Rudarski radovi br 4 2011 - Institut za rudarstvo i metalurgiju Bor

Step 2<br />
If it is not possible to determine by<br />
step 1 if one fuzzy number is smaller or<br />
larger than the other, then we proceed to<br />
step 2. This step compares the scope values<br />
of both fuzzy numbers which are assigned<br />
the highest values of possibility<br />
distribution functions.<br />
Formally, step 2 is represented as follows:<br />
• max ( μ ( x ) )<br />
is the assigned<br />
M<br />
value of the fuzzy number<br />
*<br />
M scope which is denoted as x<br />
• assigned value of the fuzzy number<br />
*<br />
N scope which is denoted as x<br />
Now, it the two fuzzy numbers are given<br />
be M = { x, μ ( x),<br />
} and N = { y, μ ( y)<br />
} .<br />
M<br />
N<br />
Table 1. List of general activities with duration in days<br />
No. of activities in<br />
network layout<br />
M<br />
N<br />
It is considered that the fuzzy number M is<br />
smaller than the fuzzy number N if and<br />
* *<br />
only if the following is valid: x < x<br />
M N<br />
Step 3<br />
This step is performed when it is not<br />
possible to determine in the first two steps<br />
how much one fuzzy number is bigger or<br />
smaller than the other. In this step we<br />
compare the “bases” of fuzzy numbers.<br />
The term “base” determines a length of<br />
the fuzzy number basis.<br />
PRACTICAL USE THE FUZZY<br />
NUMBER COMPARISON METHOD<br />
There is a list of general activities with<br />
duration in days for an industrial hall (Table<br />
1) which includes the works on the<br />
construction site as well as the works on<br />
prefabrication the assembling elements.<br />
Description of activities l m r<br />
1. Fulfilling the contract obligations towards the contractor 2 3 4<br />
2. Preliminary works (building of commercial construction site) 5 7 9<br />
3. Prefabrication of concrete facade elements 24 30 35<br />
4. Prefabrication of concrete columns and rain-water girders 14 16 18<br />
5. Removal of humus topsoil and location levelling 3 4 5<br />
6. Fabrication of the main roof beams (truss) 7 10 12<br />
7. Construction of transport routes around the facility 9 12 14<br />
8. Spot footing pits excavation 1 2 3<br />
9. Fabrication of secondary roof beams (purlins, bracings) 13 15 17<br />
10. Construction the base for hall floor plate 3 4 5<br />
11. Excavation of external installation ducts 3 4 5<br />
12. Making of transport route wearing course 1 2 3<br />
13. Concreting of spot footings and ground beams 8 10 12<br />
14. Transport and stockpiling of steel structure 1 3 4<br />
15. Erection of concrete columns and rain-water girders 2 3 4<br />
16. Construction of the hall floor slab with waterproofing 4 6 7<br />
17. Connecting the truss parts into a whole 1 2 3<br />
No 4, 2011. 163<br />
MINING ENGINEERING