A rough set approach for evaluating vague customer requirement of industrial product-service system_Wenyan Songa
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Table 4. Rough weight <strong>of</strong> IPS 2 <strong>requirement</strong>.<br />
IPS 2 <strong>requirement</strong> Sub-<strong>requirement</strong> Rough weight Normalised <strong>rough</strong> weight<br />
R 1 (easy and accurate decision-making <strong>of</strong><br />
R 11 [1.000, 1.000] [0.788, 1.454] [0.082, 0.151]<br />
air compressor selection), [0.788, 1.454]<br />
R 2 (procurement process support), [0.360, 0.743] R 21 [0.329, 0.427] [0.118, 0.318] [0.012, 0.033]<br />
R 22 [1.296, 1.968] [0.466, 1.463] [0.048, 0.152]<br />
R 23 [1.355, 2.057] [0.488, 1.529] [0.051, 0.159]<br />
R 3 (quick start using <strong>of</strong> the air<br />
R 31 [0.680, 1.278] [0.161, 0.367] [0.017, 0.038]<br />
compressor <strong>system</strong>), [0.237, 0.287]<br />
R 32 [0.418, 0.925] [0.099, 0.266] [0.010, 0.028]<br />
R 4 (guarantee and optimisation <strong>of</strong><br />
normal operation), [2.495, 3.575]<br />
R 5 (efficient, and reliable MRO with<br />
accurate operation in<strong>for</strong>mation <strong>of</strong><br />
air compressor), [1.745, 3.081]<br />
International Journal <strong>of</strong> Production Research 6695<br />
R 33 [1.230, 2.420] [0.292, 0.695] [0.030, 0.072]<br />
R 41 [1.527, 2.696] [3.809, 9.639] [0.395 ,1.000]<br />
R 42 [0.331, 0.507] [0.825, 1.812] [0.086, 0.188]<br />
R 43 [1.037, 2.443] [2.588, 8.736] [0.269, 0.906]<br />
R 44 [0.533, 1.500] [1.330, 5.363] [0.138, 0.556]<br />
R 45 [0.643, 1.688] [1.605, 6.035] [0.167, 0.626]<br />
R 51 [0.373, 0.775] [0.650, 2.387] [0.067, 0.248]<br />
R 52 [1.024, 1.788] [1.786, 5.510] [0.185, 0.572]<br />
R 53 [0.986, 1.920] [1.720, 5.915] [0.178, 0.614]<br />
Table 5. Crisp <strong>requirement</strong> weight and rank <strong>of</strong> IPS 2 <strong>requirement</strong> under different <strong>vague</strong>ness.<br />
IPS 2 <strong>requirement</strong><br />
λ =0 λ = 0.5 λ =1<br />
Crisp weight Rank Crisp weight Rank Crisp weight Rank<br />
R 11 0.082 8 0.116 9 0.151 11<br />
R 21 0.012 14 0.023 14 0.033 14<br />
R 22 0.048 11 0.100 11 0.152 10<br />
R 23 0.051 10 0.105 10 0.159 9<br />
R 31 0.017 13 0.027 13 0.038 13<br />
R 32 0.010 15 0.019 15 0.028 15<br />
R 33 0.030 12 0.051 12 0.072 12<br />
R 41 0.395 1 0.698 1 1.000 1<br />
R 42 0.086 7 0.137 8 0.188 8<br />
R 43 0.269 2 0.587 2 0.906 2<br />
R 44 0.138 6 0.347 6 0.556 6<br />
R 45 0.167 5 0.396 3 0.626 3<br />
R 51 0.067 9 0.158 7 0.248 7<br />
R 52 0.185 3 0.378 5 0.572 5<br />
R 53 0.178 4 0.396 4 0.614 4<br />
Step 4 IPS 2 <strong>requirement</strong> prioritisation<br />
Then, IPS 2 <strong>requirement</strong> management team introduces the optimistic indicator λ = 0, 0.5 and 1, respectively, trans<strong>for</strong>ming<br />
the normalised <strong>rough</strong> weight <strong>of</strong> <strong>requirement</strong> into crisp value with <strong>for</strong>mula (17) (see Table 5).<br />
The weight <strong>of</strong> IPS 2 <strong>requirement</strong> can be seen in Table 5. When experts are more cautious (λ = 0), the priority <strong>of</strong> IPS 2<br />
<strong>requirement</strong> is as follows:<br />
R 41 > R 43 > R 52 > R 53 > R 45 > R 44 > R 42 > R 11 > R 51 > R 23 > R 22 > R 33 > R 31 > R 21 > R 32 :<br />
When experts have a moderate propensity (λ = 0.5), the priority <strong>of</strong> IPS 2 <strong>requirement</strong> is as follows:<br />
R 41 > R 43 > R 45 > R 53 > R 52 > R 44 > R 51 > R 42 > R 11 > R 23 > R 22 > R 33 > R 31 > R 21 > R 32 :<br />
When experts have much optimistic propensity (λ = 1), the priority <strong>of</strong> IPS 2 <strong>requirement</strong> is as follows:<br />
R 41 > R 43 > R 45 > R 53 > R 52 > R 44 > R 51 > R 42 > R 23 > R 22 > R 11 > R 33 > R 31 > R 21 > R 32 :
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