanti'cations in
respect to certain questions-
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a label
represent a possible *a in *hichthe linguistic %ariables are ordered+
hus- $or the linguistic variable *$air1-
one coul# associate the label .
Similarly-the linguistic variable *slightly goo#1
coul# be associate# with the label 4-
the linguistic variable *goo#1
coul# be associate# with the label 2an# the linguistic variable *"oor1
coul# be associate# with the label 2.
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here$ore- a linguistic label set
with o## number o$elements
can be re"resente# as
SIA sJ BJIt-tK4-+4--4-..t4-tC
where
with the label sJcan be- in "rinci"le-
attache# any "ossible real number .
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Follo*ing the pre%ious e"ample, the linguistic %ariable-$air. corresponds to the linguistic label s/,
the linguistic %ariable -slightl good. corresponds tothe linguistic label s1 and so on,
and so,
instead o$ considering a set o$ linguistic %ariables lie
S2-e"tremel poor.4++ -e"tremel good.
*e admit that there must be some order in thesequanti'cation
and consider instead a set o$ linguistic labels
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S2 s6 62&t,&t81,4&1,/,1,++t&1,t
*here
t29,s&92-e"tremel poor.,4,
s/2.$air.,4+,
s92.e"tremel good.+
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,n the 09; $ramework $or instance- Saaty "reestablishe# the ne!t linguistic label set6S2s&:,s&7,4s&1,s/,s1,4s:
;or, shorter,S2 s6 62&:,&7,4&1,/,1,++7,:n Saat;C/1/< there are presented se%eral e"amples;the Distance roblem, the Gptics roblem, the NationIealth roblem and the Ieight Estimation roblem
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