=Paper=
{{Paper
|id=Vol-3611/paper8
|storemode=property
|title=Simulation-based comparison of objective weighting methods
|pdfUrl=https://ceur-ws.org/Vol-3611/paper8.pdf
|volume=Vol-3611
|authors=Üzeyir Fidan,Musab T. Akpinar
|dblpUrl=https://dblp.org/rec/conf/ivus/FidanA22
}}
==Simulation-based comparison of objective weighting methods==
https://ceur-ws.org/Vol-3611/paper8.pdf
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Sample data
ϭ Ϯ ϯ ϰ ϱ ϲ ϳ ϴ ϵ ϭϬ
ϭ 10,0049 9,9980 10,0033 10,0121 10,0404 9,9708 9,9777 9,9904 9,9950 10,0005
Ϯ 9,9939 10,0215 9,9753 9,9752 9,9937 9,9469 9,9806 9,9719 10,0798 9,9834
ϯ 10,0389 9,9953 9,9850 9,9818 10,0223 10,0004 9,9344 9,9754 9,9889 10,0372
ϰ 9,9999 10,0379 9,9724 10,0163 10,0616 10,0104 10,0272 9,9542 9,9790 10,0304
ϱ 10,0170 9,9550 10,0353 9,9412 10,0077 10,0256 10,0745 10,0251 9,9745 9,9943
ϲ 9,9916 10,0131 10,0024 10,0259 10,0730 9,9753 9,9857 10,0019 10,0314 10,0153
ϳ 10,0184 9,9952 9,9776 9,9912 9,9550 10,0085 10,0070 10,0089 9,9593 9,9646
ϴ 10,0095 9,9830 9,9794 10,0164 10,0314 10,0111 9,9932 10,0067 10,0070 9,9177
ϵ 10,0034 10,0025 9,9478 9,9828 10,0005 9,9590 10,0363 9,9991 10,0023 10,0004
ϭϬ 10,0613 9,9799 9,9845 9,9903 9,9816 10,0397 10,0020 9,9558 9,9763 10,0437
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Normalized data
ϭ Ϯ ϯ ϰ ϱ ϲ ϳ ϴ ϵ ϭϬ
ϭ 0,9944 0,9960 0,9968 0,9986 0,9968 0,9931 0,9904 0,9965 0,9916 0,9957
Ϯ 0,9933 0,9984 0,9940 0,9949 0,9921 0,9908 0,9907 0,9947 1,0000 0,9940
ϯ 0,9978 0,9958 0,9950 0,9956 0,9950 0,9961 0,9861 0,9950 0,9910 0,9994
ϰ 0,9939 1,0000 0,9937 0,9990 0,9989 0,9971 0,9953 0,9929 0,9900 0,9987
ϱ 0,9956 0,9917 1,0000 0,9916 0,9935 0,9986 1,0000 1,0000 0,9896 0,9951
ϲ 0,9931 0,9975 0,9967 1,0000 1,0000 0,9936 0,9912 0,9977 0,9952 0,9972
ϳ 0,9957 0,9957 0,9943 0,9965 0,9883 0,9969 0,9933 0,9984 0,9880 0,9921
ϴ 0,9949 0,9945 0,9944 0,9991 0,9959 0,9972 0,9919 0,9982 0,9928 0,9875
ϵ 0,9942 0,9965 0,9913 0,9957 0,9928 0,9920 0,9962 0,9974 0,9923 0,9957
ϭϬ 1,0000 0,9942 0,9949 0,9964 0,9909 1,0000 0,9928 0,9931 0,9897 1,0000
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ϯ͘Ϯ͘ ĂůĐƵůĂƚŝŽŶŽĨĐƌŝƚĞƌŝĂ The criteria weights obtained as a result of the
ǁĞŝŐŚƚƐ comparative analysis
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LQ WKH VDPSOH GDWD VHW ZHUH FDOFXODWHG DQG ݓଵ 0,1000 0,0514 0,0791 0,0734 0,0939
FRPSDUHG ZLWK WKH PHWKRGV PHQWLRQHG LQ ݓଶ 0,1000 0,0590 0,0827 0,0787 0,0789
WKH VWXG\ (TXDO ZHLJKWLQJ (QWURS\ ݓଷ 0,1000 0,0599 0,0733 0,0792 0,0973
&5,7,& 6WDQGDUG GHYLDWLRQ DQG 0(5(& LQ ݓସ 0,1000 0,0710 0,0846 0,0863 0,0647
7DEOH ݓହ 0,1000 0,1455 0,1087 0,1234 0,1114
ݓ0,1000 0,1010 0,1006 0,1029 0,0892
ݓ0,1000 0,1600 0,1319 0,1292 0,1440
଼ݓ0,1000 0,0624 0,0876 0,0809 0,0719
ݓଽ 0,1000 0,1330 0,1291 0,1178 0,1594
ݓଵ 0,1000 0,1568 0,1225 0,1282 0,0893
T h e crit eri a w ei g hts of t h e m et h o ds ot h er As c a n b e s e e n i n Fi g . 1, alt h o u g h t h e
t h a n t h e e q u al w ei g ht m et h o d s h o w si mil ar e q u al w ei g ht m et h o d is i n cl u d e d i n t h e
c h a n g es. T he vis u ali z e d f or m of c o m p ari s o n pr o c ess b y b ei n g a c c e pt e d a m o n g
crit eri o n w ei g hts is pr es e nt e d i n Fi g. 1. t h e o bj e cti v e w ei g hti n g m et h o ds, it d o es n ot
c orr el at e wit h ot h er w ei g hti n g m et h o ds
( T a bl e 4 ).
Si mil ar t o t h e m et h o d us e d i n t h e c al c ul ati o n
of t h e c orr el ati o ns, t h e di ssimil ariti es b et w e e n
t h e crit eri o n w ei g hts o bt ai n e d b y diff er e nt
m et h o ds ar e c al c ul at e d b y E u cli d Dist a n c e a n d
pr es e nt e d i n T a bl e 5 .
T a bl e 5
T h e dist a n c e m e as ur e v al u es of c o m p aris o n i n
diff er e nt m et h o ds
E q u al St a n d ar d
E ntr o p y Criti c
W ei g ht D e vi ati o n
E ntr o p y 0, 1 3 4 0
Fi g ur e 1 : T h e w ei g hts of t h e c o m p ar ati v e Criti c 0, 0 6 5 5 0, 0 7 5 6
St a n d ar d D e vi ati o n 0, 0 6 8 2 0, 0 6 6 0 0, 0 2 2 6
a n al ysis M er e c 0, 1 0 6 1 0, 0 7 8 0 0, 0 8 0 2 0, 0 6 5 0
3. 3. C o m p aris o n of o bj e cti v e
4. C o n cl usi o ns
w ei g hti n g m et h o ds
D et er mi ni n g t h e crit eri o n w ei g hts i n t h e
I n t his s u bs e cti o n, t h e r es ults of t h e crit eri o n m ulti- crit eri a d e cisi o n- m a ki n g pr o c ess h as a
w ei g hti n g o p er ati o ns p erf or m e d o n t h e d at a s et dir e ct eff e ct o n t h e s ol uti o n of t h e pr o bl e m.
c o nsisti n g of 1 0 crit eri a a n d 1 0 alt er n ati v es E v e n if s u bj e cti v e w ei g hti n g m et h o ds ar e
pr o d u c e d b y si m ul ati o n ar e c o m p ar e d. T w o cl ai m e d t o b e m or e s u c c essf ul i n s o m e d e cisi o n
m et h o ds w er e f oll o w e d w hil e m a ki n g t h e sit u ati o ns w h er e t h e n u m b er of crit eri a is l o w,
c o m p aris o n: t he P e ars o n C orr el ati o n o bj e cti v e w ei g hti n g m et h o ds c o m e t o t h e f or e
C o effi ci e nt ( E q. 1 7) a n d t h e dissi mil arit y v al u es d u e t o b ot h t h e l o w pr o c essi n g a n d ti m e c osts
wit h t h e h el p of E u cli d e a n Dist a n c es ( E q. 1 8). a n d t h e r eli a bilit y of t h e c h ar a ct eristi cs of t h e
∑ 𝑚𝑖 = 1 ( 𝑤 𝑖 𝑗 − ̅𝑤 𝑗 ). ( 𝑤 𝑖 𝑘 − ̅𝑤 𝑘 ) d at a.
𝑊𝜌 𝑗𝑘 = (1 7 ) I n t his st u d y, t h e r el ati o ns hi p b et w e e n t h e
2
√ ∑ 𝑚𝑖 = 1 ( 𝑤 𝑖 𝑗 − ̅𝑤 𝑗 ) .∑ 𝑚𝑖 = 1 ( 𝑤 𝑖 𝑘 − ̅𝑤 𝑘 ) 2 o bj e cti v e crit eri o n w ei g hti n g m et h o ds, w hi c h
r es e ar c h ers fr e q u e ntl y us e i n d e cisi o n- m a ki n g
𝑛 pr o bl e ms, w as e v al u at e d wit h t h e P e ars o n
𝐷 𝑗 𝑘 = √ ∑( 𝑤 𝑤 𝑖 𝑘)2 (1 8 ) C orr el ati o n C o effi ci e nt, a n d t h e dissi mil arit y
𝑖𝑗 −
𝑖 =1 l e v els w er e e v al u at e d wit h t h e E u cli d Dist a n c e
m etri c.
C orr el ati o n v al u es b et w e e n o bj e cti v e T h e first d e cisi o n t o f o c us o n is t h e c h oi c e
crit eri o n w ei g hti n g m et h o ds ar e pr es e nt e d b et w e e n t h e E q u al W ei g hti n g M et h o d a n d ot h er
i n T a bl e 4 . m et h o ds [ 1 9]. B e c a us e t h e E q u al W ei g hti n g
M et h o d c a n b e t h o u g ht of as n ot assi g ni n g a
T a bl e 4 w ei g ht t o a n y of t h e crit eri a. C o m p aris o n
T h e c orr el ati o n v al u es o f c o m p aris o n i n r es ults i n t h e st u d y als o s u p p ort t his i d e a. W h e n
diff er e nt m et h o ds t h e r es ults of t h e c orr el ati o n a n al ysis ar e
E q u al
E ntr o p y Criti c
St a n d ar d e x a mi n e d, t h e E q u al W ei g hti n g M et h o d h as
W ei g ht D e vi ati o n
z er o c orr el ati o n wit h ot h er m et h o ds.
E ntr o p y 0, 0 0 0 0
Criti c 0, 0 0 0 0 0, 9 4 1 5
A n ot h er sit u ati o n t h at s h o ul d b e f o c us e d o n
St a n d ar d D e vi ati o n 0, 0 0 0 0 0, 9 9 8 4 0, 9 4 3 5 is t h at t h e w ei g ht v al u es o bt ai n e d fr o m t h e
M er e c 0, 0 0 0 0 0, 8 1 3 2 0, 6 5 6 5 0, 8 0 7 0 o bj e cti v e crit eri o n w ei g hti n g m et h o ds ar e
diff er e nt fr o m e a c h ot h er. T h er ef or e, alt h o u g h
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