Modified Floyd–Warshall’s Algorithm for Maximum Connectivity in Wireless Sensor Networks under Uncertainty

Sahoo, Laxminarayan; Sen, Supriyan; Tiwary, Kalishankar; Samanta, Sovan; Senapati, Tapan

doi:https://doi.org/10.1155/2022/5973433

Discrete Dynamics in Nature and Society

On this page

Abstract Introduction Data Availability Conflicts of Interest References Copyright Related Articles

Special Issue

Fuzzy Graph Theory and Influential Nodes and Links in Complex Networks

View this Special Issue

Research Article | Open Access

Volume 2022 | Article ID 5973433 | https://doi.org/10.1155/2022/5973433

Modified Floyd–Warshall’s Algorithm for Maximum Connectivity in Wireless Sensor Networks under Uncertainty

Laxminarayan Sahoo,¹Supriyan Sen,¹Kalishankar Tiwary,²Sovan Samanta,³and Tapan Senapati⁴

Academic Editor: Giulio E. Cantarella

Received19 Jan 2022

Revised03 Feb 2022

Accepted16 Feb 2022

Published15 Apr 2022

Abstract

The main objective of this paper is to find the duration of maximum time connectivity of sensor nodes under uncertainty utilizing the prespecified voltage/power of each sensor node. Wireless sensor networks (WSNs) are composed of nodes that transmit data between each other over routing. A variety of routing protocols and algorithms exist, each related to a particular set of conditions. There are a variety of routing algorithms available, some of which can be used in WSNs for routing. The goal of the fastest distance routing algorithms in a WSN is to use the least amount of energy possible. In a WSN, Dijkstra’s algorithm is typically used for shortest path routing. The Floyd–Warshall’s algorithm is used to compute the shortest paths between distinct nodes in a regular graph, but due to the absence of a communication mode, this algorithm is not ideal for routing in wireless networks. In this research work, we have considered a WSN to find out the maximum connectivity time utilizing optimum voltage. On the other hand, duration of connectivity and energy/voltage are two vital parameters that are difficult to manage. Because of limited resources and safety concerns, safety implementation is limited. Also, due to the irregular/hazardous environmental situations, the distance between sensor nodes and its voltage to link up the nodes are totally unpredictable. In this work, we employ triangular fuzzy numbers to express unpredictability. Then, utilizing defuzzification of fuzzy numbers, the associated WSN problem was transformed into a crisp one. The widely used signed distance approach has been applied for the defuzzification of fuzzy numbers in this case. To determine the best outcome and to illustrate the usefulness of the suggested technique, a numerical example has been solved using the modified Floyd–Warshall’s algorithm. Finally, concluding remarks on the proposed approach as well as future studies have been provided.

1. Introduction

A WSN is made up of many small devices known as nodes. All of those are sensitive enough to detect their environment, interpret, and transfer data to a designated pick-up location within a certain area. The nodes are connected directly with one another or with a base station (BS) located outside the area. The nodes’ battery, computational power, and bandwidth are all limited [1]. Energy minimization is the most important issue in WSN among all resource constraints. One of several main key objectives of WSN is to perform data transfer in an energy-efficient manner while striving to prolong the network’s life. The primary concern in these networks is power consumption. Instead of increasing channel capacity or decreasing the number of nodes, the central issue in these systems is prolonging network lifetime and resilience to chaotic phenomena [2, 3].

Sensor nodes are made up of four types of units, viz. sensing units, processing units, communication units, and power units. Figure 1 illustrates the fundamental design of a WSN node. Sensing units: sensors play a significant role in sensing devices by bridging the gap between the technological and physical domains. A sensor is a physical device that detects and responds to changes in the physical condition of an area of interest. Sensors perceive their surroundings, collect data, and convert it to fundamental data (current, voltage, and so on) before transmitting it to be analyzed further. It converts analog data (information gathered from the environment) to digital data, which is then delivered to the microcontroller for processing. Processing units: to accomplish the processing capabilities, the sensor node has a microcontroller with a processing unit, memory, converters, timer, and Universal Asynchronous Receive and Transmit (UART) interfaces. This unit is responsible for data acquisition, processing incoming and outgoing data, and establishing and modifying packet forwarding information based on communication performance. Communication unit: to enable connectivity, sensor nodes use radio frequencies or optical communication. Radio units in sensor nodes manage such an activity, using the electromagnetic spectrum to transmit information to their destinations. Generally, every sensor node transmits information directly to other nodes or sinks, or via multihop routing. Power units: the power units in the sensor node require energy for processing and data transmission. A node has a power unit that is responsible for supplying power to all of its units. The basic power consumption at the node is related to calculation and transmission, with transmission being the most power-intensive operation at the sensor node. Sensor nodes are typically battery-powered, but they can also harvest energy from renewable sources using solar cells.

The work of Wang et al. [4] can indeed be referred to for more detail regarding sensor nodes (SNs). A sensor network’s design, deployment, and implementation necessitate an understanding of signal processing, connectivity and interfaces, systems integration, data security, and distributed algorithms. Additionally, WSNs include sensors that continuously monitor and transfer data or information regarding environmental or physical aspects like temperatures, moisture, sounds, and pressures to a centralized controller over a large distance [5]. The output signal is distributed to the control tower via the shortest available path that used appropriate wireless communication routing protocols [6]. WSN is particularly effective in situations when access or continuous monitoring is hampered by geographical boundaries or other physical factors.

Generally, WSNs are positioned in challenging regions where battery restoration is problematic and personal monitoring is impossible. Numerous general concerns exist, including power conflict, allocated processing capacity, and diverse surroundings; electromagnetic affinities lead sensor nodes to malfunction intermittently [7]. Once all the installation is complete, all nodes keep monitoring the data, resulting in an exponential gain in battery performance. When a node detects an activity, it notifies another node or the central node via a confirmation. Furthermore, it demonstrates that equivalent knowledge is acquired from surrounding sensor nodes and from the base station that propagates the network’s flaw.

Also, due to node deployment, transmission media, connectivity, network topology, coverage, data aggregation, quality of service (QoS), and other factors, sensor nodes have an impact on routing operations. The network’s performance is then assessed using quantified characteristics known as performance metrics. This, however, varies depending upon the requirements and type of sensor node (SN). However, there are a number of metrics that can be used to measure the success of WSNs. Table 1 specifically explains a few of these metrics.

Data redundancy of data is a significant concern in WSNs; to minimize data recurrence and to build a strong network, various routing methods with distinct methodologies have previously been proposed in this study [8]. One of these efficient techniques is the cluster-based routing protocol, which divides sensor nodes into many bundles, each of which is referred to as a cluster. Choose a leading node in each cluster to serve as the Cluster Head. When any sensor node detects an action in the environment, it sends a notification to the relating cluster heads. The message is being sent to the cell tower by the cluster heads. As a result, choosing the right cluster head can reduce the amount of energy lost considerably. WSNs with a compact footprint can provide a low-cost, low-power communication network in a limited space. Additionally, wireless communication is growing in importance in today’s society, as it is used in a variety of crucial transactions. Duration of connectivity and energy are two major parameters that are difficult to manage. Because of limited resources and safety concerns, safety implementation is limited. Other media’s routing protocols cannot be used on a WSN. Instead, routing should be carried out in an energy-efficient manner. Such networks have a wide range of applications, including military, security, and home applications, among others [9–13]. The renowned works of Praveen Kumar et al. [14, 15] and Sah et al. [16] might be referenced for more information. Considerable influences of the different authors towards the WSNs problem are listed in Table 2.

1.1. Motivation

In WSNs, it has been generally assumed that the parameters relating to the communication system are precisely valued such as distance between sensor nodes, voltage, energy consumption. However, because of the anomalous climate factors, it is possible that all of the characteristics of the WSNs will not be rectified. Furthermore, due to the different geographical situations, the distance between sensor nodes and its voltage to link up the nodes are completely unexpected. Motivated from this fact, the issue can be viewed through the lens of uncertainty, with times and voltages treated as unspecific/ambiguous in nature. In such rare situations, fuzzy set theory comes in handy to deal with the situation. Zadeh [31] established the notion of fuzzy set in 1965, and it has proven to be effective in dealing with inaccuracy and ambiguity in real-life circumstances. Bellman and Zadeh [32] established the notion of stance with uncertainty in 1970. Here, we considered uncertain times/voltages using fuzzy numbers. As a result, the fuzzy WSN issue creates a basis for efficiently solving real-world WSN challenges with unclear parameters. To represent unpredictability, several techniques have been utilized in the literature, including interval, fuzzy, stochastic, and fuzzy-stochastic approaches. Several researchers have formulated and solved WSNs problems by considering fuzzy parameters. For details, Table 3 summarizes the authors’ considerable effects on WSN in a fuzzy environment.

In this work, we employ triangular fuzzy numbers to express unpredictability. Then, utilizing the defuzzification of fuzzy numbers, the associated WSN problem was transformed into a crisp one. The widely used signed distance approach [51] has been applied to defuzzify the fuzzy number in this case. In this paper, a modified Floyd–Warshall’s algorithm is proposed for finding the duration of maximum time connectivity of sensor nodes using prespecified voltage/power of each sensor node. By selecting the most trusted optimal path and connectivity, the proposed routing scheme extends network durability. To determine the best outcome and to demonstrate the applicability of the suggested method, a mathematical formulation has been addressed. Finally, the proposed approach’s concluding remarks and future research have been given.

1.2. Contributions

The following are the contributions of the proposed research work:(1)We developed and solved the WSNs issue in the presence of uncertainty(2)We used fuzzy sets/fuzzy numbers to convey uncertainty(3)To express all of the parameters, such as the distance between sensor nodes and the voltage/power required to connect the nodes, we used Triangular Fuzzy Numbers (TFNs)(4)The defuzzification of fuzzy parameters has been accomplished using the signed distance method(5)For determining the period of maximum time connectivity of sensor nodes, a modified Floyd–Warshall algorithm has been implemented(6)In a fuzzy context, a modified Floyd–Warshall algorithm has been described(7)-test has been carried out in order to discuss the numerical result(8)Concluding remarks have been presented, along with the future direction of the proposed research work

Most of the work carried out in this study can be summarized in this way:(i)In WSNs, the distance between sensor nodes and its voltage/power to link up the nodes are considered as TFNs(ii)Signed-distance method has been employed to defuzzification of fuzzy parameters(iii)A modified Floyd–Warshall’s algorithm is proposed for finding the duration of maximum time connectivity of sensor nodes using prespecified voltage/power of each sensor node

The remaining part of the paper is arranged as follows: Section 2 provides some basic mathematical foundations of fuzzy sets. Section 3 contains assumptions and notations. Section 4 addressed a modified Floyd–Warshall’s algorithm for the intention of solution methodology. Section 5 presented a problem description in a fuzzy environment. Section 6 presents a numerical example to illustrate the relationship between the result and the explanation. Section 7 possesses the conclusions of this study along with the future direction of the proposed research.

2. Basic Mathematical Foundations

This section outlines certain terminology and basic ideas linked to fuzzy sets, fuzzy numbers, and the signed distance method adopted for this research.

2.1. Definitions of the Term Fuzzy Set

A membership function that maps each element in to a real number in the interval forms a fuzzy set. The function represents the degree of membership of in the fuzzy set .

Definition 1. The -cut of a fuzzy set is a crisp subset of and is denoted by , where is the membership function of and .

Definition 2. A fuzzy set is called a normal fuzzy set if there exists at least one such that .

Definition 3. A fuzzy set is called convex if for every pair of , , the membership function of satisfies , where .

Definition 4. A fuzzy number is a fuzzy set that is both convex and normal.

Definition 5. The triangular fuzzy number (TFN) is a normal fuzzy number denoted as where and its membership function is defined by

2.2. Level Set of Triangular Fuzzy Number

Let be a triangular fuzzy number, then level set of the triangular fuzzy number is , where and , . Now, we can represent as . We can derive the signed distance [51] from to as .

Let be a fuzzy set on . We denote as the -cut off , . Now, for each , and uniquely exist and are integrable. In addition to that let be the family of all these fuzzy sets on . Consequently, we have the following definition.

Definition 6. Let , we defined the signed distance of measured from as .

Remark 1. Let be the triangular fuzzy number then and , respectively where . and exist and are integrable for . Therefore, and by the definition, we have .

2.3. Chi-Square Test Statistics

To perform the Chi-square test of independence, we need to have the following steps: Step 1: compute , where is the observed value and is the expected value in the i-th row and j-th column of the bivariate data Step 2: Step 3: calculate Step 4: calculate the value and set level of significance Step 5: stated null hypothesis and alternative hypothesis Step 6: if , then reject and accept otherwise do not have enough evidence to reject

3. Assumptions and Notations

We considered the following assumptions and notations while writing the entire paper:

3.1. Assumptions

(i)The Links distance between every pair of sensor nodes is always the same and triangular fuzzy number(ii)The sensor node can change its position after its deployment(iii)Every sensor node discharges its energy/power depending on its prefixed rate which is also a triangular fuzzy number

3.2. Notations

The distance/weight of a path from sensor node to The distance/weight of a path from sensor node j to i Energy/power capacity of i-th node (in percent) Energy/power capacity of j-th node (in percent) Rate of discharge of energy/power per unit time of i-th node Rate of discharge of energy/power per unit time of j-th node The time that a sensor node i can hold the connection to the sensor node j The time that a sensor node j can hold the connection to the sensor node i

4. Modified Floyd–Warshall's Algorithm for the Intention of Solution Methodology

4.1. Modified Floyd–Warshall’s Algorithm

Let be the maximum connectivity time that a sensor node can hold the connection from sensor node to sensor node for all intermediate sensor nodes are in the set . When , a path from vertices to with no intermediate vertices numbered higher than no intermediate at all. Such a time path has at most one edge and consequently

Now the recursive definition is as follows:

Now our aim is to find which gives the maximum time connectivity from vertices to where intermediate vertices are in the set

The pseudo code for a modified Floyd–Warshall’s algorithm is given as follows:

4.2. Modified Floyd–Warshall’s Algorithm in Fuzzy Environment

To solve our proposed WSN problem under a fuzzy environment we have implemented a modified Floyd–Warshall’s algorithm in a fuzzy environment. The pseudo code of this algorithm is as follows:

4.3. Time Complexity Analysis of Modified Floyd–Warshall’s Algorithm in Fuzzy Environment

Let be the number of vertices/nodes in a WSN. To find the current value of , we need to compute , which is an matrix already computed in the previous stage, Hence, the time complexity is . Now to find all pair maximum connectivity time for the entire WSN, we need to compute such matrix. Again, to compute we need computation each computation takes a constant amount of time. Hence, the total time complexity to compute the algorithm is .

5. Problem Description in Fuzzy Environment

Let us assume that a WSN communicated with the help of distinct link over distinct sensor node. Furthermore, assume that the distance between any two sensor nodes is from to and from to . We also assume that the distance and may be different because of node displacement. Here, source node i and sink sensor node j are discharging their charges at a rate of and over the link per unit distance (see Figure 2). Let be the time that a sensor node can hold the connection from sensor node to sensor node for all intermediate sensor nodes are in the set . Then the amount of time that the sensor node can hold the connection represented as can be calculated as for sensor nodes to and for sensor nodes to . Therefore, our aim is to find all pairs’ maximum link holding time so that the entire WSN system can be in an operative state. Therefore, the corresponding problem is defined recursively as follows:

6. Result and Discussion with a Numerical Example

To illustrate the proposed solution procedure, we have considered the following example:

Presume there is a WSN comprised of six sensor nodes (see Figure 3). We also presume that every node is located in a separate place. The network has twelve links, and the distance of each link is measured in meters which is also a triangular fuzzy number. Figure 1 depicts the existence of an acknowledgement link between each pair of sensor nodes. Besides this, the link length is the same for each pair of nodes, but the acknowledgement link length may vary from the sender link because all sensor nodes are deployed. All input data have been given in Table 4 and 5.

Using signed distance measure for sensor nodes to and the signed distance measure for sensor nodes to the weight matrix has been presented in Table 6. The value infinity in the matrix indicates that there is no self-connectivity between the same sensor nodes. Now, to solve the proposed WSN problem mentioned in example 6, we have solved the same using the weight matrix given in Table 5 and the modified Floyd–Warshall’s algorithm in a fuzzy environment which has been described in Section 4.2. The modified Floyd–Warshall algorithm has been coded in C++ on the Linux operating system, and the results are reported in Table 7.

According to the input in Table 7, there is really no time to connect the same node since there is no self-connectivity between the same sensor nodes and therefore do not discharge voltage/power. Again, the output matrix is not symmetric here due to the different voltage/power of the sensor nodes. For example, the connection time between sensor nodes 1 and 2 is 2.98 but 2 and 1 is 4.37 as node 1 discharges more voltage than sensor node 2. Also, the connection between (node to node ) and (node to node ), are independent (see Chi-square test). The direct and intermediate time connectivity between any two nodes has also been present graphically. The time duration between source node 1 to 2 (direct connection) and other node’s intermediate connection has been presented in Figure 4. Similarly, the time duration between source nodes 2, 3, 4, 5, and 6 and their corresponding, direct, and intermediate connections are depicted in Figures 5–8, respectively. Furthermore, it is to be noted that the time complexity for solving the problem is as we have computed all pair maximum connectivity for the entire WSN configurations under uncertain setup. However, it is stated explicitly that Sah et al. [16] have given a time-consuming technique (time complexity ) to produce datasets for sensor node placement and packet creation.

6.1. Chi-Square Test

We have stated the hypothesis as follows: : connection between (node to node ) and (node to node ), are independent : connection between (node to node ) and (node to node ), are not independent

Let the level of significant and is a random variable having distribution. From Table 6, we have calculated with 25 degrees of freedom (see Figure 9). As , then we do not have enough evidence to reject the null hypothesis . Therefore, the connection between ( to ) and ( to ), are independent.

7. Conclusions of this Study

For the first time, a modified version of the Floyd–Warshall’s Algorithm with imprecise parameters has been developed in this study to find the maximum connectivity time. This modified algorithm is a maximum time connectivity algorithm that can be applied to WSNs. The modified Floyd–Warshall algorithm has been written in C++ on the Linux platform. Because of the different voltage/power of the sensor nodes, the output matrix is not symmetric in this case. The maximum time connectivity among sensor nodes varies depending on the amount of voltage/power in each sensor node and the rate of discharge of voltage/power during the communication process. The proposed modified Floyd–Warshall algorithm has been discussed with a numerical example. The proposed algorithm discussed here is very simple and very easy to implement and to apply for solving other WSNs involving fuzzy parameters. The modified algorithm has been found to be useful for determining the maximum time duration linking in WSNs. It is also stated that the synchronization mode between sender and receiver nodes is extremely crucial for communicating in a WSN.

7.1. Future Scope of Research

The solution presented here is quite straightforward and simple to implement, and it can be stated that the overall process performed in this work will perform well enough to overcome numerous different WSN problems such as energy-efficient routing protocol for Wireless Sensor Networks, Sink Path Determination in Wireless Sensor Networks, Lifetime computation of WSN, dataset network-induced for wireless network networks, routing with deflections in WSNs.

Data Availability

No data were used to support this study.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References

A. Chamam and S. Pierre, “On the planning of wireless sensor networks: energy-efficient clustering under the joint routing and coverage constraint,” IEEE, vol. 8, no. 8, pp. 1077–1086, 2009.
View at: Publisher Site | Google Scholar
M. M. Shurman, M. F. Al-Mistarihi, A. N. Mohammad, K. A. Darabkh, and A. A. Ababnah, “Hierarchical Clustering Using Genetic Algorithm in Wireless Sensor Networks,” in Proceedings of the International Convention on Information and Communication Technology, Electronics and Microelectronics (MIPRO), pp. 20–24, Opatija, Croatia, May, 2013.
View at: Google Scholar
M. Dawood, N. Zaman, A. Khan, and M. Salih, “Designing of energy efficient routing protocol for wireless sensor network (WSN) using location aware (LA) algorithm,” Journal of Information & Communication Technology, vol. 3, no. 2, 2009.
View at: Google Scholar
Y. Wang, G. Attebury, and B. Ramamurthy, “A survey of security issues in wireless sensor networks,” IEEE communication surveys, vol. 8, no. 2, 2006.
View at: Publisher Site | Google Scholar
P. Khan, A. Ghosh, G. Konar, and N. Chakraborty, “Temperature and humidity monitoring through wireless sensor network using shortest path algorithm,” in Proceedings of the 2014 International Conference on Control, Instrumentation, Energy and Communication (CIEC), pp. 249–253, Calcutta, India, February, 2014.
View at: Publisher Site | Google Scholar
S. Farahani, ZigBee Wireless Networks and Transceivers, Elscvier, Amsterdam, Netherlands, pp. 207–224, 2008.
View at: Publisher Site
P. Nayak and A. Devulapalli, “A fuzzy logic-based clustering algorithm for WSN to extend the network lifetime,” IEEE Sensors Journal, vol. 16, no. 1, pp. 137–144, 2016.
View at: Publisher Site | Google Scholar
J. Kim, S. Park, Y. Han, and T. Chung, “CHEF: cluster head election mechanism using fuzzy logic in wireless sensor networks,” in Proceedings of the International Conference on Advance Communications Technology, pp. 654–659, Gangwon, Korea (South), February, 2008.
View at: Publisher Site | Google Scholar
S. Mahajan and J. Malhotra, “Energy efficient path determination in wireless sensor network using BFS approach,” Wireless Sensor Network, vol. 03, no. 11, pp. 351–356, 2011.
View at: Publisher Site | Google Scholar
A. Mainwaring, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson, “Wireless sensor networks for habitat monitoring,” Proceeding of ACM WSNA, vol. 2, 2002.
View at: Publisher Site | Google Scholar
I. Akyildiz, T. Melodia, and K. Chowdury, “Wireless multimedia sensor networks: a survey,” IEEE Wireless Communications, vol. 14, no. 6, pp. 32–39, 2007.
View at: Publisher Site | Google Scholar
M. Y. Aalsalem, W. Z. Khan, W. Gharibi, M. K. Khan, and Q. Arshad, “Wireless Sensor Networks in oil and gas industry: recent advances, taxonomy, requirements, and open challenges,” Journal of Network and Computer Applications, vol. 113, pp. 87–97, 2018.
View at: Publisher Site | Google Scholar
A. Flammini, P. Ferrari, D. Marioli, E. Sisinni, and A. Taroni, “Wired and wireless sensor networks for industrial applications,” Microelectronics Journal, vol. 40, no. 9, pp. 1322–1336, 2009.
View at: Publisher Site | Google Scholar
D. Praveen Kumar, T. Amgoth, and C. S. R. Annavarapu, “Machine learning algorithms for wireless sensor networks: a survey,” Information Fusion, vol. 49, pp. 1–25, 2019.
View at: Publisher Site | Google Scholar
D. Praveen Kumar, T. Amgoth, and C. S. Rao Annavarapu, “An extended ACO-based mobile sink path determination in wireless sensor networks,” Journal of Ambient Intelligence and Humanized Computing, vol. 12, pp. 8991–9006, 2021.
View at: Google Scholar
D. K. Sah, K. Cengiz, P. K. Donta, V. N. Inukollu, and T. Amgoth, “EDGF: empirical dataset generation framework for wireless sensor networks,” Computer Communications, vol. 180, pp. 48–56, 2021.
View at: Publisher Site | Google Scholar
E. W. Dijkstra, “A note on two problems in connexion with graphs,” Numerische Mathematik, vol. 1, no. 1, pp. 269–271, 1959.
View at: Publisher Site | Google Scholar
L. M. Feeney, “An energy-consumption model for performance analysis of routing protocols for mobile ad-hoc networks,” Mobile Networks and Applications, vol. 6, no. 3, pp. 239–249, 2001.
View at: Google Scholar
C. Intanagonwiwat, R. Govindan, D. Estin, J. Heidemann, and F. Silva, “Directed diffusion for WSN,” IEEE/ACM, vol. 11, no. 1, pp. 2–16, 2001.
View at: Google Scholar
J. Champ and C. Saad, “An energy-efficient geographic routing with location errors in wireless sensor networks,” in Proceedings of the International Symposium on Parallel Architectures, Algorithms, and Networks (I-SPAN), Sydney, NSW, Australia, May, 2008.
View at: Publisher Site | Google Scholar
S. A. Attarde, L. L. Ragha, and S. K. Dhamal, “An enhanced spanning tree topology for wireless sensor networks,” International Journal of Computer Application, vol. 1, no. 19, 2010.
View at: Publisher Site | Google Scholar
N. V. Doohan, D. K. Mishra, and S. Tokekar, “Shortest path routing protocol (SPRP) for highly data-centric wireless sensor networks,” in Proceedings of the 2011 Second Asian Himalayas International Conference on Internet (AH-ICI), pp. 1–4, Kathmundu, Nepal, November, 2011.
View at: Publisher Site | Google Scholar
B. Musznicki, M. Tomczak, and P. Zwierzykowski, “Dijkstra-based localized multicast routing in wireless sensor networks,” in Proceedings of the 2012 8th IEEE International Symposium on Communication Systems, Networks and Digital Signal Processing (CSNDSP), pp. 1–6, Poznan, Poland, July, 2012.
View at: Publisher Site | Google Scholar
D. Salvatore and S. H. Yang, “Routing algorithm of WSN under interference environment,” in Proceedings of the IET Conference on Wireless Sensor Systems (WSS 2012), London, UK, June, 2012.
View at: Publisher Site | Google Scholar
S. R. J. Ramson and D. J. Moni, “Applications of wireless sensor networks—a survey,” in Proceedings of the 2017 International Conference on Innovations in Electrical, Electronics, Instrumentation and Media Technology (ICEEIMT), pp. 325–329, Coimbatore, India, February, 2017.
View at: Google Scholar
X. Xu, N. Fallahi, and H. Yang, “Efficient CUF-based FEM analysis of thin-wall structures with Lagrange polynomial expansion,” Mechanics of Advanced Materials and Structures, pp. 1–22, 2020.
View at: Publisher Site | Google Scholar
C. J. Raman, J. Ali, N. Gobalakrishnan, and K. Pradeep, “An overview of the routing techniques employed in wireless sensor network,” in Proceedings of the 2020 International Conference on Communication and Signal Processing (ICCSP), pp. 332–336, Chennai, India, July, 2020.
View at: Publisher Site | Google Scholar
X. Yu, F. Li, T. Li, N. Wu, H. Wang, and H. Zhou, “Trust-based secure directed diffusion routing protocol in WSN,” Journal of Ambient Intelligence and Humanized Computing, vol. 13, pp. 1–13, 2020.
View at: Publisher Site | Google Scholar
I. Daanoune, B. Abdennaceur, and A. Ballouk, “A comprehensive survey on LEACH-based clustering routing protocols in Wireless Sensor Networks,” Ad Hoc Networks, vol. 114, no. 2, 2021.
View at: Publisher Site | Google Scholar
Z. Ullah, “A survey on hybrid, energy efficient and distributed (HEED) based energy efficient clustering protocols for wireless sensor networks,” Wireless Personal Communications, vol. 112, no. 4, pp. 2685–2713, 2020.
View at: Publisher Site | Google Scholar
L. A. Zadeh, “Information and Control,” Fuzzy sets, vol. 8, no. 3, pp. 338–353, 1965.
View at: Publisher Site | Google Scholar
R. E. Bellman and L. A. Zadeh, “Decision making in a fuzzy environment,” Management Science, vol. 17, no. 4, pp. 141–164, 1970.
View at: Publisher Site | Google Scholar
F. Torfi, R. Z. Farahani, and S. Rezapour, “Fuzzy AHP to determine the relative weights of evaluation criteria and fuzzy TOPSIS to rank the alternatives,” Applied Soft Computing, vol. 10, no. 2, pp. 520–528, 2010.
View at: Publisher Site | Google Scholar
H. Bagci and A. Yazici, “An energy aware fuzzy unequal clustering algorithm for wireless sensor networks,” in Proceedings of the 6th IEEE World Congress on Computational Intelligence (WCCI ’10), Barcelona, Spain, July 2010.
View at: Publisher Site | Google Scholar
H. Taheri, P. Neamatollahi, O. M. Younis, S. Naghibzadeh, and M. H. Yaghmaee, “An energy-aware distributed clustering protocol in wireless sensor networks using fuzzy logic,” Ad Hoc Networks, vol. 10, no. 7, pp. 1469–1481, 2012.
View at: Publisher Site | Google Scholar
P. Azad and V. Sharma, “Cluster head selection in wireless sensor networks under fuzzy environment,” ISRN Sensor Networks, vol. 2013, Article ID 909086, 8 pages, 2013.
View at: Publisher Site | Google Scholar
P. Purusothaman and S. Sivakumar, “Fuzzy RSSI based localization in wireless sensor networks,” International Journal of Engineering Research and Technology, vol. 2, no. 8, pp. 1323–1328, 2013.
View at: Google Scholar
H. Bagci and A. Yazici, “An energy aware fuzzy approach to unequal clustering in wireless sensor networks,” Applied Soft Computing, vol. 13, no. 4, pp. 1741–1749, 2013.
View at: Publisher Site | Google Scholar
K. Gotefode and K. Kolhe, “Energy efficiency in wireless sensor network using fuzzy rule and tree based routing protocol,” in Proceedings of the International Conference on Energy Systems and Applications (ICESA), pp. 712–717, Pune, India, November, 2015.
View at: Publisher Site | Google Scholar
M. Nagarajan, T. Dhanapalan, and S. Jayanthi, “WSN life time enhancement using fuzzy clustering and intrusion recognition with EAS,” IJISET-International Journal of Innovative Science, Engineering & Technology, vol. 2, no. 4, pp. 1058–1062, 2015.
View at: Google Scholar
D. V. Pushpalatha and P. Nayak, “A clustering algorithm for WSN to optimize the network lifetime using type-2 fuzzy logic model,” in Proceedings of the 2015 3rd International Conference on Artificial Intelligence, Modelling and Simulation (AIMS), pp. 53–58, Kota Kinabalu, Malaysia, December, 2015.
View at: Publisher Site | Google Scholar
P. Sethi and N. S. Dhillon, “Energy efficient Clustering for improving network life time in WSN using Fuzzy based technique: a Review,” International Journal on Emerging Technologies, vol. 7, no. 1, pp. 80–83, 2016.
View at: Google Scholar
R. S. Uppal and K. Kaur, “Fuzzy link cost measure for energy efficient routing in WSN,” International Journal of Engineering Sciences, vol. 17, pp. 486–493, 2016.
View at: Google Scholar
B. Balakrishnan and S. Balachandran, “FLECH: fuzzy logic based energy efficient clustering hierarchy for nonuniform wireless sensor networks,” Wireless Communications and Mobile Computing, vol. 2017, Article ID 1214720, 13 pages, 2017.
View at: Publisher Site | Google Scholar
H. El Alami and A. Najid, “Fuzzy logic based clustering algorithm for wireless sensor networks,” International Journal of Fuzzy System Applications, vol. 6, no. 4, pp. 63–82, 2017.
View at: Publisher Site | Google Scholar
A. Shokrollahi and B. Mazloom-Nezhad Maybodi, “An energy-efficient clustering algorithm using fuzzy C-means and genetic fuzzy system for wireless sensor network,” Journal of Circuits, Systems, and Computers, vol. 26, no. 1, Article ID 1750004, 2017.
View at: Google Scholar
M. Mirzaie and S. M. Mazinani, “MCFL: an energy efficient multi-clustering algorithm using fuzzy logic in wireless sensor network,” Wireless Networks, vol. 24, no. 6, pp. 2251–2266, 2018.
View at: Publisher Site | Google Scholar
Q. Wang, S. Guo, J. Hu, and Y. Yang, “Spectral partitioning and fuzzy C-means based clustering algorithm for big data wireless sensor networks,” EURASIP Journal on Wireless Communications and Networking, vol. 2018, no. 1, pp. 54–64, 2018.
View at: Publisher Site | Google Scholar
M. Ali and F. Gared, “Energy optimization of wireless sensor network using neuro-fuzzy algorithms,” Ethiopian Journal of Science and Technology, vol. 12, no. 2, pp. 167–183, 2019.
View at: Google Scholar
S. Lata, S. Mehfuz, S. Urooj, and F. Alrowais, “Fuzzy clustering algorithm for enhancing reliability and network lifetime of wireless sensor networks,” IEEE Access, vol. 8, Article ID 66013, 2020.
View at: Publisher Site | Google Scholar
J.-S. Yao and K. Wu, “Ranking fuzzy numbers based on decomposition principle and signed distance,” Fuzzy Sets and Systems, vol. 116, no. 2, pp. 275–288, 2000.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2022 Laxminarayan Sahoo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

1576

Downloads

631

Citations