Algorithm 1: The Cluster-head (CH) and Vice-CH election.

for s ← 1 to #nodes do

τs ← τs + Δτκ;

${\tau }_s\leftarrow \frac{{\tau }_s}{(1+\mathrm{\Delta }{\tau }^{\kappa })};$

Determine the value of the linguistic variable, etas;

ηs ← defuzzification of etas;

$p_s^{\kappa }=\{\begin{array}{ll}{\mathcal{A}}_s=\frac{w{\tau }_s+(1-w){\eta }_s}{w+(1-w)(|{\mathcal{N}}_s|-1)},\hfill & \text{if}s\notin {ℳ}^{\kappa },\hfill \\ 0,\hfill & \text{if}s\in {ℳ}^{\kappa },\hfill \end{array}$;

${\mathtt{\text{chance}}}_s\leftarrow p_s^{\kappa }$;

Advertise the value of chances;

Receive the other advertisements and compare them;

if the value of chances is greater than of the others then

Advertise a CH message;

else

if the value of chances is the next higher value then

Advertise a vice CH message;

else

Select the closest CH as its coordinator;

Join the cluster.

end

end

end