Advances in Operations Research / 2019 / Article / Tab 9 / Research Article
An Examination of Ranking Quality for Simulated Pairwise Judgments in relation to Performance of the Selected Consistency Measure Table 9 Performance of TSL (A ) index under the action of LLSM as the PP . Statistical characteristics of the MAEs distribution in relation to various levels of
TSL (
A ) within a given
for
i =1,…,15. The results are based on 10,000 perturbed random reciprocal PCMs with application of Saaty’s scales and were generated on the basis of
as the simulation
. The table contains results for
, presented consecutively.
for Mean in –quantiles of MAEs among w and w (LLSM)Average MAEs among w and =0.05 =0.1 =0.5 =0.9 =0.951 0.057912 0.0039186 0.0049954 0.0109799 0.0221753 0.0274887 0.0127898 2 0.099124 0.0056158 0.0073876 0.0157136 0.0324243 0.0398139 0.0183201 3 0.116088 0.0063140 0.0079525 0.0184299 0.0389673 0.0490687 0.0214159 4 0.133907 0.0075132 0.0102233 0.0230429 0.0443459 0.0539668 0.0258898 5 0.151127 0.0099921 0.0129535 0.0261046 0.0486044 0.0581258 0.0290851 6 0.167911 0.0113191 0.0142543 0.0289546 0.0558904 0.0682777 0.0328936 7 0.184671 0.0125612 0.0158052 0.0320054 0.0594491 0.0730399 0.0357402 8 0.201896 0.0136853 0.0171375 0.0339101 0.0640703 0.0789391 0.0380755 9 0.219329 0.0142803 0.0178080 0.0361548 0.0711273 0.0839402 0.0408705 10 0.236371 0.0150518 0.0185369 0.0380656 0.0762136 0.0919801 0.0435024 11 0.253302 0.0161087 0.0208189 0.0405464 0.0789105 0.0929572 0.0462684 12 0.270523 0.0160427 0.0205586 0.0431223 0.0821647 0.0965329 0.0482168 13 0.288211 0.0165698 0.0209757 0.0457022 0.0865715 0.100490 0.0504072 14 0.305099 0.0177870 0.0226112 0.0455671 0.0859316 0.100544 0.0507868 15 0.357080 0.0186614 0.0241816 0.0493007 0.0932224 0.107664 0.0547348 i for TSL (A )Mean TSL (A ) in p –quantiles of MAEs among w and w (LLSM)Average MAEs among w and p =0.05p =0.1p =0.5p =0.9p =0.951 0.0618775 0.0036042 0.0044511 0.0090509 0.0175099 0.0212066 0.0102634 2 0.096694 0.00584585 0.0072472 0.0147877 0.0255157 0.0297767 0.0158427 3 0.109186 0.0071783 0.0088408 0.0167774 0.0304119 0.0360603 0.0186253 4 0.121228 0.00831565 0.0102091 0.0192100 0.0349865 0.0420209 0.0214601 5 0.133028 0.0088771 0.0109435 0.0208206 0.0393504 0.0481357 0.0236802 6 0.144977 0.0097898 0.0118208 0.0225534 0.0439163 0.0538868 0.0259512 7 0.156874 0.0101678 0.0126009 0.0248914 0.0500528 0.0613696 0.0288113 8 0.169306 0.0113233 0.0138144 0.0274455 0.0552421 0.0656847 0.0317599 9 0.181783 0.0120341 0.0147276 0.0297646 0.0587297 0.0700824 0.0339487 10 0.193745 0.0124796 0.0157621 0.0317564 0.0613300 0.0720410 0.0356610 11 0.205758 0.0137977 0.0167981 0.0329443 0.0622977 0.0721443 0.0368687 12 0.218204 0.0140878 0.0175574 0.0347152 0.0652521 0.0774105 0.0386492 13 0.230723 0.0140705 0.0177333 0.0369638 0.0672822 0.0764555 0.0402684 14 0.242818 0.0146810 0.0186397 0.0381558 0.0692375 0.0786225 0.0413928 15 0.279499 0.0168309 0.0207854 0.0401272 0.0721349 0.0829652 0.0439267 i for TSL (A )Mean TSL (A ) in p –quantiles of MAEs among w and w (LLSM)Average MAEs among w and p =0.05p =0.1p =0.5p =0.9p =0.951 0.061626 0.00329141 0.0040063 0.0079292 0.0153184 0.017980 0.0089902 2 0.085354 0.00558449 0.0066781 0.0124836 0.0217916 0.0254877 0.0136394 3 0.095128 0.00622084 0.0074651 0.0136346 0.0241580 0.0288301 0.0151410 4 0.105046 0.00677146 0.0081844 0.0150571 0.0277432 0.0343089 0.0170348 5 0.114884 0.00728075 0.0089529 0.0164708 0.0329745 0.0408782 0.0192642 6 0.124902 0.00792417 0.0097471 0.0185168 0.0378364 0.0464765 0.0217170 7 0.134949 0.00851189 0.0104389 0.0202075 0.0415434 0.0507830 0.0236614 8 0.144883 0.00952136 0.0115606 0.0224145 0.0446314 0.0531641 0.0257116 9 0.155416 0.0101888 0.0121602 0.0241178 0.0465694 0.0553538 0.0275101 10 0.165845 0.0110535 0.0132394 0.0261677 0.0499157 0.0583309 0.0293786 11 0.175874 0.0116123 0.0139639 0.0273006 0.0515428 0.0596329 0.0304575 12 0.185981 0.0121824 0.0150547 0.0293308 0.0532065 0.0613544 0.0320030 13 0.195819 0.0122294 0.0152015 0.0299135 0.0553010 0.0642011 0.0330142 14 0.205937 0.0132402 0.0164008 0.0321805 0.0552598 0.0636846 0.0343310 15 0.235348 0.0147413 0.0179580 0.0321805 0.0586515 0.0682411 0.0363445 i for TSL (A )Mean TSL (A ) in p –quantiles of MAEs among w and w (LLSM)Average MAEs among w and p =0.05p =0.1p =0.5p =0.9p =0.951 0.056493 0.0029930 0.0036359 0.0071723 0.0129253 0.0151100 0.0079193 2 0.073616 0.0047668 0.0056647 0.0098201 0.0165545 0.0197820 0.0107659 3 0.082558 0.0051148 0.00615425 0.0108293 0.0189720 0.0232764 0.0121106 4 0.090957 0.0054815 0.0067644 0.0120701 0.0230822 0.0289636 0.0139455 5 0.0995085 0.0062208 0.0074045 0.0134360 0.0267488 0.0338094 0.0157422 6 0.108507 0.0065308 0.0079148 0.0148310 0.0307300 0.0379708 0.0175495 7 0.117503 0.0073636 0.0087983 0.0166204 0.0342287 0.0402093 0.0192815 8 0.126447 0.0077367 0.00920785 0.0182781 0.0366835 0.0432579 0.0209778 9 0.135467 0.0081883 0.0099817 0.0200944 0.0391024 0.0463982 0.0227669 10 0.144406 0.00893715 0.0109052 0.0215995 0.0404294 0.0465999 0.0240918 11 0.153395 0.0096365 0.0118788 0.0228543 0.0420224 0.0488816 0.0252208 12 0.162379 0.0105213 0.0128739 0.0250637 0.0441591 0.0509963 0.0270496 13 0.171319 0.0109917 0.0133182 0.0253654 0.0446033 0.0525163 0.0275815 14 0.180246 0.0120041 0.0144395 0.0266159 0.0464516 0.0529339 0.0289197 15 0.205854 0.0127740 0.0155662 0.0283804 0.0479564 0.0549310 0.0304352 i for TSL (A )Mean TSL (A ) in p –quantiles of MAEs among w and w (LLSM)Average MAEs among w and p =0.05p =0.1p =0.5p =0.9p =0.951 0.051197 0.0026372 0.0031677 0.0061278 0.0107141 0.0122502 0.0066588 2 0.064092 0.0040166 0.0047872 0.0079722 0.0133870 0.0158901 0.0087678 3 0.072019 0.0044127 0.0052033 0.0089180 0.0154595 0.0189767 0.0099818 4 0.080495 0.0046625 0.0055923 0.0098746 0.0183837 0.0234965 0.0114040 5 0.089047 0.0052813 0.0062378 0.0110158 0.0221043 0.0279174 0.0129826 6 0.097017 0.0056575 0.0067669 0.0124636 0.0261396 0.0326188 0.0147615 7 0.105051 0.0061505 0.0074036 0.0138920 0.0290254 0.0358010 0.0164984 8 0.113488 0.0066692 0.0079686 0.0153474 0.0308319 0.0365922 0.0177312 9 0.122009 0.0073133 0.0087907 0.0171076 0.0330852 0.0388189 0.0193438 10 0.129857 0.0076181 0.0092912 0.0186416 0.0343317 0.0401595 0.0204982 11 0.137970 0.0083801 0.0102174 0.0199779 0.0355818 0.0416818 0.0216939 12 0.146298 0.0091112 0.0107807 0.0212040 0.0376109 0.0430078 0.0229256 13 0.154883 0.0097330 0.0118942 0.0219635 0.0378245 0.0435528 0.0237785 14 0.162793 0.0102563 0.0125995 0.0228089 0.0390630 0.0443591 0.0244409 15 0.184864 0.0115601 0.0138072 0.0242891 0.0403012 0.0468790 0.0259996