## 4 The Proposed Scheme HFECS
### Cluster Formation
\(\alpha\), \(\beta\), \(\gamma\), \(\sigma\) and \(\delta\) are the appropriate weights assigned to time-frequency parameter, residual energy, link quality factor, distance to the BS and number of supported sensor nodes, respectively. The time-frequency parameter depends on working-sleeping cycle \(W_{v}/S_{p}\) and status transition frequency \(F_{ST}\). We can calculate the time-frequency parameter \(TF_{V_{CM(i)}V_{CM(j)}}\) using Equation (13) as  
\[TF_{V_{CM(i)}V_{CM(j)}}=\left(\frac{F_{STV_{CM(i)}}}{F_{ST_{max}}}\times\frac{W_{ V_{CM(i)}}}{T_{CP}}\right)\left(\frac{F_{STV_{CM(j)}}}{F_{ST_{max}}}\times\frac{W_{V_{ CM(j)}}}{T_{CP}}\right) \tag{13}\]  
where \(W_{V_{CM(i)}}\) and \(W_{V_{CM(j)}}\) are the total working time of the adjacent nodes \(V_{CM(i)}\) and \(V_{CM(j)}\), \(T_{CP}\) is the data collection period, \(F_{STCM(i)}\) and \(F_{STCM(j)}\) are the status transition frequencies of the adjacent nodes \(V_{CM(i)}\) and \(V_{CM(j)}\), and \(F_{STmax}\) is the max status transition frequency value obtained during \(T_{CP}\). Then, \(V_{CM(i)}\) acquires the sensory data, integrates it while removing the redundant information, and forwards the integrated data along with the link connectivity information to the current CH. ```
Input: CH election procedure executed Output: Executing all tasks relevant to CM after CH election procedure Begin:
1. if (CH_Announce message received from multiple potential CH), then Send the Con_Req to potential CH with highest attribute value \(\alpha_{\sigma(4)}>D_{F4}\) else if (CH_Announce message received from single potential CH), then Send the Con_Req to that potential CH else Wait till the CH_Announce message is received from any potential CH endif Wait till the TDMA schedule is received from new CH if (TDMA based schedule received from new CH), then Store the schedule (especially CM timeslot) in local buffer if (timeslot = CM timeslot), then Calculate Link connectivity of \(V_{CM(i)}\) with \(V_{CM(j)}\) using Equation (12) Integrate data and remove the redundant and identical info. for every time period T while\(D_{T_{i}}\
eq D_{T_{i-1}}\), do // detecting the change in integrated data Transmit the integrated data \(D_{T_{i}}\) to CH along with \(L_{V_{CM(i)}V_{CM(j)}}\) endwhile elseif (timeslot \(\
eq\) CM timeslot), then Wait until timeslot = CM timeslot endif endif
```  
**Algorithm 3**HFECS (CM Side)  
Besides the benefits of hesitant fuzzy entropy in the CH election procedure of heterogeneous clustering scheme, it can also help in predicting an event in the heterogeneous clustering scheme and in reducing the number of transmissions in the network by applying reliable data fusion. Let us assume that CH requires time period \(T\) to transmit aggregated data packet to BS, and CM requires time period \(t\) to transmit the integrated data to CH where \(T=nt\). Moreover, we considered context-based data forwarding, which means that when the CH receives the integrated data from \(V_{CM(i)}\), it performs lossless aggregation by concatenating multiple data packets into single packet of specified length. In addition, CH also standardizes the received integrated data, calculates the hesitant fuzzy entropy and assign corresponding weight coefficients to integrated data of all sensor nodes. Then, CH synthesizes the attribute values of each sensor node to determine the threshold attribute values. After that, the threshold attribute values are compared with original attribute values to make a decision about data forwarding to the BS. If the original attribute values (current integrated data) are greater than threshold attribute values, it means that integrated data is changed after time period T, only then the CH transmits the result to the BS so that the BS can initiate the Standard Operating Procedure (SOP) accordingly against the event occurred in the cluster, but if the original attribute values are less than threshold attribute values, it means that the integrated data are not changed after time period T and CHs do not need to forward the integrated data to the BS.