Çalışma kapsamında çok kriterli karar verme yöntemlerinde kullanılmak üzere ağırlıklandırma yöntemi olarak geliştirilen Normalize Edilmiş Maksimum Değerler (NMD) yönteminin R’da uygulanmasını sağlamak amacıyla NMD fonksiyonu oluşturulmuştur. Fonksiyon ile kriterlerin ağırlık düzeyleri belirlenebilmektedir. Kriterlere ilişkin ağırlıklar, değerlerine göre büyükten küçüğe grafikler üzerinde gösterilmiştir. NMD yöntemiyle ilgili olarak daha detaylı bilgi için aşağıdaki linke tıklayınız.
Normalize Edilmiş Maksimum Değerler [NMD] Metodu
Yüklenen kütüphaneler
kütüphane<-c("dplyr","tibble","tidyr","ggplot2","ggthemes", "kableExtra", "forcats")
yükle<-sapply(kütüphane, require, character.only = TRUE, warn.conflicts = FALSE)
#Kütüphane yüklenme durumunu gösteren tablo
tibble(Sıra=1:length(kütüphane), Kütüphane=names(yükle), Durumu=as.logical(yükle)) %>% mutate(Durumu=if_else(Durumu==TRUE, "Yüklendi", "Paket Kurulumu Gerekli"))
Yukarıda yazılı R kod bloğunun çalıştırılmasından sonra yüklenen kütüphaneler aşağıdaki tabloda verilmiştir.
Örnek olay
Uygulamayı daha da kalıcı hale getirmek adına Microsoft Excel üzerinde oluşturduğum bir karar matrisini R üzerinde okutup kriter ağırlıkları hesaplanmıştır. Ardında ise kriter ağırlıklarının grafiği çizilmiştir. Örnek karar matrisi veri setimizi aşağıdaki linkten indirebilirsiniz.
İlk olarak klasör içine kaydettiğimiz xlsx uzantılı excel dokümanını okutalım ve karar matrisinin boyutlarına bakalım.
library(readxl)
kararmatrisi <- read_excel("kararmatrisi.xlsx")
dim(kararmatrisi)
Yukarıdaki kod bloğu çalıştırıldığında karar matrisimizin 416×12 yani 416 satır ve 12 sütundan oluştuğu görülecektir. Sütunlarımızda kriterler, satırlarımızda ise alternatiflerin kriter değerleri bulunmaktadır. Buradan bakıldığında 416 alternatife karşılık 12 kriterimiz bulunmaktadır. Amacımız NMD fonksiyonunu kullanarak 416 alternatifin değerlerinden yola çıkarak 12 kriterin ağırlıklarının belirlenmesidir. Aşağıda yazılan kod bloğunda xlsx uzantılı karar matrisi veri setini matris formatına dönüştürerek aşağıdaki NMD fonksiyonunu çalıştırıyoruz ve kriter ağırlıklarını hesaplıyoruz.
NMD= function(km){
colnames(km)=paste("K", 1:ncol(km), sep="") #kriterler
rownames(km)=paste("A", 1:nrow(km), sep="") #alternatifler
km2 <- km
for (r in 1:nrow(km)){
for (c in 1:ncol(km)){
km2[r,c] <- km[r,c]/ apply(km[,c],2, sum)
}
}
omak=apply(km2,2,max) # 3. aşama
ort=apply(km2,2,mean) # 3. aşama
ss=apply(km2,2,sd) # 3. aşama
nd=(omak-ort)/ss # 3. aşama
ka=round(nd/sum(nd),3) # 4. aşama
return(list(Karar_Matrisi=as.matrix(km), Asama_2=as.matrix(km2), Asama_3=as.matrix(nd), KA=as.matrix(ka)))
}
NMD(km1)
Gördüğünüz üzere işlem bu kadar basit. Sonuçlar liste halinde aşağıda verilmiştir.
K1 K2 K3 K4 K5 K6 K7 K8 K9 K10 K11 K12
A1 -171 -4201 4770 -2429 3693 1569 3564 6308 -4724 -4907 -9543 6597
A2 -5736 -4589 8071 5649 4203 5652 -5898 8363 -8161 -3935 -5811 -2981
A3 -62 -4021 -7298 9730 -8911 -6269 -224 9187 9039 1950 -9941 -6663
A4 5258 -8973 4678 -1080 -3299 9045 9608 6207 1857 7130 2053 2030
A5 1718 -6607 -505 -792 -9522 -4029 -8934 9125 7768 1210 5439 -5206
A6 -2521 996 -4003 -3574 2790 -3167 4018 -6073 3222 9945 1720 -3967
A7 2928 7587 -5276 -3728 -9849 9239 -3535 4366 -6637 8342 -1585 -9847
A8 -6523 -1021 8922 -5927 6203 9655 4642 -1723 2546 8188 -6016 5131
A9 648 537 -7285 -3226 7989 -4661 -7845 -5644 -4927 -220 -3284 3203
A10 -9120 3017 9178 2050 7124 30 3499 -3600 9557 9401 -9378 -4700
A11 -8468 -562 51 -7312 -3983 6453 9573 2317 4725 -7249 5181 5952
A12 -4007 -9542 -5362 -7525 -4102 4099 -2218 6019 -8427 634 -2509 -436
A13 -3741 -9061 -2860 -6003 -4582 -9916 -2187 561 -7420 8646 9076 7003
A14 1010 9792 -925 -262 -2050 430 4131 7948 4323 -3732 -5805 -1074
A15 5410 -7342 763 -9148 -4803 -7270 3665 4966 -9739 2058 -5571 -2393
A16 -8425 5177 501 5719 -2338 -4460 -8965 9171 4582 -9098 21 7521
A17 4682 -1129 556 3241 -8511 8788 3353 -6686 -7981 1527 1377 -2021
A18 -8234 -3765 -3601 6841 -8547 2430 8784 -2181 -2392 -4028 -8981 -6268
A19 -3354 -2205 4886 -4497 -3375 1542 -8791 4256 -9499 2592 -2178 -8391
A20 -424 858 -5618 4778 -6742 -3720 6323 -6894 1075 -9503 -2031 4999
A21 -5029 4176 -2977 3560 6636 -2049 3514 4774 -7591 2980 5039 9879
A22 5268 3482 7553 -9531 -735 6155 -9984 7506 3676 -3781 -4007 -4131
A23 -7590 6422 579 2119 -4756 -4296 -1399 5970 -3867 -1559 -5128 -299
A24 -7476 -3667 962 -3431 -3544 -4588 -2029 -7373 -7285 2268 69 -5488
A25 -8898 -913 5877 4408 -897 8439 -7689 -6651 -1432 -7182 1006 -2953
A26 -3528 -427 2561 6962 -761 512 7485 5625 9378 -5595 1652 3001
A27 9399 4320 1697 -858 8659 -5197 -2237 3972 8982 9574 -2081 -7822
A28 -5651 5564 -4388 403 -1449 -3543 -5955 -108 3106 6728 3412 7792
A29 -1648 -2657 2892 -883 1574 3618 -3666 -361 9333 -526 -7853 -6202
A30 8209 4723 -5740 -3094 -255 -1628 5055 -4878 2948 -900 5370 -8171
A31 2053 9819 3401 7551 1828 6625 9453 9246 -9226 4507 -797 5354
A32 674 -7104 5971 -3416 222 -8418 6387 7768 6132 -7787 -7686 9864
A33 7050 3729 -2809 -148 9377 5757 -9148 -9381 9908 1579 1164 -3900
A34 3611 -3480 -9223 4112 -8060 -1025 5129 3799 3692 3258 -8373 -58
A35 -6482 -537 -3744 -3376 8308 -3208 -7773 83 -4183 5401 -7849 4790
A36 -9339 -7499 -6766 -787 -4546 -4582 1033 -7679 -9327 -5041 -9722 5096
A37 -9432 4396 -6666 -3633 9406 3317 1653 855 -3024 -5737 -2688 1608
A38 -7462 -5666 188 4422 8528 9041 -19 -9152 -5601 8600 -8315 -1483
A39 -3035 -2254 4676 5397 -6919 2377 2264 117 -8939 5876 -5400 -1218
A40 -8695 3898 -7583 6932 8909 4396 290 -7005 -3254 5801 -9501 8258
A41 5875 -3534 7810 -6466 1032 -4328 1420 9236 4865 -6158 -6528 4347
A42 -3843 -2658 -8825 -6055 -4473 -5481 -2406 -9657 -7012 -7724 -6303 3140
A43 6535 -9781 -4668 279 -3803 6012 -9352 -3963 -4423 2198 3074 -7431
A44 8107 -1801 1478 3127 -2436 -1381 6520 3773 -5056 -3812 2619 -3612
A45 7497 2241 5484 894 -5379 2968 -8257 381 8062 -6429 -5899 1691
A46 2958 -3151 -550 1808 -2681 -3327 5684 6185 -4732 -285 -9887 -1074
A47 -6541 5534 7864 3984 8692 7284 1094 7915 -8875 -8038 5950 -2680
A48 2914 6249 -4106 1874 5517 -5311 -8605 4419 -4452 405 2268 2757
A49 -3540 -8544 -7895 -7042 1934 -2142 2491 362 7226 1586 -4572 -908
A50 -9934 -9316 -5302 -9277 -6008 9795 2169 -5082 3509 -7448 -9019 71
A51 -9660 1468 -993 9456 8466 3839 9425 9498 -6953 2759 2581 5077
A52 3550 741 -2740 4626 -8184 9659 5929 -3708 -4446 3421 -4731 -5907
A53 -4805 1293 6772 -9454 -9473 1274 6601 -6909 -4962 -2051 -5891 -8991
A54 775 9060 7208 4916 -4467 6437 2074 -7708 -308 9843 -8783 -6389
A55 -2517 -6508 2971 3537 41 8975 -4422 -2490 -1061 6673 -1932 -5165
A56 5983 780 3080 -8739 3314 -1202 -4463 -2512 5815 -4870 -2901 -1598
A57 1817 -5383 -4600 -8715 -445 -9680 -5903 -8675 9295 5691 9443 4111
A58 -1685 -8024 -5145 -3467 -2893 -143 -5311 4520 -2681 -8625 -5495 -4065
A59 7125 -6442 2689 9984 8667 4437 -3694 -3286 9131 5726 9272 -9704
A60 -1220 -7565 -714 4499 5574 -4575 -7147 -6801 -9797 8459 -8066 -3561
A61 9875 -1584 -6411 -1625 -1175 -7589 1904 652 3432 -5532 9587 -2127
A62 3046 -4492 4753 7639 -8901 4787 -437 3485 497 -8059 3689 6743
A63 -9452 2820 2908 4250 3543 99 -7252 -6837 2951 5476 -3036 -7474
A64 5534 4590 -6071 -5767 -6802 -648 -3269 6440 546 -4678 4987 42
A65 4983 9905 -2825 -4424 2090 -5086 2562 8815 1350 -394 6640 1259
A66 1842 -6242 -1856 -1942 -8419 -7755 8562 -9792 3510 7338 -6840 6834
A67 2841 605 6153 -8819 2894 -9626 -7731 -7341 5476 -1873 9229 -8830
A68 6272 5814 4245 -1387 -5249 3882 5565 8009 -5638 -3948 4411 -3945
A69 5069 -8682 4307 3354 9254 -8604 -7930 2545 7169 -1071 -6116 -8930
A70 -6930 -3698 8323 -5026 -2359 -5118 4287 -4030 -7778 -8950 5769 -8191
A71 1595 -1070 -8418 -7641 -3696 -9203 7068 -3118 2078 7667 -3165 1644
A72 3822 6105 -4145 9450 8906 7042 2879 7574 -3559 -5832 -4518 9116
A73 6722 1593 9982 -6010 4111 6074 -3604 -9714 481 6011 1465 -5892
A74 2616 -8232 3128 -9910 2795 -61 -3113 7718 -7305 1650 6646 -9042
A75 785 -8707 -7795 6449 -2039 5143 9247 -6319 -660 -7418 4298 -6186
A76 -9465 1282 -3367 -8526 7252 -3044 4962 8434 4179 5361 -3219 2816
A77 -4935 3739 -5535 -9585 -6177 -8357 -6630 232 3557 -6411 -6874 5397
A78 -5623 4009 -1102 2687 2431 -7586 7659 6568 -4463 -6893 646 -277
A79 1440 8573 -2253 884 6332 -9723 -6593 8099 2876 658 9859 4370
A80 -2416 -641 4613 5487 7195 3463 3605 -4003 -8892 -6628 615 -8049
A81 5443 7816 9751 -7644 670 7127 -4062 -2298 -9058 777 -7923 6565
A82 -2535 8919 1891 4581 826 9548 -8471 3926 -3202 3666 6882 8094
A83 5214 -2341 1166 4219 -6927 63 6695 -1184 6273 181 5917 -5290
[ reached getOption("max.print") -- omitted 333 rows ]
$Asama_2
K1 K2 K3 K4 K5 K6 K7 K8 K9 K10
[1,] 7.269759e-04 -0.0723312672 -2.110423e-02 -0.0382911642 -0.082231129 0.170654775 0.1007064142 5.569191e-02 -0.0989775394 -6.591443e-02
[2,] 2.438558e-02 -0.0790117080 -3.570907e-02 0.0890517853 -0.093587174 0.614748749 -0.1666572478 7.383504e-02 -0.1709897754 -5.285781e-02
[3,] 2.635819e-04 -0.0692320937 3.228904e-02 0.1533853551 0.198419060 -0.681857733 -0.0063294716 8.110995e-02 0.1893856856 2.619383e-02
[4,] -2.235345e-02 -0.1544938017 -2.069719e-02 -0.0170253015 0.073458027 0.983793779 0.2714891212 5.480020e-02 0.0389079785 9.577540e-02
[5,] -7.303770e-03 -0.1137568871 2.234306e-03 -0.0124852211 0.212024048 -0.438220579 -0.2524441933 8.056257e-02 0.1627556152 1.625361e-02
[6,] 1.071758e-02 0.0171487603 1.771074e-02 -0.0563411366 -0.062124248 -0.344463781 0.1135348969 -5.361715e-02 0.0675075427 1.335886e-01
[7,] -1.244787e-02 0.1306301653 2.334296e-02 -0.0587688185 0.219305277 1.004894496 -0.0998869737 3.854643e-02 -0.1390588334 1.120559e-01
[8,] 2.773137e-02 -0.0175792011 -3.947421e-02 -0.0934342240 -0.138120686 1.050141397 0.1311669963 -1.521198e-02 0.0533439490 1.099872e-01
[9,] -2.754856e-03 0.0092458678 3.223152e-02 -0.0508552061 -0.177889112 -0.506961062 -0.2216727889 -4.982960e-02 -0.1032308079 -2.955202e-03
[10,] 3.877205e-02 0.0519455923 -4.060685e-02 0.0323165445 -0.158628368 0.003262998 0.0988697372 -3.178359e-02 0.2002388535 1.262811e-01
[11,] 3.600019e-02 -0.0096763085 -2.256428e-04 -0.1152675968 0.088688488 0.701870785 0.2705001413 2.045627e-02 0.0989984915 -9.737390e-02
[12,] 1.703504e-02 -0.1642906336 2.372346e-02 -0.1186253645 0.091338232 0.445834240 -0.0626730715 5.314040e-02 -0.1765630238 8.516354e-03
[13,] 1.590419e-02 -0.1560089532 1.265369e-02 -0.0946323008 0.102026275 -1.078529476 -0.0617971178 4.952943e-03 -0.1554642977 1.161394e-01
[14,] -4.293834e-03 0.1685950413 4.092540e-03 -0.0041302120 0.045646849 0.046769632 0.1167278892 7.017110e-02 0.0905757627 -5.013097e-02
[15,] -2.299965e-02 -0.1264118457 -3.375793e-03 -0.1442106093 0.106947228 -0.790733087 0.1035603278 4.384370e-02 -0.2040521287 2.764457e-02
[16,] 3.581738e-02 0.0891356749 -2.216608e-03 0.0901552771 0.052059675 -0.485098978 -0.2533201469 8.096869e-02 0.0960023466 -1.222110e-01
[17,] -1.990469e-02 -0.0194387052 -2.459948e-03 0.0510916686 0.189512358 0.955840766 0.0947442780 -5.902919e-02 -0.1672184043 2.051179e-02
[18,] 3.500538e-02 -0.0648243802 1.593215e-02 0.1078426736 0.190313961 0.264302806 0.2482057078 -1.925556e-02 -0.0501173315 -5.410706e-02
[19,] 1.425893e-02 -0.0379648760 -2.161746e-02 -0.0708914637 0.075150301 0.167718077 -0.2484035038 3.757527e-02 -0.1990236339 3.481765e-02
[20,] 1.802560e-03 0.0147727273 2.485610e-02 0.0753211949 0.150122467 -0.404611703 0.1786662899 -6.086557e-02 0.0225234663 -1.276513e-01
[21,] 2.137989e-02 0.0719008264 1.317134e-02 0.0561204382 -0.147762191 -0.222862737 0.0992935858 4.214857e-02 -0.1590471002 4.002955e-02
[22,] -2.239596e-02 0.0599517906 -3.341725e-02 -0.1502482856 0.016366065 0.669458342 -0.2821135914 6.626878e-02 0.0770197787 -5.078917e-02
[23,] 3.226753e-02 0.1105716253 -2.561709e-03 0.0334042721 0.105900690 -0.467261257 -0.0395309409 5.270779e-02 -0.0810216225 -2.094163e-02
[24,] 3.178288e-02 -0.0631370523 -4.256242e-03 -0.0540868606 0.078913382 -0.499021101 -0.0573325798 -6.509456e-02 -0.1526357694 3.046544e-02
[25,] 3.782826e-02 -0.0157196970 -2.600201e-02 0.0694884527 0.019973280 0.917881227 -0.2172647641 -5.872018e-02 -0.0300033523 -9.647391e-02
[26,] 1.499866e-02 -0.0073519284 -1.133081e-02 0.1097501379 0.016945001 0.055688492 0.2115004238 4.966186e-02 0.1964884345 -7.515616e-02
[27,] -3.995817e-02 0.0743801653 -7.508152e-03 -0.0135256562 -0.192807838 -0.565259952 -0.0632099463 3.506789e-02 0.1881914180 1.286050e-01
[28,] 2.402422e-02 0.0957988981 1.941413e-02 0.0063529597 0.032264529 -0.385360017 -0.1682678723 -9.535077e-04 0.0650771036 9.037544e-02
[29,] 7.006177e-03 -0.0457472452 -1.279527e-02 -0.0139197604 -0.035047874 0.393517511 -0.1035885843 -3.187188e-03 0.1955455917 -7.065619e-03
[30,] -3.489909e-02 0.0813188705 2.539587e-02 -0.0487743359 0.005678023 -0.177072003 0.1428369596 -4.306676e-02 0.0617666778 -1.208946e-02
[31,] -8.727962e-03 0.1690599174 -1.504727e-02 0.1190352329 -0.040703629 0.720578638 0.2671093529 8.163085e-02 -0.1933037211 6.054134e-02
[32,] -2.865390e-03 -0.1223140496 -2.641790e-02 -0.0538503980 -0.004943220 -0.915597129 0.1804747104 6.858192e-02 0.1284780422 -1.046007e-01
[33,] -2.997181e-02 0.0642045455 1.242805e-02 -0.0023330969 -0.208795369 0.626169241 -0.2584910992 -8.282274e-02 0.2075930272 2.121029e-02
[34,] -1.535152e-02 -0.0599173554 4.080594e-02 0.0648222590 0.179470051 -0.111485752 0.1449279457 3.354052e-02 0.0773550117 4.376385e-02
[35,] 2.755706e-02 -0.0092458678 1.656483e-02 -0.0532198313 -0.184992207 -0.348923211 -0.2196383159 7.327883e-04 -0.0876424740 7.255020e-02
[36,] 3.970309e-02 -0.1291150138 2.993527e-02 -0.0124064003 0.101224672 -0.498368501 0.0291890365 -6.779616e-02 -0.1954198793 -6.771442e-02
[37,] 4.009846e-02 0.0756887052 2.949283e-02 -0.0572712225 -0.209441104 0.360778769 0.0467081096 7.548602e-03 -0.0633590345 -7.706360e-02
[38,] 3.172336e-02 -0.0975550964 -8.317811e-04 0.0697091511 -0.189890893 0.983358712 -0.0005368748 -8.080095e-02 -0.1173524975 1.155215e-01
[39,] 1.290276e-02 -0.0388085399 -2.068834e-02 0.0850792149 0.154063683 0.258538177 0.0639728737 1.032967e-03 -0.1872904794 7.893075e-02
[40,] 3.696524e-02 0.0671143251 3.354998e-02 0.1092772129 -0.198374527 0.478137916 0.0081944052 -6.184557e-02 -0.0681780087 7.792330e-02
[41,] -2.497651e-02 -0.0608471074 -3.455431e-02 -0.1019311106 -0.022979292 -0.470741788 0.0401243289 8.154256e-02 0.1019317801 -8.271879e-02
[42,] 1.633783e-02 -0.0457644628 3.904504e-02 -0.0954520375 0.099599198 -0.596149663 -0.0679853066 -8.525948e-02 -0.1469158565 -1.037544e-01
[43,] -2.778238e-02 -0.1684056474 2.065295e-02 0.0043982029 0.084680472 0.653904720 -0.2642554394 -3.498843e-02 -0.0926709688 2.952515e-02
[44,] -3.446546e-02 -0.0310089532 -6.539215e-03 0.0492945535 0.054241817 -0.150206657 0.1842328341 3.331097e-02 -0.1059336239 -5.120559e-02
[45,] -3.187215e-02 0.0385847107 -2.426323e-02 0.0140931662 0.119772879 0.322819230 -0.2333144956 3.363763e-03 0.1689155213 -8.635906e-02
[46,] -1.257541e-02 -0.0542527548 2.433402e-03 0.0285016158 0.059697172 -0.361866435 0.1606103419 5.460597e-02 -0.0991451559 -3.828330e-03
[47,] 2.780789e-02 0.0952823691 -3.479323e-02 0.0628044455 -0.193542641 0.792255819 0.0309126872 6.987975e-02 -0.1859495474 -1.079723e-01
[48,] -1.238835e-02 0.1075929752 1.816645e-02 0.0295420509 -0.122845691 -0.577659343 -0.2431477819 3.901436e-02 -0.0932785786 5.440258e-03
[49,] 1.504968e-02 -0.1471074380 3.493038e-02 -0.1110112714 -0.043063906 -0.232978029 0.0703871150 3.196016e-03 0.1513995977 2.130432e-02
[50,] 4.223262e-02 -0.1603994490 2.345800e-02 -0.1462441870 0.133778668 1.065368719 0.0612884996 -4.486783e-02 0.0735207844 -1.000470e-01
[51,] 4.106776e-02 0.0252754821 4.393397e-03 0.1490659730 -0.188510354 0.417554927 0.2663181690 8.385570e-02 -0.1456796849 3.706092e-02
[52,] -1.509219e-02 0.0127582645 1.212277e-02 0.0729250414 0.182231129 1.050576463 0.1675332015 -3.273710e-02 -0.0931528662 4.595339e-02
[53,] 2.042760e-02 0.0222623967 -2.996182e-02 -0.1490344447 0.210932977 0.138568632 0.1865216163 -6.099800e-02 -0.1039641301 -2.755054e-02
[54,] -3.294774e-03 0.1559917355 -3.189084e-02 0.0774966501 0.099465598 0.700130520 0.0586041255 -6.805220e-02 -0.0064532350 1.322184e-01
[55,] 1.070058e-02 -0.1120523416 -1.314480e-02 0.0557578624 -0.000912937 0.976180117 -0.1249505510 -2.198365e-02 -0.0222301374 8.963664e-02
[56,] -2.543565e-02 0.0134297521 -1.362705e-02 -0.1377630646 -0.073792029 -0.130737437 -0.1261090704 -2.217788e-02 0.1218362387 -6.541742e-02
[57,] -7.724650e-03 -0.0926825069 2.035209e-02 -0.1373847245 0.009908706 -1.052860561 -0.1667985307 -7.658962e-02 0.1947494133 7.644570e-02
[58,] 7.163476e-03 -0.1381542700 2.276337e-02 -0.0546543706 0.064417724 -0.015553622 -0.1500706414 3.990606e-02 -0.0561724774 -1.158573e-01
[59,] -3.029066e-02 -0.1109159780 -1.189712e-02 0.1573894538 -0.192985972 0.482597346 -0.1043797683 -2.901135e-02 0.1913132752 7.691584e-02
[60,] 5.186612e-03 -0.1302513774 3.158999e-03 0.0709229920 -0.124114896 -0.497607135 -0.2019497033 -6.004450e-02 -0.2052673483 1.136275e-01
[61,] -4.198180e-02 -0.0272727273 2.836462e-02 -0.0256167731 0.026163438 -0.825429628 0.0538005086 5.756361e-03 0.0719074757 -7.430989e-02
[62,] -1.294952e-02 -0.0773415978 -2.102902e-02 0.1204224797 0.198196393 0.520665652 -0.0123481209 3.076828e-02 0.0104131747 -1.082544e-01
[63,] 4.018349e-02 0.0485537190 -1.286606e-02 0.0669977142 -0.078891116 0.010767892 -0.2049166431 -6.036233e-02 0.0618295340 7.355766e-02
[64,] -2.352681e-02 0.0790289256 2.686034e-02 -0.0909119571 0.151458473 -0.070480748 -0.0923707262 5.685731e-02 0.0114398257 -6.283834e-02
[65,] -2.118433e-02 0.1705406336 1.249884e-02 -0.0697406794 -0.046537519 -0.553186861 0.0723933314 7.782565e-02 0.0282852833 -5.292498e-03
[66,] -7.830933e-03 -0.1074724518 8.211626e-03 -0.0306140143 0.187463817 -0.843484881 0.2419327494 -8.645136e-02 0.0735417365 9.856941e-02
[67,] -1.207800e-02 0.0104166667 -2.722313e-02 -0.1390241980 -0.064439991 -1.046987166 -0.2184515400 -6.481204e-02 0.1147334898 -2.515951e-02
[68,] -2.666429e-02 0.1001033058 -1.878144e-02 -0.0218649011 0.116878201 0.422231890 0.1572478101 7.070966e-02 -0.1181277238 -5.303244e-02
[69,] -2.154995e-02 -0.1494834711 -1.905575e-02 0.0528730196 -0.206056558 -0.935827714 -0.2240745973 2.246923e-02 0.1502053302 -1.438646e-02
[70,] 2.946166e-02 -0.0636707989 -3.682401e-02 -0.0792307086 0.052527277 -0.556667392 0.1211359141 -3.557996e-02 -0.1629651358 -1.202230e-01
[71,] -6.780857e-03 -0.0184228650 3.724433e-02 -0.1204540080 0.082297929 -1.000978899 0.1997174343 -2.752812e-02 0.0435383842 1.029888e-01
[72,] -1.624855e-02 0.1051136364 1.833900e-02 0.1489713880 -0.198307727 0.765934305 0.0813506640 6.686914e-02 -0.0745683875 -7.833971e-02
[73,] -2.857738e-02 0.0274276860 -4.416404e-02 -0.0947426500 -0.091538633 0.660648249 -0.1018366770 -8.576272e-02 0.0100779417 8.074417e-02
[74,] -1.112146e-02 -0.1417355372 -1.383942e-02 -0.1562229053 -0.062235582 -0.006634762 -0.0879627013 6.814048e-02 -0.1530548106 2.216401e-02
[75,] -3.337287e-03 -0.1499139118 3.448795e-02 0.1016631197 0.045401915 0.559386556 0.2612884996 -5.578903e-02 -0.0138283607 -9.964403e-02
[76,] 4.023875e-02 0.0220730028 1.489685e-02 -0.1344052968 -0.161478513 -0.331085491 0.1402090986 7.446189e-02 0.0875586658 7.201290e-02
[77,] 2.098027e-02 0.0643767218 2.448887e-02 -0.1510995507 0.137541750 -0.908962367 -0.1873410568 2.048276e-03 0.0745264834 -8.611727e-02
[78,] 2.390518e-02 0.0690254821 4.875653e-03 0.0423583195 -0.054130483 -0.825103328 0.2164170670 5.798739e-02 -0.0935090513 -9.259185e-02
[79,] -6.121902e-03 0.1476067493 9.968100e-03 0.0139355246 -0.140993097 -1.057537524 -0.1862955637 7.150425e-02 0.0602581294 8.838740e-03
[80,] 1.027119e-02 -0.0110365014 -2.040961e-02 0.0864979901 -0.160209308 0.376658690 0.1018649336 -3.534159e-02 -0.1863057325 -8.903217e-02
[81,] -2.313994e-02 0.1345730028 -4.314201e-02 -0.1205013005 -0.014918726 0.775179465 -0.1147781859 -2.028852e-02 -0.1897837747 1.043724e-02
[82,] 1.077710e-02 0.1535640496 -8.366479e-03 0.0722156538 -0.018392340 1.038503372 -0.2393614015 3.466177e-02 -0.0670885015 4.924441e-02
[83,] -2.216639e-02 -0.0403064738 -5.158813e-03 0.0665090250 0.154241817 0.006852295 0.1891777338 -1.045327e-02 0.1314322829 2.431325e-03
K11 K12
[1,] 0.0629107857 -0.0375083153
[2,] 0.0383081396 0.0169489598
[3,] 0.0655345406 0.0378835690
[4,] -0.0135340923 -0.0115418948
[5,] -0.0358557858 0.0295995588
[6,] -0.0113388401 0.0225550230
[7,] 0.0104488730 0.0559867183
[8,] 0.0396595711 -0.0291731341
[9,] 0.0216492739 -0.0182111769
[10,] 0.0618230482 0.0267226136
[11,] -0.0341549598 -0.0338410630
[12,] 0.0165402034 0.0024789488
[13,] -0.0598321588 -0.0398166942
[14,] 0.0382685855 0.0061064015
[15,] 0.0367259758 0.0136057903
[16,] -0.0001384393 -0.0427618674
[17,] -0.0090776645 0.0114907238
[18,] 0.0592058856 0.0356377323
[19,] 0.0143581359 0.0477083937
[20,] 0.0133890607 -0.0284226267
[21,] -0.0332188462 -0.0561686595
[22,] 0.0264155421 0.0234874716
[23,] 0.0338055653 0.0017000131
[24,] -0.0004548721 0.0312029156
[25,] -0.0066319030 0.0167897613
[26,] -0.0108905604 -0.0170626731
[27,] 0.0137186781 0.0444732518
[28,] -0.0224930945 -0.0443026819
[29,] 0.0517697161 0.0352624786
[30,] -0.0354009137 0.0464575480
[31,] 0.0052541021 -0.0304410368
[32,] 0.0506687938 -0.0560833746
[33,] -0.0076734941 0.0221740836
[34,] 0.0551977375 0.0003297684
[35,] 0.0517433467 -0.0272343232
[36,] 0.0640908162 -0.0289741359
[37,] 0.0177202339 -0.0091425452
[38,] 0.0548153813 0.0084318374
[39,] 0.0355986842 0.0069251369
[40,] 0.0626339071 -0.0469522006
[41,] 0.0430348537 -0.0247155747
[42,] 0.0415515752 -0.0178529801
[43,] -0.0202648806 0.0422501578
[44,] -0.0172653618 0.0205366128
[45,] 0.0388882663 -0.0096144552
[46,] 0.0651785538 0.0061064015
[47,] -0.0392244761 0.0152375754
[48,] -0.0149514474 -0.0156753714
[49,] 0.0301402193 0.0051625815
[50,] 0.0594563949 -0.0004036820
[51,] -0.0170148526 -0.0288661083
[52,] 0.0311884027 0.0335852082
[53,] 0.0388355275 0.0511197912
[54,] 0.0579006006 0.0363256975
[55,] 0.0127364181 0.0293664466
[56,] 0.0191244042 0.0090856886
[57,] -0.0622515509 -0.0233737584
[58,] 0.0362249573 0.0231122179
[59,] -0.0611242592 0.0551736686
[60,] 0.0531738864 0.0202466440
[61,] -0.0632008491 0.0120934041
[62,] -0.0243191752 -0.0383384220
[63,] 0.0200143713 0.0424946413
[64,] -0.0328760441 -0.0002387978
[65,] -0.0437731968 -0.0071582490
[66,] 0.0450916666 -0.0388558173
[67,] -0.0608407882 0.0502043996
[68,] -0.0290788511 0.0224299384
[69,] 0.0403188060 0.0507729658
[70,] -0.0380312609 0.0465712613
[71,] 0.0208647843 -0.0093472291
[72,] 0.0297842324 -0.0518304990
[73,] -0.0096577912 0.0334999232
[74,] -0.0438127509 0.0514097600
[75,] -0.0283339157 0.0351715080
[76,] 0.0212207712 -0.0160108255
[77,] 0.0453158065 -0.0306855203
[78,] -0.0042586574 0.0015749285
[79,] -0.0649939680 -0.0248463450
[80,] -0.0040542946 0.0457638972
[81,] 0.0522311805 -0.0373263741
[82,] -0.0453685453 -0.0460197520
[83,] -0.0390069286 0.0300771544
[ reached getOption("max.print") -- omitted 333 rows ]
$Asama_3
[,1]
K1 1.638503
K2 1.687319
K3 1.689942
K4 1.738051
K5 1.725793
K6 1.700281
K7 1.713241
K8 1.628322
K9 1.691720
K10 1.761540
K11 1.660501
K12 1.627682
$KA
[,1]
K1 0.081
K2 0.083
K3 0.083
K4 0.086
K5 0.085
K6 0.084
K7 0.085
K8 0.080
K9 0.083
K10 0.087
K11 0.082
K12 0.080
Yukarıdaki kod bloğu çalıştırıldığında elde edilen kriter ağırlıkları aşağıda verilmiştir.
$KA
[,1]
K1 0.081
K2 0.083
K3 0.083
K4 0.086
K5 0.085
K6 0.084
K7 0.085
K8 0.080
K9 0.083
K10 0.087
K11 0.082
K12 0.080
Şimdi de elde ettiğimiz bu kriter ağırlıklarını aşağıda yazılan kod ile büyükten küçüğe doğru igray teması ile grafik üzerinde gösterelim.
b=NMD(km1)
tibble(Kriter=paste("K", 1:ncol(km1), sep=""), Ağırlık=round(b$KA,3)) %>% mutate(Kriter = fct_reorder(Kriter, Ağırlık)) %>%
ggplot(aes(x=Kriter, y=Ağırlık)) +
geom_bar(stat="identity", fill="#ff4d4d", alpha=.6, width=.6) +
geom_text(aes(label=Ağırlık), vjust=0.5, size=4)+
coord_flip() +
xlab("Kriter") +
theme_igray()
Yukarıdaki R kod bloğunun çalıştırılmasından sonra 12 kriterimize ait ağırlık değerleri aşağıdaki grafik üzerinde verilmiştir.
Eğer NMD sonuçlarını Microsoft Excel çalışma kitabına yazdırmak istersek aşağıda kodu yazmamız yeterlidir.
library(openxlsx)
#sonuçları yazdırmak için
y=NMD(km1)
cikti <- list('Karar Matrisi' = y$Karar_Matrisi, '2. Aşama Matrisi' = y$Asama_2, '3.Aşama Matrisi' = y$Asama_3, "Kriter Ağırlıkları"=y$KA)
baslik_stili <- createStyle(
textDecoration = "BOLD", fontColour = "#FFFFFF", fontSize = 12,
fontName = "Arial Narrow", fgFill = "#4F80BD", halign = "center")
#elde edilen sonuçları "sonuçlar.xlsx" excel çalışma kitabına yazdırılması
write.xlsx(cikti, file = 'sonuclar.xlsx', asTable = FALSE, overwrite = TRUE, rowNames = TRUE, borders = "rows", headerStyle = baslik_stili, colWidths="auto", Widths="auto")
Yukarıdaki R kod bloğu çalıştırılmasından sonra elde edilen xlsx uzantılı dosya aşağıdaki linkte verilmiştir.
NMD Kullanım Alanları
Ağırlıklandırma işlemi gerektiren;
- Sıralama (ranking)
- Seçim (selection)
- Etkinlik ve verimlilik ölçümleri (measurements of efficiency and productivity)
- Performans değenlendirme (performance evaluation)
- Risk tahmini (risk estimation)
- Optimal çözüm (optimal solution)
gibi bütün karar verme problemlerinin çözümünde sektör ayrımı olmaksızın rahatlıkla uygulanabilir. Yönteminin kullanıldığı çalışmalar:
- Bağcı, H. & Sarıay, İ. (2021). Halka Açık Piyasa Değeri ve Piyasa Değerinin İşletme Performansındaki Rolü: BİST Halka Arz Endeksi’nde Bir Uygulama. Finansal Araştırmalar ve Çalışmalar Dergisi, 13 (24):36-54. DOI:10.14784/marufacd.880613.
- Çağdaş Sağ, Sezgi. (2022). Görsel sanatlar öğretmen adayı seçim sınavında yeni bir boyut: Kişilik testi. Pamukkale Üniversitesi, Eğitim Bilimleri Enstitüsü, Yüksek Lisans Tezi, Denizli. URL: http://acikerisim.pau.edu.tr/xmlui/handle/11499/45600.
Sonuç
Özetle, bu çalışmayla ÇKKV problemlerinin çözümünde ağırlıklandırma yöntemi olarak geliştirilen NMD metodunun R programlama dilinde oluşturulan fonksiyonu ile uygulanmasına yer verilerek bu yöntemi kullanacak akademi ve saha çalışanlarına bir katkı sunulması amaçlanmıştır.
Faydalı olması dileğiyle.
Bilimle ve teknolojiyle kalınız.
Bu çalışmaya atıf yapmak için aşağıdaki alıntı gösterme şeklini kullanabilirsiniz.
- Bulut, T. (2022). R’da Normalize Edilmiş Maksimum Değerler [NMD] Metodu. URL: https://tevfikbulut.net/rda-normalize-edilmis-maksimum-degerler-nmd-metodu/
- Bulut, T. (2022). Normalize Edilmiş Maksimum Değerler [NMD] Metodu. URL: https://tevfikbulut.net/normalize-edilmis-maksimum-degerler-nmd-metodu/
- Bulut, T. (2017). Çok Kriterli Karar Verme (ÇKKV) Modellerinde Kriterlerin Ağırlıklandırılmasına Yönelik Bir Model Önerisi: Normalize Edilmiş Maksimum Değerler [NMD] Metodu (Normalized Maximum Values [NMV] Method), URL: https://tevfikbulutcom.wordpress.com/2017/06/21/coklu-karar-verme-modellerinde-kriterlerin-agirliklandirilmasina-yonelik-model-onerisi/.
Not/Note
- Kaynak gösterilmeden alıntı yapılamaz veya kopyalanamaz.
- It can not be cited or copied without referencing.
Yararlanılan Kaynaklar
- Çok Kriterli Karar Verme (ÇKKV) Modellerinde Kriterlerin Ağırlıklandırılmasına Yönelik Bir Model Önerisi: Normalize Edilmiş Maksimum Değerler [NMD] Metodu (Normalized Maximum Values [NMV] Method), URL:https://tevfikbulutcom.wordpress.com/2017/06/21/coklu-karar-verme-modellerinde-kriterlerin-agirliklandirilmasina-yonelik-model-onerisi/.
- Normalize Edilmiş Maksimum Değerler [NMD] Metodu, URL: https://rpubs.com/tevfik1461/nmd.
- Normalize Edilmiş Maksimum Değerler [NMD] Metodu, https://tevfikbulut.net/normalize-edilmis-maksimum-degerler-nmd-metodu/.
- Bağcı, H. & Sarıay, İ. (2021). Halka Açık Piyasa Değeri ve Piyasa Değerinin İşletme Performansındaki Rolü: BİST Halka Arz Endeksi’nde Bir Uygulama. Finansal Araştırmalar ve Çalışmalar Dergisi , 13 (24) , 36-54 . DOI: 10.14784/marufacd.880613.
- Çağdaş Sağ, Sezgi. (2022). Görsel sanatlar öğretmen adayı seçim sınavında yeni bir boyut: Kişilik testi. Pamukkale Üniversitesi, Eğitim Bilimleri Enstitüsü, Yüksek Lisans Tezi, Denizli. URL: http://acikerisim.pau.edu.tr/xmlui/handle/11499/45600.
- Microsoft Office Excel 2016. Microsoft Corporation.
- R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL: https://www.R-project.org/.
- DiagrammeR kütüphanesi, URL: https://github.com/rich-iannone/DiagrammeR.
- JJ Allaire and Yihui Xie and Jonathan McPherson and Javier Luraschi and Kevin Ushey and Aron Atkins and Hadley Wickham and Joe Cheng and Winston Chang and Richard Iannone (2021). rmarkdown: Dynamic Documents for R. R package version 2.11. URL https://rmarkdown.rstudio.com.