Page 108 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

Table 2 – Simple decision matrix. loss of the wireless link of technology would change
4
the selected technology from to . This would cause
1 2 3 1 3
1 1.024537 7.828443 8.650221 a technology switch which will require energy and does
not bring any overall improvement.
2 4.226149 0.09865402 4.673396
3 8.026353 5.455392 2.536936 It is to be noted that rank reversal is not a theoretical
4 1.700537 1.398855 0.7656412 issue for multi‐technology WSN devices. Actually, the
wireless technologies’ links’ quality depends on many fac‐
5. The distances between each alternative and the pos‐ tors such as atmospheric and environmental conditions,
+
−
itive and negative ideal alternatives and are which vary heavily across the year. This may results in
computed according to Equation (6). broken links, thus removing a technology from the set
of alternatives and potentially resulting in rank reversal,
√ as seen in the previous example. The frequency of such
√
+
+
= √ ∑( − ) 2 events is entirely dependent on external factors and can‐

⎷ =1 (6) not be anticipated, thus links’ quality has to be considered
√ in the NIS process. Rank reversal could lead to the selec‐
√
−
−
= √ ∑( − ) 2 tion of a sub‐optimal technology, on top of spending en‐

⎷ =1 ergy for switching between technologies.
AsecondissueposedbyTOPSIS‐basedNISonconstrained
6. Finally, the relative closeness to the ideal solution
devices is the complex computations that are required.
is computed for each alternative according to Equa‐
The TOPSIS method as seen in Section 3 is based on com‐
tion (7) and a ranking is established based on those
putations that use numerous operations and memory ac‐
values.
− cesses. WSN devices are generally hardware constrained,
= − + (7) energy‐limited and a repetitive execution of the TOPSIS
+

method will have a considerable impact on the energy
When using TOPSIS for NIS, the technology with the high‐ consumption of nodes. As an example, the Pycom FiPy’s
est value of is selected. A graphical represen‐ CPU [17] holds two cores that can go up to 240 MHz. A
tation of the TOPSIS method with three alternatives and classic laptop CPU, e.g., the Intel® Core™ i7‐8650U, holds
two attributes is depicted in Fig. 1. four cores that can go up to 4.20 GHz.
4. TOPSIS PROBLEM STATEMENT 5. LIGHTWEIGHT TOPSIS FOR WSN
TOPSIS is particularly interesting, as it grades alternatives As stated in Section 4, the rank reversal issue is due to
based not only on the closeness from the best alternative TOPSIS’ normalization which computes normalized val‐
but also on the distance from the worst one. However, ues based on all the other alternatives’ values. Moreover,
TOPSIS suffers from an issue known as rank reversal that this normalization method is rather complex, and may in‐
can happen when a non‐optimal alternative is removed crease the energy consumption of nodes.
from the ranking. This can alter the quality and perti‐ Thus, we propose to use a simpli ied normalization
nence of the ranking. Rank reversal is an issue common to method, which will not cause rank reversal and simplify
several MADM methods. With an ideal method, the rank‐ the computations. Rank reversal happens because other
ing of alternatives should not be altered when another al‐ alternatives are taken into account when computing nor‐
ternative is removed. The cause of rank reversal is the malized values. Thus, our proposition is to compute those
normalization algorithm. Indeed, the TOPSIS normaliza‐ values without taking into account other alternatives’ val‐
tion (a.k.a. euclidean normalization) computes the nor‐ ues. Therefore, we need a stable normalization referen‐
malized values for an attribute based on the values of all tial to measure our values against. We know that multi‐
the other alternatives for that same attribute. Thus if set technology devices have a ixed set of technologies avail‐
changes, the result of Equation (1) also changes, which able. Those are not supposed to change after deployment,
may modify the inal ranking. and they have ixed maximum and minimum capabilities.
To clarify rank reversal let us consider an example. Ta‐ We propose to use those maximum and minimum bounds
ble 2 represents a simple decision matrix randomly illed. as referential for our normalization.
Running TOPSIS on it outputs a ranking order corre‐
sponding to [ , , , ]. If the alternative was to 5.1 Algorithm
4
2
4
1
3
be removed from the ranking (e.g. because of a broken
link for example), it is expected that the ranking of the That simpli ication takes the form of Algorithm 1, which
remaining alternatives should not be altered and there‐ replaces Equation (1) in the steps of our lightweight TOP‐
fore should correspond to [ , , ]. However, running SIS. Each value is normalized by being divided with
2
1

3
TOPSIS on Table 2 after removal of alternative out‐ the upper or the lower bound of its attribute . Upward
4
puts a ranking corresponding to [ , , ]. This corre‐ attributes’ values are divided by their upper bound, while
3
1
2
spondstoarankreversal. AppliedtoNIS,itmeansthatthe downward attributes divide their lower bound. The set
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