Modelling and Simulation in Engineering / 2019 / Article / Tab 5

Research Article

The Quality of Ranking during Simulated Pairwise Judgments for Examined Approximation Procedures

Table 5

Mean performance measures of arbitrarily selected five different approximation procedures for various uniformly drawn 100,000 AHP models–1,000 hypothetic decisional problems perturbed 100 times each.

Scenario detailsProcedureMRERankMSRCRankMRRRankMean rank

Geometric scalen, m ∈ {3, 4, …, 7}FR-PCMLLSM0.12328840.91628111.0464632.6 (6)
REV0.12303010.91505651.0454612.3 (3)
LUA0.12304430.91548921.0469943
SRDM0.12303820.91547631.0456722.3 (3)
SNCS0.13292650.91522841.0586554.6 (6)
NR-PCMLLSM0.10051110.93024241.0295343
REV0.10152340.93016451.0293834
LUA0.10065820.93096521.0292622
SRDM0.10131030.93051031.0292512.3 (3)
SNCS0.10868950.93102611.0431553.6 (6)
n, m ∈ {8, 9, …, 12}FR-PCMLLSM0.07974840.93139611.0331943
REV0.07911010.92826651.0311612.3 (3)
LUA0.07932130.92881721.0317332.6 (6)
SRDM0.07928620.92876941.0316622.6 (6)
SNCS0.08622350.92879931.0393554.3 (3)
NR-PCMLLSM0.06393640.94339331.0225243.6 (6)
REV0.06273530.94239951.0207013
LUA0.06175710.94459311.0210931.6 (6)
SRDM0.06185220.94431421.0210522
SNCS0.06898150.94276441.0287954.6 (6)

Saaty’s scalen, m ∈ {3, 4, …, 7}FR-PCMLLSM0.14365040.91138111.0657843
REV0.14296710.91115141.0649812
LUA0.14306930.91134721.0652032.6 (6)
SRDM0.14305420.91132031.0651722.3 (3)
SNCS0.15569450.91073551.0785055
NR-PCMLLSM0.11609510.92745511.0468131.6 (6)
REV0.11699440.92695541.0470544
LUA0.11633720.92712931.0465712
SRDM0.11696230.92653251.0465823.3 (3)
SNCS0.12715450.92739721.0605154
n, m ∈ {8, 9, …, 12}FR-PCMLLSM0.10027940.91723111.0485643
REV0.09808410.91583341.0463012
LUA0.09864830.91624521.0469532.6 (6)
SRDM0.09856920.91619331.0468722.3 (3)
SNCS0.10667450.91563351.0542455
NR-PCMLLSM0.07846440.93819231.0356343.6 (6)
REV0.07700230.93783741.0342212.6 (6)
LUA0.07676210.93966911.0346931.6 (6)
SRDM0.07678920.93941521.0346422
SNCS0.08430750.93779651.0412555
Average mean rankLLSM = 2.958REV = 2.792LUA = 2.292SRDM = 2.417SNCS = 4.542
Order43125

Note: AHP models drawn randomly (uniformly) for the assigned set of criteria and alternatives. The scenario assumes application of both the perturbation factor drawn with F-Snedecor probability for n1 = 14 and n2 = 40 degrees of freedom and rounding errors associated with a given scale (geometric or Saaty’s). It assumes calculation of performance measures either for reciprocal PCMs (FR-PCMs) or nonreciprocal PCMs (NR-PCMs).

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