# Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background and the Related Work

#### 2.1. Background and Related Work

#### 2.2. Basic Concepts of Fuzzy Sets

#### 2.3. Computation of Criteria Weights Based on Entropy Measure

- Step 1:
- calculate ${\Omega}_{j}=-\frac{1}{\mathrm{log}(m)}{\displaystyle \sum _{i=1}^{m}{p}_{ij}}\mathrm{log}({p}_{ij})$, $j=1,2,\mathrm{\dots},n$ where ${p}_{ij}=\frac{{\pi}_{ij}}{{\displaystyle \sum _{i=1}^{m}{\pi}_{ij}}}\hspace{0.17em}$.

- Step 2:
- calculate ${\Psi}_{j}=1-{\Omega}_{j},\hspace{0.17em}j=1,2,\mathrm{\dots},n$;
- Step 3:
- calculate ${w}_{j}=\frac{{\Psi}_{j}}{{\displaystyle \sum _{j=1}^{n}{\Psi}_{j}}},\hspace{0.17em}j=1,2,\mathrm{\dots},n$.

#### 2.4. Finding the Best Alternative Using TOPSIS Method Based on TFNs

## 3. Some Assertions and Symbols

- Nodes are distributed at random places inside a square area;
- The base station is positioned outside the square’s bounds, enabling communication with nodes inclined to multi-path attenuation. Multi-path attenuation does not influence communication between nodes;
- The nodes are cohesive because they share the same capabilities and initial battery energy while performing different tasks depending on the time of day;
- Communication between any node, the BS, or any other node is possible.
- The nodes are immobile;
- Every node senses its environment and emits a signal of the same length;
- Numerous aspects of sensor nodes, including the primary energy of nodes, the distance between sensor nodes and receiving stations, the size of information packets, and estimates of voltage and transmission power, among others, have imprecise values due to erratic/dangerous natural conditions.

## 4. Cluster Heads Formation Method for WSN

#### 4.1. Node Selection Criteria:

#### 4.2. WSNs Lifetime Extension Algorithm via MCDM and TOPSIS Technique

Algorithm1. WSN Lifetime Extension Algorithm |

Step 1: Distribute 100 nodes in an entire network with BS location (50,175) and spread nodes randomly over $100\times 100{\mathrm{m}}^{2}$ areas. Step 2: In order to find the values of different parameters, all nodes will send the data to BS for the first round of simulation. Step 3: The network is divided into ${O}_{c}$ a number of clusters using Equation (8). Step 4: Weight is assigned to each node using the entropy-weighted approach. The TOPSIS technique is used to select CHs from each cluster for the second round of simulation based on the weight of predefined parameters for CH selection. Step 5: Repeat steps 6 to 13 until the residual energy of all the nodes has yet to be finished. Step 6: When a node’s residual energy exceeds all other nodes in the same cluster, the counter increases. Step 7: When a node’s distance from the sink is less than that of all other nodes in the same cluster, the counter increases. Step 8: When a node’s number of neighbors exceeds that of all other nodes in the same cluster, the counter increases. Step 9: When the average distance of cluster nodes is smaller than that of all other Cluster nodes within the same cluster, the counter increases. Step 10: When the distance ratio of a node is smaller than the distance ratio of all other nodes within the same cluster, the counter increases. Step 11: The node with the largest counter value is designated as a CH for the next round. Step 12: If a cluster has fewer than three nodes, nodes will be added to the closest cluster, considering each cluster’s reliability. Step 13: Jump to the next round. Step 14: Stop. |

## 5. Numerical Experiment and Discussions

Cluster Head | Residual Energy | Number of Neighbors | Distance from the Sink | Average Distance of Clusters Nodes | Distance Ratio | Reliability |
---|---|---|---|---|---|---|

CH1 | 0.9695 | 8 | 157.203 | 13.232 | 0.0819 | 0.92 |

CH2 | 0.9654 | 4 | 77.223 | 15.527 | 0.0774 | 0.96 |

CH3 | 0.9698 | 8 | 141.173 | 26.937 | 0.0442 | 0.92 |

CH4 | 0.9653 | 7 | 135.059 | 31.049 | 0.0396 | 0.93 |

CH5 | 0.9688 | 4 | 92.444 | 47.752 | 0.0318 | 0.96 |

CH6 | 0.9641 | 3 | 115.069 | 22.688 | 0.0528 | 0.97 |

CH7 | 0.9647 | 4 | 85.988 | 22.348 | 0.0564 | 0.96 |

CH8 | 0.9657 | 5 | 106.367 | 24.433 | 0.0503 | 0.95 |

CH9 | 0.9649 | 6 | 102.181 | 15.694 | 0.0735 | 0.94 |

CH10 | 0.9656 | 10 | 93.391 | 33.724 | 0.0404 | 0.9 |

CH11 | 0.9698 | 9 | 119.436 | 17.016 | 0.0671 | 0.91 |

CH12 | 0.9688 | 6 | 109.224 | 28.863 | 0.0438 | 0.94 |

CH13 | 0.9698 | 2 | 85.158 | 29.5 | 0.0456 | 0.98 |

CH14 | 0.9656 | 10 | 147.868 | 17.706 | 0.0632 | 0.9 |

#### 5.1. Time Complexity of Our Proposed Algorithm

#### 5.2. Result Validation

**Null Hypothesis (**${\mathrm{H}}_{\mathrm{o}}$

**):**the average number of simulation rounds falls within the 95% confidence interval, specifically between 1800 and 2300.

**Alternate Hypothesis (**${\mathrm{H}}_{1}$

**):**the number of simulation rounds does not fall within the 95% confidence interval.

## 6. Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Yetgin, H.; Cheung, K.T.K.; El-Hajjar, M.; Hanzo, L.H. A survey of network lifetime maximization techniques in wireless sensor networks. IEEE Commun. Surv. Tutor.
**2017**, 19, 828–854. [Google Scholar] [CrossRef] - Wang, P.; Sun, Z.; Vurun, M.C.; Al-Rodhaan, M.A.; Al-Dhelaan, A.M.; Akyildiz, I.F. On network connectivity of wireless sensor networks for sandstorm monitoring. Comput. Netw.
**2011**, 55, 1150–1157. [Google Scholar] [CrossRef] - Villaverde, B.C.; Rea, S.; Pesh, D. InRout-A QoS aware route selection algorithm for industrial wireless sensor networks. Ad Hoc Netw.
**2012**, 10, 458–478. [Google Scholar] [CrossRef] - Komar, C.; Donmez, M.Y.; Ersoy, C. Detection quality of border surveillance wireless sensor networks in the existence of trespassers’ favorite paths. Comput. Commun.
**2012**, 35, 1185–1199. [Google Scholar] [CrossRef] - Corchado, J.M.; Bajo, J.; Tapia, D.I.; Abraham, A. Using heterogeneous wireless sensor networks in atelemonitoring system for healthcare. IEEE Trans. Inf. Technol. Biomed.
**2010**, 14, 234–240. [Google Scholar] [CrossRef] - Yu, J.Y.; Chong, P.H.J. A survey on clustering schemes for mobile ad hoc networks. IEEE Commun. Surv. Tutor.
**2005**, 7, 32–48. [Google Scholar] [CrossRef] - Abbas, A.A.; Younis, M. A survey on clustering algorithms for wireless sensor networks. Comput. Commun.
**2007**, 30, 2826–2841. [Google Scholar] [CrossRef] - Wu, H.; Miao, Z.; Wang, Y.; Lin, M. Optimized recognization with few instances based on semantic distance. Vis. Comput.
**2015**, 31, 367–375. [Google Scholar] [CrossRef] - Lin, B.; Guo, W.; Xiong, N.; Chen, G.; Vasilakos, A.V.; Zhang, H. A pretreatment Workflow Scheduling Approach for Big Data Applications in MulticloudEnviorments. IEEE Trans. Netw. Serv. Manag.
**2015**, 13, 581–594. [Google Scholar] [CrossRef] - Alaidad, A.; Zhou, L. Patients’ adoption of WSN-based smart home healthcare system: An integrated model of facilitators and barriers. IEEE Trans. Prof. Commun.
**2017**, 60, 4–23. [Google Scholar] [CrossRef] - Boubrima, A.; Bechkit, W.; Rivano, H. Optimal WSN deployment models for air pollution monitoring. IEEE Trans. Wirel. Commun.
**2017**, 16, 2723–2735. [Google Scholar] [CrossRef] - Kadri, B.; Bouyeddou, B.; Moussaoui, D. Early Fire Detection System Using Wireless Sensor Networks. In Proceedings of the 2018 International Conference on Applied Smart Systems (ICAAA), Medea, Algeria, 24–25 November 2018; pp. 1–4. [Google Scholar]
- Lule, E.; Bulega, T.E. A Scalable Wireless Sensor Network (WSN) Based Architecture for Fire Disaster Monitoring in the Developing World. Int. J. Comput. Netw. Inf. Secur.
**2015**, 2, 45–49. [Google Scholar] [CrossRef] - Guleria, K.; Verma, A.K. Comprehensive review for energy efficient hierarchical protocols on wireless sensor networks. Wirel. Netw.
**2019**, 25, 1159–1183. [Google Scholar] [CrossRef] - Heinzelman, W.R.; Chandrakasan, A.; Balakrisnan, H. Energy-efficient communication protocol for wireless microsensor networks. In Proceedings of the 2000 International Conference on System Sciences, Maui, HI, USA, 7 January 2000; pp. 1–10. [Google Scholar]
- Lata, S.; Mehfuz, S.; Urooj, S.; Alrowais, F. Fuzzy clustering algorithm for enhancing reliability and network lifetime of wireless sensor networks. IEEE Access
**2020**, 8, 66013–66024. [Google Scholar] [CrossRef] - Abdul Latiff, N.M.; Tsimenidis, C.C.; Sharif, B.S. Energy-Aware Clustering for Wireless Sensor Networks using Particle Swarm Optimization. In Proceeding of the 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Communications, Athens, Greece, 3–7 September 2007; pp. 1–5. [Google Scholar]
- Zanakis, S.H.; Solomon, A.; Wishart, N.; Dublish, S. Multi-attribute decision making: A simulation comparison of select methods. Eur. J. Oper. Res.
**1998**, 107, 507–529. [Google Scholar] [CrossRef] - Zopounidis, C.; Doumpos, M. Multicriteria classification and sorting methods: A literature review. Eur. J. Oper. Res.
**2002**, 138, 229–246. [Google Scholar] [CrossRef] - Jahan, A.; Mustapha, F.; Ismail, M.Y.; Sapuan, S.M.; Bahraminasab, M. A comprehensive VIKOR method for material selection. Mater. Des.
**2011**, 32, 1215–1221. [Google Scholar] [CrossRef] - Chauhan, A.; Vaish, R. Pareto optimal microwave dielectric materials. Adv. Sci. Eng. Med.
**2013**, 5, 149–155. [Google Scholar] [CrossRef] - Xu, X.; Fallahi, N.; Yang, H. Efficient CUF-based FEM analysis of thin-wall structures with Lagrange polynomial expansion. Mech. Adv. Mater. Struct.
**2022**, 29, 1316–1337. [Google Scholar] [CrossRef] - Azad, P.; Sharma, V. Cluster head selection in wireless sensor networks under fuzzy environment. ISRN Sens. Netw.
**2013**, 2013, 909086. [Google Scholar] [CrossRef] - Senapati, T.; Yager, R.; Fermatean, R. fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Eng. Appl. Artif. Intell.
**2019**, 85, 112–121. [Google Scholar] [CrossRef] - Bai, Z.Y. An interval valued intuitionistic fuzzy TOPSIS method based on an improved score function. Sci. World J.
**2013**, 2013, 879089. [Google Scholar] [CrossRef] [PubMed] - Sahoo, L. Some Score Functions on Fermatean Fuzzy Sets and Its Application to Bride Selection Based on TOPSIS Method. Int. J. Fuzzy Syst. Appl.
**2021**, 10, 18–29. [Google Scholar] [CrossRef] - Sahoo, L.; Sen, S.; Tiwary, K.; Samanta, S.; Senapati, T. Modified Floyd-Warshall’s algorithm for maximum connectivity in Wireless Sensor Networks under uncertainty. Discret. Dyn. Nat. Soc.
**2022**, 2022, 5973433. [Google Scholar] [CrossRef] - Sahoo, L.; Sen, S.; Tiwary, K.; Samanta, S.; Senapati, T. Optimization of data distributed network system under uncertainty. Discret. Dyn. Nat. Soc.
**2022**, 2022, 7806083. [Google Scholar] [CrossRef] - Zadeh, L.A. Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst.
**1996**, 4, 103–111. [Google Scholar] [CrossRef] - Zadeh, L.A. Fuzzy Sets. Inf. Control
**1965**, 8, 338–353. [Google Scholar] [CrossRef] - Chakeres, I.D.; Belding-Royer, E.M. AODV routing protocol implementation design. In Proceedings of the 2004 24th International Conference on Distributed Computing Systems Workshops, Tokyo, Japan, 23–24 March 2004; pp. 698–703. [Google Scholar]
- Torfi, F.; Farahani, R.Z.; Rezapur, S. Fuzzy AHP to determine the relative weights of evaluation criteria and fuzzy TOPSIS to rank the alternatives. Appl. Soft Comput. J.
**2010**, 10, 520–528. [Google Scholar] [CrossRef] - Sen, S.; Sahoo, L.; Tiwary, K.; Simic, V.; Senapati, T. Wireless Sensor Network Lifetime Extension via K-Medoids and MCDM Techniques in Uncertain Environment. Appl. Sci.
**2023**, 13, 3196. [Google Scholar] [CrossRef] - Feeney, L.M. An Energy-Consumption Model for Performance Analysis of Routing Protocols for Mobile Ad-hoc Networks. Mob. Netw. Appl.
**2001**, 6, 239–249. [Google Scholar] [CrossRef] - Farahani, S. ZigBee Wireless Networks and Transceivers. In Newnes; Elsevier: Amsterdam, The Netherlands, 2011. [Google Scholar]
- Karaca, O.; Sokulla, R.; Prasad, N.R.; Prasad, R. Application oriented multi criteria optimization in WSN using on AHP. Wirel. Pers. Commun.
**2012**, 65, 689–712. [Google Scholar] [CrossRef] - Mainwaring, A.; Polastre, J.; Szewczyk, R.; Culler, D.; Anderson, J. Wireless sensor networks for habitat monitoring. In Proceedings of the First ACM International Workshop on Wireless Sensor Networks and Applications 2002, Atlanta, GA, USA, 28 September 2002; pp. 1–10. [Google Scholar]
- Dalia, R.; Gupta, R. Cluster Head Election in Wireless Sensor Network: A comprehensive Study and Future Directions. Int. J. Comput. Netw. Appl.
**2021**, 7, 178–192. [Google Scholar] - Raman, C.J.; Ali, L.; Gobalakrishnan, N.; Pradeep, K. An Overview of the Routing Techniques Employed in Wireless Sensor Network. In Proceedings of the 2020 International Conference on Communication and Signal Processing (ICCSP), Chennai, India, 28–30 July 2020; pp. 332–336. [Google Scholar]
- Ma, J.; Wang, S.; Meng, C.; Ge, Y.; Du, J. Hybrid energy-efficient APTEEN protocol based on ant colony algorithm in wireless sensor network. EURASIP J. Wirel. Commun. Netw.
**2018**, 2018, 102. [Google Scholar] [CrossRef] - Misra, S.; Kumar, R. An analytical study of LEACH and PEGASIS protocol in wireless sensor networks. In Proceedings of the 2017 International Conference on Innovations in Information, Embedded and Communication Systems, Coimbatore, India, 17–18 March 2017; pp. 1–5. [Google Scholar]
- Heinzelman, W.R.; Chandrakasan, A.P.; Balakrishnan, H. An application-specific protocol architecture for wireless microsensor networks. IEEE Trans. Wirel. Commun.
**2002**, 1, 660–670. [Google Scholar] [CrossRef] - Tay, M.; Senturk, A. A New Energy-Aware Cluster Head Selection Algorithm for Wireless Sensor Networks. Wirel. Pers. Commun.
**2022**, 122, 2235–2251. [Google Scholar] [CrossRef] - Ullah, Z. A Survey on Hybrid, Energy Efficient and Distributed (HEED) Based Energy Efficient Clustering Protocols for Wireless Sensor Networks. Wirel. Pers. Commun.
**2021**, 124, 2685–2713. [Google Scholar] [CrossRef] - Zhao, L.; Qu, S.; Yi, Y. A modified cluster-head selection algorithm in wireless sensor networks based on LEACH. EURASIP J. Wirel. Commun. Netw.
**2018**, 2018, 287. [Google Scholar] [CrossRef] - Ali, M.S.; Dey, T.; Biswas, R. ALEACH: Advanced LEACH Routing Protocol for Wireless Micro-sensor Networks. In Proceedings of the 2008 International Conference on Electrical and Computer Engineering, Dhaka, Bangladesh, 20–22 December 2008; pp. 909–914. [Google Scholar]
- Clausius, R. Ueber die bewegende Kraft der Wärme und die Gesetze, welchesichdaraus für die Wärmelehreselbstableitenlassen. Ann. Phys.
**1950**, 155, 368–397. [Google Scholar] [CrossRef] - Shannon, C. A Mathematical Theory of Communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - Dong, X.; Lu, H.; Xia, Y.; Xiong, Z. Decision-making Model under Risk Assessment Based on Entropy. Entropy
**2016**, 18, 404. [Google Scholar] [CrossRef]

Symbol | Description |
---|---|

$db$ | Distance to the base station |

$d{b}_{0}$ | Fixed measuring distance to the base station |

$ds$ | Distance from the sink |

$d{n}_{c}$ | A node’s distance from each node in a cluster or its number of neighbors |

$(X,Y)\hspace{0.17em}$ | Position of CHs in a WSN |

$({W}_{x},{W}_{y})$ | Position of nodes in a WSN |

${I}_{energy}$ | Initial energy |

$E{L}_{e}$ | Electronics energy |

$E{T}_{e}$ | The energy used for data transmission |

${e}_{fs}$ | Amplification of energy to overcome open space |

${e}_{mp}$ | Amplification of energy to navigate the multi-path |

$E{D}_{rx}$ | The usage of energy during data receipt |

${O}_{c}$ | The optimal number of cluster heads |

$Z$ | The dimensions of the square area |

${N}_{node}$ | The total number of nodes in the network |

${N}_{c}$ | The number of nodes in a cluster |

$R$ | The reliability of a cluster |

Parameters | Parametric Value as per Assumptions | Defuzzified Value |
---|---|---|

${N}_{n}$ | $100$ | |

${\tilde{I}}_{i}$ | (0.7, 1, 1.2) | 0.975 |

Coordinate of BS | (50, 175) | |

Size of the data packet | (495, 500, 510) | 501.25 |

Hello/broadcast/CH join message | (22,25,28) | 25 |

${\tilde{e}}_{fs}$ | (8, 10, 12) | 10 |

${\tilde{e}}_{mp}$ | (0.001, 0.0013, 0.0015) | 0.001275 |

${\tilde{EL}}_{e}$ | (47, 50, 52) | 49.75 |

**Table 4.**Separation evaluates $s{m}_{i}^{+}$ and $s{m}_{i}^{-}$ of each alternative in relation to positive ideal and negative ideal solutions.

CHs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$s{m}_{i}^{+}$ | 26.20 | 12.99 | 23.88 | 23.02 | 17.33 | 19.43 | 14.69 | 18.08 | 17.12 | 16.53 | 20.03 | 18.74 | 14.92 | 24.75 |

$s{m}_{i}^{-}$ | 107.11 | 26.33 | 88.94 | 82.68 | 46.87 | 58.88 | 33.65 | 51.01 | 45.70 | 42.65 | 62.57 | 54.79 | 34.70 | 95.57 |

CHs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

$R{C}_{i}({A}_{i})$ | 0.80 | 0.67 | 0.79 | 0.78 | 0.73 | 0.75 | 0.70 | 0.74 | 0.73 | 0.72 | 0.76 | 0.75 | 0.70 | 0.79 |

**Table 6.**Selection of the nine cluster heads as per the highest closeness coefficient of each alternative for Option 1.

$R{C}_{i}({A}_{i})$ | 0.80 | 0.79 | 0.79 | 0.78 | 0.76 | 0.75 | 0.75 | 0.74 | 0.73 |

Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

CHs | 1 | 3 | 14 | 4 | 11 | 6 | 12 | 8 | 5 |

**Table 7.**Selection of the nine cluster heads as per the highest closeness coefficient of each alternative for Option 2.

$R{C}_{i}({A}_{i})$ | 0.80 | 0.79 | 0.79 | 0.78 | 0.76 | 0.75 | 0.75 | 0.74 | 0.73 |

Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

CHs | 1 | 3 | 14 | 4 | 11 | 6 | 12 | 8 | 9 |

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## Share and Cite

**MDPI and ACS Style**

Sen, S.; Sahoo, L.; Tiwary, K.; Senapati, T.
Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty. *Telecom* **2023**, *4*, 678-692.
https://doi.org/10.3390/telecom4040030

**AMA Style**

Sen S, Sahoo L, Tiwary K, Senapati T.
Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty. *Telecom*. 2023; 4(4):678-692.
https://doi.org/10.3390/telecom4040030

**Chicago/Turabian Style**

Sen, Supriyan, Laxminarayan Sahoo, Kalishankar Tiwary, and Tapan Senapati.
2023. "Entropy Weighted TOPSIS Based Cluster Head Selection in Wireless Sensor Networks under Uncertainty" *Telecom* 4, no. 4: 678-692.
https://doi.org/10.3390/telecom4040030