Business Decision Processes

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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