Interval type-2 fuzzy logic based transmission power allocation strategy for lifetime maximization of WSNs

Engineering Applications of Artificial Intelligence 87 (2020) 103269

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Engineering Applications of Artificial Intelligence journal homepage: www.elsevier.com/locate/engappai

Interval type-2 fuzzy logic based transmission power allocation strategy for lifetime maximization of WSNs✩ Wei Peng a , Chengdong Li a ,∗, Guiqing Zhang a , Jianqiang Yi b a b

School of Information and Electrical Engineering, Shandong Jianzhu University, Jinan 250101, China Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China

ARTICLE

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Keywords: Transmission power allocation Type-2 fuzzy Wireless sensor network Network lifetime

ABSTRACT In wireless sensor networks (WSNs), it is critical to design an advisable transmission power allocation strategy for balancing the latency and energy efficiency, and prolonging the lifetime of WSNs. However, some measured key parameters, e.g., data latency, energy consumption and communication radius, are with high levels of uncertainties, which deteriorate the transmission power allocation performance greatly. How to employ an advanced method to deal with the uncertainties and to further improve the network performance is a pressing issue. Type-2 fuzzy logic system (T2FLS) as a powerful tool for handling the uncertainties provides an effective way for designing such advisable allocation strategies. Therefore, this paper adopts the interval T2FLS (IT2FLS) to design the transmission power allocation (TPA) strategy for lifetime maximization of WSNs. Firstly, the problem of lifetime enhancement in WSNs is formulated in detail, and then it is converted into a TPA problem. Secondly, the IT2FLS method is applied to the transmission power decision making process for maximizing the lifetime of WSNs. In the designed IT2FLS-based TPA strategy, expected latency, residual energy and distance between nodes are taken as input variables, while the transmission power and communication radius are considered as the output variables. Finally, both simulation and experiment results are given. The results indicate that the proposed TPA strategy using IT2FLS can effectively realize the tradeoff between the latency and energy efficiency, and can prolong the network lifetime of the WSNs. Moreover, compared with other TPA strategies, including the minimum total energy algorithm, the flow augmentation algorithm and the type1 fuzzy logic method, the proposed IT2FLS-based TPA strategy has obvious advantages in terms of network lifetime, average latency and energy consumption.

1. Introduction Due to the easy and flexible deployment, wireless sensor networks (WSNs) are widely used in many applications, especially in Internet of Things (IoT), wireless body area networks (WBANs) and vehicle ad hoc networks (VANET) etc (Yang et al., 2018). Limited calculation capacity and energy resource are still two crucial constraints factors for improving the network performance. Hence, it is of great significance to provide an advanced method for realizing the tradeoff between energy efficiency and latency, and for prolonging the network lifetime in WSNs. Furthermore, both energy consumption and latency are two key parameters with high level of uncertainties, and are closely related with the transmission power of nodes. Hence, in order to balance the energy consumption and the latency while enhancing the network lifetime, the intelligent transmission power allocation (TPA) algorithm should effectively cope with the uncertainties of parameters.

In recent years, many researchers paid attentions to the TPA issues for saving energy, reducing latency and enhancing lifetime of WSNs. Soleymani et al. (2018) formulated the transmission power as a function of the packet success rate using IEEE 802.15.4 standard, and then proposed an approximate value iteration algorithm for obtaining the near-optimal transmission power policy. Ren et al. (2018) converted the TPA issues into a power estimation problem, then used an infinite horizon average cost function to estimate it. Li et al. (2017b) further optimized the estimation accuracy by considering the power constraints which were caused by the energy harvesting. Sodhro et al. (2018) presented the energy efficiency comparison between TPA and data rate control for wireless body sensor networks in two different cases. Di Franco et al. (2014) proposed a TPA scheme used for IEEE 802.15.6 WBANs operating in beacon mode with super frame boundaries. All of the above mentioned TPA methods supposed that the transmission power was stable and could be crisply measured or estimated. In fact,

✩ No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. For full disclosure statements refer to https://doi.org/10.1016/j.engappai.2019.103269. ∗ Corresponding author. E-mail address: [email protected] (C. Li).

https://doi.org/10.1016/j.engappai.2019.103269 Received 26 January 2019; Received in revised form 19 August 2019; Accepted 30 September 2019 Available online xxxx 0952-1976/© 2019 Elsevier Ltd. All rights reserved.

W. Peng, C. Li, G. Zhang et al.

Engineering Applications of Artificial Intelligence 87 (2020) 103269

problem. Furthermore, in Kayacan et al. (2018), Kayacan et al. presented the type-2 fuzzy elliptic MFs for modeling uncertainty. In Wang et al. (2018), a centroid-based type-2 fuzzy-probabilistic programming approach was proposed for the conjunctive water management under multiple uncertainties. In Muhuri et al. (2018), Muhuri et al. proposed a novel formulation of multi-objective reliability redundancy allocation problem, termed as interval type-2 fuzzy multi-objective optimization problem (IT2FMORRAP), and then used the non-dominated sorting genetic algorithm II to solve the proposed IT2FMORRAP. For a class of the non-linear continuous-time systems with time-varying delay and parameter uncertainties, Du et al. (2019a,b) designed the interval type2 fuzzy sampled-data controller to realize the asymptotical stabilization of the closed-loop systems. In Rathi and Prabha (2019), Rathi et al. designed the interval type-2 fuzzy logic based controller to deal with the high uncertainties associated with the electric power system. At present, several researchers have taken the advantages of IT2FLS to WSNs for handling the existing uncertainties. Shu et al. (2008) creatively presented an IT2FLS based approach to analyze the lifetime of WSNs. Baccar and Bouallegue (2016) applied the IT2FLS to solve the indoor location problem for WSNs. Peng et al. (2018b,a) applied the IT2FLS to realize the energy-efficiency of multi-radio resource management in multi-radio WSNs. Arjunan and Sujatha (2017) presented a novel IT2FLS based method to extend the lifetime of the energy constrained WSNs. Xie et al. (2015) proposed a clustering routing protocol for WSNs based on the T2FLS and ant colony optimization algorithm. Nevertheless, to the authors’ knowledge, there are few attempts to investigate the implement of IT2FLS for designing the TPA strategy in WSNs. In this paper, IT2FLS will be adopted to design the TPA strategy to optimize the transmission power and to enhance the network lifetime. The main contributions and novelties of this paper are summarized as follows:

the measured parameters, including the transmission power, the energy consumption, the latency and the communication distance, are timevariable and are with high levels of uncertainties, because they can be easily affected by the deployment environments and the obstacles. Although all of those works provided many effective methods for improving the performance of WSNs, none of them considered the high levels of uncertainties existed in WSNs. Hence, how to apply the advanced methods to design an intelligent TPA strategy for effectively handling such high levels of uncertainties and for improving the performance of WSNs is a great challenge. Fuzzy logic systems (FLSs) have found lots of applications in different areas (Li et al., 2017a, 2018a, 2020). Since the 1990s, it has been proven that the type-2 fuzzy logic system (T2FLS) could efficiently deal with high levels of uncertainties better than its counterpart — the type-1 fuzzy logic system (T1FLS) and than other traditional non-fuzzy methods, because it has the additional degree of freedom provided by the footprint of uncertainty (FOU) of type-2 fuzzy sets (T2FSs) (Mendel, 2001; Castillo and Melin, 2008; Mendel et al., 2016). T2FSs and T2FLS include the general type-2 case and the interval type-2 case. In recent years, general type-2 fuzzy sets (GT2FSs) and generalized type-2 fuzzy logic systems (GT2FLSs) have attracted more and more attentions. In Mendel (2013), the Karnik–Mendel algorithm was given to achieve the type-reduction of GT2FSs. In Ontiveros et al. (2018), Ontiveros et al. proposed the Newton-Cotes quadrature for the 𝛼-planes integration to reduce the computational cost of GT2FSs. GT2FSs and GT2FLSs have found applications in several research domains. For example, in Shukla and Muhuri (2019b), Shukla et al. proposed a more efficient decision making method called the ‘‘generalized type-2 fuzzy decision making (GT2FDM)’’, which utilized GT2FSs to model the fuzzy goals and fuzzy constraints in a problem. Then they applied the GT2FDM method to solve the problem of the convenient travel time selection using a real-time traffic data set. In Melin et al. (2019), Melin et al. presented a GT2FLS model based on the shadowed type-2 fuzzy sets and then applied this approach to solve the control problems. And, in Castillo and Amador-Angulo (2018), Castillo et al. proposed a GT2FLS approach for the dynamic parameter adaptation in meta-heuristics and for optimal fuzzy controller design. However, due to the heavy computational burden of the GT2FSs and GT2FLSs, nowadays, the interval T2FSs (IT2FSs) and interval T2FLSs (IT2FLS) draw most of attentions (Mendel and Liu, 2013; El-Nagar and El-Bardini, 2014; Liang and Mendel, 2000; Li et al., 2014). The IT2FLSs have been wildly applied in various real-world fields, such as the modeling, forecasting, classification, decision making, and the control applications (Juang and Chen, 2014; Hamza et al., 2016; Baklouti et al., 2018; Jana et al., 2019; Shukla and Muhuri, 2019; Olivas et al., 2019; Wang et al., 2019; Urena et al., 2019; Muhuri and Shukla, 2017; Kayacan et al., 2018; Wang et al., 2018; Muhuri et al., 2018; Du et al., 2019a,b; Rathi and Prabha, 2019). In Juang and Chen (2014), an interval type-2 neural fuzzy chip with on-chip incremental learning ability was given for the time-varying data sequence prediction and system control. In Hamza et al. (2016), the authors utilized the meta-heuristic algorithms to optimize IT2FLSs for prediction, classification, clustering and pattern recognition applications. In Baklouti et al. (2018), a beta basis function interval type-2 fuzzy neural network was proposed for time series applications. In Jana et al. (2019), the interval type-2 fuzzy logic approach was applied for the assessment of the occupational safety risks performance in industries. In Shukla and Muhuri (2019), the IT2FSs were applied to cope with the uncertainty of gene expression in big data sets, and then the IT2FSs based uncertainty model was obtained. In Olivas et al. (2019), Olivas et al. proposed a method for dynamically adjusting parameters in gravitational search algorithm (GSA) based on the IT2FLS. Wang et al. (2019) and Urena et al. (2019) applied the interval type-2 fuzzy method in the decision making area. In Muhuri and Shukla (2017), Muhuri et al. proposed the generation technique for interval type-2 semi-elliptic membership function (MF) and applied the novel semi-elliptic fuzzy numbers to solve the real-time task scheduling

• The relationships among the network lifetime, the transmission power, the communication distance and the energy consumption in multi-hops WSNs are analyzed firstly. Then three hard related parameters to the network lifetime e.g., communication latency, residual energy, distance between nodes, are respectively formulated. Based on the above analysis, the estimation models of the three key parameters are built in detail. Finally, the lifetime enhancement in WSNs is converted into a TPA problem. • The IT2FLS is applied to deal with the uncertainties existed in parameter estimation process, including the communication latency estimation, the residual energy computation, and the distance estimation, and to enhance the network lifetime in multi-hops WSNs. Then the IT2FLS-based TPA strategy is designed in detail by considering the data latency, the energy consumption and the distance as input variables and taking the transmission power and the communication radius as output variables. The key parts of IT2FLS, such as MFs for the inputs and output variables, the fuzzy rules and fuzzy inference, are designed according to the knowledge of this application. • In order to verify the effectiveness and the advantages of the proposed IT2FLS-based TPA strategy, detailed simulations and experiments are deployed. In simulations, the performance of proposed IT2FLS-based TPA strategy is compared with other TPA strategies in terms of network lifetime, average latency and energy consumption under different traffic rates. In the real-world experiments, the proposed IT2FLS-based TPA strategy is compared with the method without the TPA strategy. Simulation and experimental results reveal that the designed IT2FLS-based TPA strategy performs best in terms of the network lifetime, the average latency and the energy consumption. The rest of this paper is organized as follows. Section 2 will briefly introduce the IT2FS and IT2FLS. Section 3 will formulate the TPA problem in multi-hops WSNs and will present the IT2FLS-based TPA strategy in detail. Section 4 will evaluate the performance of the proposed TPA algorithm. Conclusions will be made in Section 5. 2

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

Fig. 1. The Triangular T1FS (a) and IT2FS (b).

Fig. 2. The inference structure of the IT2FLS.

2. Type-2 fuzzy logic system

The triangular T1FS and the trapezoidal IT2FS are taken as examples and shown in Fig. 1(a) and (b), respectively. The MF of the triangular T1FS can be expressed as

2.1. Type-1 and type-2 fuzzy sets

⎧ ⎪ 𝜇𝐴 (𝑥) = ⎨ ⎪ ⎩

A crisp set can be converted into fuzzy set (FS) by defining the membership grades in the real interval [0, 1] for every element of the set. The major difference between type-1 FS (T1FS) and type-2 FS (T2FS) is that the membership grades are crisp values for the former while the membership grades are fuzzy ones for the later (Mendel, 2001; Castillo and Melin, 2008; Mendel et al., 2016). A T1FS, denoted as 𝐴 in universes of discourse 𝑋, is commonly characterized as (Mendel, 2001; Castillo and Melin, 2008; Mendel et al., 2016) 𝐴=

∫𝑥∈𝑋

⎧ ⎪ ⎪ 𝜇 𝐴̃ (𝑥) = ⎨ ⎪ ⎪ ⎩

1

, 𝑢2 < 𝑥 ≤ 𝑢3 𝑢 3 < 𝑥 ≤ 𝑢4

(10)

𝑢4 −𝑥 , 𝑢4 −𝑢3

(11)

The IT2FSs are wildly employed in the rule-based fuzzy logic systems, because it can handle high levels of uncertainties that can be hardly modeled by T1FSs. The type-2 fuzzy rule-based logic systems have found applications in different areas, including the modeling, identification, prediction, control applications. Such applications have verified that IT2FLS can produce more complex input–output mappings and better results compared with its counterpart — the T1FLS. The basic inference structure of IT2FLS is similar to that of T1FLS. As shown in Fig. 2, the inference structure of IT2FLS includes the fuzzifier, the fuzzy rule base, the fuzzy inference engine, and the output processing block (Mendel and Liu, 2013; Liang and Mendel, 2000). The output processing part consists of one type-reducer and one defuzzifier. In this study, we adopt the following type-2 fuzzy rule base, which is the most widely-used one in modeling and control applications. ̃ 𝑘 , and 𝑥2 is 𝑋 ̃ 𝑘 , ⋯, and 𝑥𝑝 is 𝑋 ̃ 𝑘 , then 𝑦 is 𝑌̃ 𝑘 , Rule 𝑘: if 𝑥1 is 𝑋 𝑝 1 2 ̃𝑘 s where 𝑘 = 1, 2, … , 𝑀, 𝑝 is the number of the input variables, 𝑋 𝑖 𝑘 ̃ are the antecedent IT2FSs for the input variables, and 𝑌 s are the consequent IT2FSs. In this study, we firstly compute the centroid of 𝑌̃ 𝑘 through the type-reducer, and then represent the consequent IT2FS 𝑌̃ 𝑘 by its centroid [𝑦𝑘𝑙 , 𝑦𝑘𝑟 ]. Then, the type-2 fuzzy rule base can be transformed to be the following form ̃ 𝑘 , and 𝑥2 is 𝑋 ̃ 𝑘 , ⋯, and 𝑥𝑝 is 𝑋 ̃ 𝑘 , then 𝑦 is [𝑦𝑘 , 𝑦𝑘 ]. Rule 𝑘: if 𝑥1 is 𝑋 𝑝 𝑟 𝑙 1 2 ( )𝑇 Once a crisp input 𝑥 = 𝑥1 , 𝑥2 , … , 𝑥𝑝 is applied to the IT2FLS, through the singleton fuzzifier and the type-2 fuzzy inference, the interval firing strength of Rule 𝑘 can be computed by the product operation as ] [ 𝑘 𝑥) 𝑥) = 𝑓 𝑘 (𝑥 𝑥) , 𝑓 (𝑥 (12) 𝐹 𝑘 (𝑥

(3)

where 𝜇𝐴̃(𝑥) is the fuzzy membership grade of the element 𝑥, and 𝐽𝑥 is the primary membership grade of 𝑥 which is the domain of the secondary MF. Such a bounded region is called the footprint of uncertainty (FOU) (Mendel, 2001; Castillo and Melin, 2008; Mendel et al., 2016), i.e. ( ) { } 𝐹 𝑂𝑈 𝐴̃ = (𝑥, 𝑢) ∈ 𝑋 × [0, 1] |𝜇𝐴̃ (𝑥, 𝑢) > 0 (4) An upper MF and a lower MF are two type-1 MFs that are bounds ̃ The upper MF and the lower MF are associated for the FOU of a T2FS 𝐴. ( ) ( ) with the upper bound of 𝐹 𝑂𝑈 𝐴̃ and the lower bound of 𝐹 𝑂𝑈 𝐴̃ , respectively. Then, they are denoted as 𝜇 𝐴̃ (𝑥) and 𝜇 ̃ (𝑥), for ∀𝑥 ∈ 𝑋, 𝐴 i.e. ( ) 𝜇 𝐴̃ (𝑥) = 𝐹 𝑂𝑈 𝐴̃ (5) ( ) 𝜇 ̃ (𝑥) = 𝐹 𝑂𝑈 𝐴̃ (6) 𝐴

𝐴

, 𝑥 ≤ 𝑢1 𝑜𝑟 𝑥 > 𝑢4 𝑢 1 < 𝑥 ≤ 𝑢2

2.2. Interval type-2 fuzzy logic system

and

When 𝐽𝑥 is defined as follows (Mendel et al., 2016): { [ ]} 𝐽𝑥 = (𝑥, 𝑢) ∶ 𝑢 ∈ 𝜇 ̃ (𝑥) , 𝜇 𝐴̃ (𝑥)

0

𝑥−𝑢1 , 𝑢2 −𝑢1

⎧ 0 , 𝑥 ≤ 𝑙1 𝑜𝑟 𝑥 > 𝑙3 ⎪ 𝑥−𝑙1 𝜇 ̃ (𝑥) = ⎨ ℎ 𝑙2 −𝑙1 , 𝑙1 < 𝑥 ≤ 𝑙2 𝐴 ⎪ ℎ 𝑙3 −𝑥 , 𝑙 < 𝑥 ≤ 𝑙 3 ⎩ 𝑙3 −𝑙2 2

where 𝜇𝐴 (𝑥) is the crisp membership grade of the element 𝑥, ∫ denotes the union over all 𝑥 ∈ 𝑋. ̃ can be expressed as (Mendel, 2001; Castillo A T2FS, denoted as 𝐴, and Melin, 2008; Mendel et al., 2016) {( ) } 𝐴̃ = (𝑥, 𝑢) , 𝜇𝐴̃ (𝑥, 𝑢) |𝑥 ∈ 𝑋, 𝑢 ∈ [0, 1] (2) { } 𝐽𝑥 = (𝑥, 𝑢) |𝑢 ∈ [0, 1] , 𝜇𝐴̃ (𝑥, 𝑢) > 0

(9)

The upper MF 𝜇 𝐴̃ (𝑥) and lower MF 𝜇 ̃ (𝑥) of the trapezoidal IT2FS 𝐴 can be depicted, respectively, as

(1)

𝜇𝐴 (𝑥)∕𝑥

0 , 𝑥 ≤ 𝑎 𝑜𝑟 𝑥 > 𝑑 𝑎<𝑥≤𝑏 𝑏<𝑥≤𝑑

𝑥−𝑎 , 𝑏−𝑎 𝑑−𝑥 , 𝑑−𝑏

(7)

the general T2FS simplifies to be the interval T2FS (IT2FS) (also called closed IT2FS). Therefore, the IT2FS 𝐴̃ can be completely characterized by the corresponding upper MF 𝜇 𝐴̃ (𝑥) and lower MF 𝜇 ̃ (𝑥), i.e. 𝐴 [ ] 𝜇𝐴̃ (𝑥) = 𝜇 ̃ (𝑥) , 𝜇 𝐴̃ (𝑥) (8)

where 𝑥) = 𝑓 𝑘 (𝑥

𝐴

𝑝 ∏ 𝑖=1

3

( ) 𝜇 ̃ 𝑘 𝑥𝑖 𝑋𝑖

(13)

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

red solid line), the data must be forwarded four times, then received by the base station. On the contrary, if they adopt the higher transmission power, the data is only forwarded twice (marked by orange dotted line). Thus the latency of the later case is lower than the previous. However, the energy consumption in both cases is opposite to the latency. Hence, one of the most important issue is how to allocate the transmission power to achieve the balance between energy consumption and data latency, then to enhance the network lifetime. The transmission power, energy consumption and data latency are dynamic, time-varying and uncertain, since the measurements and/or estimations are extremely easy impacted by noise. Furthermore, since the latency, energy consumption, distance and transmission power are run in the nonlinear manner, the relationships between them are difficult to establish. In such situation, the IT2FLS assists to build the relationship between the inputs and outputs in a well-organized manner, so that the dynamic and uncertainties of the input variables can be well tackled. Therefore, taking the advantages of the IT2FLS to design the TPA strategy will efficiently handle the uncertainties of energy consumption and latency, and will prolong the network lifetime. This idea motivates us to research the IT2FLS-based TPA strategy for lifetime maximization of WSNs.

Fig. 3. An instance of the TPA in multi-hops WSNs.

𝑘

𝑥) = 𝑓 (𝑥

𝑝 ∏ 𝑖=1

( ) 𝜇 𝑋̃𝑘 𝑥𝑖

(14)

𝑖

The output processing block is used to realize the type-reduction, and then defuzzify the type-reduced set to produce a crisp output. There exist several different type-reduction and defuzzification methods. The IT2FLS with different type-reduction and defuzzification strategies have different input–output mappings. In this study, the widely-used centerof-sets (COS) method (Liang and Mendel, 2000) is adopted. By the COS method, the crisp output of the IT2FLS can be calculated as ) 1( 𝑥) = 𝑥) + 𝑦𝑟 (𝑥 𝑥) 𝑦 (𝑥 𝑦 (𝑥 (15) 2 𝑙 𝑥) and 𝑦𝑟 (𝑥 𝑥) are the left and right end points of the typewhere 𝑦𝑙 (𝑥 reduced interval set and can be respectively computed as { ∑𝑀 } 𝑘 𝑘| [ 𝑘 𝑘] 𝑘=1 𝑓 𝜔 || 𝑘 𝑘 𝑘 𝑥) , 𝜔 ∈ 𝑦𝑙 , 𝑦𝑟 𝑥) = min 𝑦𝑙 (𝑥 ∑𝑀 𝑘 | 𝑓 ∈ 𝐹 (𝑥 | 𝑘=1 𝑓 | [ ) 𝑘 ] 𝑘 ( ∑𝑀 𝑘 𝑘 𝑥 𝑘 𝑥) 𝑦𝑙 𝑓 (𝑥 𝑘=1 𝛿 𝑓 (𝑥 ) + 1 − 𝛿 = (16) [ ( ) 𝑘 ] ∑𝑀 𝑘 𝑘 𝑥 𝑘 𝑥) 𝑓 (𝑥 𝑘=1 𝛿 𝑓 (𝑥 ) + 1 − 𝛿 } { ∑𝑀 𝑘 𝑘| [ 𝑘 𝑘] 𝑘=1 𝑓 𝜔 || 𝑘 𝑘 𝑥 𝑘 𝑥) = max 𝑓 ∈ 𝐹 , 𝜔 ∈ 𝑦 , 𝑦 𝑦𝑟 (𝑥 (𝑥 ) ∑𝑀 𝑘 | 𝑟 𝑙 | 𝑘=1 𝑓 | [ ( ) ] 𝑘 𝑘 𝑘 𝑘 ∑𝑀 𝑥 𝑥) 𝑦𝑘𝑟 𝑓 (𝑥 𝑘=1 𝛿 𝑓 (𝑥 ) + 1 − 𝛿 = (17) ( ) 𝑘 ] 𝑘 ∑𝑀 [ 𝑘 𝑘 𝑥) 𝑥 𝑓 (𝑥 𝑘=1 𝛿 𝑓 (𝑥 ) + 1 − 𝛿

3.2. Models of the IT2FLS inputs In this subsection, the models of three important input variables of the proposed IT2FLS-based TPA strategy are presented respectively. 3.2.1. Latency estimation In multi-hops WSNs, data is transmitted to the base station through multi-nodes delivery. Thus the total latency of a packet can be estimated as follows 𝐿𝑡𝑜𝑡𝑎𝑙 =

𝑛 ∑ ( ) 𝐷𝑠𝑖𝑧𝑒 ∗ 8 ∗ 𝑡𝑟𝑎𝑑𝑖𝑜 𝑖

(18)

𝑖=1

where 𝐿𝑡𝑜𝑡𝑎𝑙 is the total latency, 𝐷𝑠𝑖𝑧𝑒 is the packet size in byte, 𝑡𝑟𝑎𝑑𝑖𝑜 = 1∕𝑅𝑏𝑖𝑡 is the required time to send 1 bit and 𝑅 𝑏𝑖𝑡 is the baud rate, 𝑛 is the total number of hops by which the data transmission passed. 3.2.2. Residual energy For any node worked under periodical data transmission and idle listening mode, the total energy consumption can be expressed as 𝐸𝑡𝑜𝑡𝑎𝑙 = 𝐸𝑡𝑟𝑎𝑛𝑠 + 𝐸𝑖𝑑𝑙𝑒 =

𝑞=𝑘+ℎ ∑

(𝑃𝑡𝑟𝑎𝑛𝑠 − 𝑝𝑖𝑑𝑙𝑒 ) 𝑡𝑞 + 𝑝𝑖𝑑𝑙𝑒 𝑇

(19)

𝑞=𝑘

where 𝐸𝑡𝑟𝑎𝑛𝑠 is the total transmission energy dissipation for sending ℎ packets, 𝑃𝑡𝑟𝑎𝑛𝑠 is the transmission power, 𝑡𝑞 is the required time for transmission the 𝑞th packet, 𝐸𝑖𝑑𝑙𝑒 is the idle listening energy consumption, 𝑝𝑖𝑑𝑙𝑒 is the idle listening power and 𝑇 is the period. Hence, the residual energy can be calculated by

𝑘

in which 𝛿 𝑘 and 𝛿 can be determined in {0, 1} by the popular Karnik– Mendel algorithm (Mendel, 2001; Mendel and Liu, 2013). Both IT2FS and IT2FLS are briefly introduced in this section. Below, they will be used to design the TPA strategy for prolonging the lifetime of multi-hops WSNs.

𝐸𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 = 𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 −

𝑚 ∑

𝐸𝑡𝑜𝑡𝑎𝑙 (𝑗)

(20)

𝑗=1

3. Problem formulation and design of the IT2FLS-based TPA strategy

where 𝐸𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 is the residual energy, 𝐸𝑖𝑛𝑖𝑡𝑖𝑎𝑙 is the initial energy of node and 𝐸𝑡𝑜𝑡𝑎𝑙 (𝑗) is the total energy consumption of the 𝑗th (𝑗 = 1, 2, … , 𝑚) data transmission and idle listening round for a node, and 𝑚 is the number of the total data transmission rounds of a node before its energy is exhausted.

3.1. Problem formulation and motivation As we all know, the energy consumption of wireless sensor node is mainly concentrated in the following processes, such as idle listening, data transmission and reception. Hence, in multi-hops WSNs, the higher the transmission power is, the higher the energy consumption is, the longer the communication distance is, the less the number of the hops is, and the lower the latency is, and vice versa. This fact is shown in Fig. 3. It is a NP-hard problem on the balance between the latency and the energy consumption. As shown in Fig. 3, when the nodes (source node and relay nodes) use the lower transmission power (marked by

3.2.3. Distance estimation In this paper, the received signal strength indicator (RSSI) which closely relates to the transmission power is used to estimate the distance between nodes. The radio propagation path loss can be calculated as follows (Luo et al., 2014) ( ) 𝑃 𝐿 (𝑑) = 𝑃 𝐿 𝑑0 + 10𝛽 lg (𝑑∕𝑑0 ) + 𝑋𝑟 (21) 4

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Engineering Applications of Artificial Intelligence 87 (2020) 103269 Table 1 Fuzzy rules for the proposed TPA strategy. Rule no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Fig. 4. The diagram of the proposed IT2FLS-based TPA strategy.

( ) where 𝑃 𝐿 (𝑑) is the signal path loss with the distance 𝑑 in dB, 𝑃 𝐿 𝑑0 is the unit path loss (𝑑0 = 1 𝑚) in dB, 𝛽 is the channel attenuation factor and can vary from 2 to 4, and 𝑋𝑟 is the Gaussian noise. Subsequently, the RSSI can be obtained by 𝑃𝑟𝑒𝑐𝑣 (𝑑) = 𝑃𝑡𝑟𝑎𝑛𝑠 + 𝐺𝑡𝑟𝑎𝑛𝑠 − 𝑃 𝐿 (𝑑)

(22)

where 𝑃𝑟𝑒𝑐𝑣 (𝑑) is the RSSI value with the distance 𝑑 in dB, 𝑃𝑡𝑟𝑎𝑛𝑠 is the transmission power, 𝐺𝑡𝑟𝑎𝑛𝑠 is the transmission antenna gain. The distance between nodes can be estimated by the following equation 𝑑 = 10[(𝑃𝑡𝑟𝑎𝑛𝑠 +𝛥−𝑃𝑟𝑒𝑐𝑣 (𝑑))∕10𝛽 ]

(23) ( ) where 𝛥 = 𝐺𝑡𝑟𝑎𝑛𝑠 − 𝑃 𝐿 𝑑0 − 𝑋𝑟 is the empirical value and can be regarded as a constant.

IF

THEN

Latency

Residual energy

Distance

Transmission power

Radius

Less Less Less Less Less Less Less Less Less Medium Medium Medium Medium Medium Medium Medium Medium Medium High High High High High High High High High

Low Low Low Average Average Average High High High Low Low Low Average Average Average High High High Low Low Low Average Average Average High High High

Near Medium Far Near Medium Far Near Medium Far Near Medium Far Near Medium Far Near Medium Far Near Medium Far Near Medium Far Near Medium Far

Very Low Low Average Low Average High Average High Very High Low Average Low Average Average High Average High Very High Low Average Average Low Average High Average High Very High

Very Short Short Average Short Average Long Average Long Very Long Short Average Short Average Average Long Average Long Very Long Short Average Average Short Average Long Average Long Very Long

size increment under the same baud rate. Hence, we divide the latency into three intervals, namely [90 ms, 140 ms), [140 ms, 230 ms), [230 ms, 280 ms]. Then, as shown in Fig. 5(a), the corresponding linguistic variables of the three intervals for the data latency are ‘‘Less’’, ‘‘Medium’’ and ‘‘High’’. Similarly, the energy consumption can be calculated according to Eq. (17). In order to ensure the entire network’s normal working status, the residual energy of each node cannot be too much less. Based on the measurement in our experiments, when the residual energy of node is lower than 0.5 J, then it cannot effectively transmit and/or relay data. This will dramatically degrade the transmission effectiveness of the entire network. On the contrast, the node can normally work when its residual energy is higher than 1.2 J. Therefore, the range of the residual energy is divided into three parts, namely [0.5 J, 0.7 J), [0.7 J, 1.0 J), [1.0 J, 1.2 J], and the linguistic variables for the corresponding three parts are considered as ‘‘Low’’, ‘‘Average’’ and ‘‘High’’, as shown in Fig. 5(b). The distance between nodes will change from 5 m to 45 m. Being similar to the above mentioned variables, the distance between nodes can also be divided into three intervals, i.e., [5 m, 15 m), [15 m, 35 m), [35 m, 45 m], and the linguistic variables for these three intervals are taken as ‘‘Near’’, ‘‘Medium’’ and ‘‘Far’’, as shown in Fig. 5(c). For the output variables, the transmission power ranges from −1 dB to 17 dB. hence, as shown in Fig. 5(d), the linguistic variables for the transmission power are characterized by ‘‘Very low’’, ‘‘Low’’, ‘‘Average’’, ‘‘High’’ and ‘‘Very high’’ respectively. For another output variable, i.e., the communication radius, it varies from 5 m to 45 m. As shown in Fig. 5(e), the linguistic variables for the communication radius are depicted as ‘‘Very Short’’, ‘‘Short’’, ‘‘Average’’, ‘‘Long’’ and ‘‘Very Long’’, whose centers are respectively set to be 5 m, 10 m 20 m, 30 m and 45 m.

3.3. IT2FLS-based TPA strategy 3.3.1. Diagram of the proposed IT2FLS-based TPA strategy The block diagram of our proposed TPA strategy using IT2FLS is shown in Fig. 4. As displayed in this figure, in the proposed TPA strategy, three important factors, i.e., the latency, the residual energy and the distance, are considered as the input variables, while the transmission power and the communication radius are regarded as the output variables. For the input variables, the data latency can be computed by the latency estimation model based on the data size and baud rate. In the similar way, both the distance of inter-nodes and the energy consumption can be calculated by the distance estimation model and the energy dissipation model, respectively. For the output variables, the transmission power and the communication radius are decided from the above three input variables according to the proposed IT2FLS-based TPA strategy. Then, the transmission power as a key input parameter of both the inter-nodes distance estimator and the energy dissipation estimator will directly affect the estimated results of both estimators. Therefore, the proposed TPA strategy constitutes a closed loop control process. 3.3.2. MFs for the input and output variables The triangular IT2FSs are used in this study for the three input variables and the two output variables. The MFs of the IT2FSs for the data latency, the residual energy and the distance between nodes are depicted in Fig. 5(a)–(c), respectively. And, the MFs of the IT2FSs for the transmission power and the communication radius are displayed in Fig. 5(d) and (e) respectively. In real world, the total data latency in the multi-hops WSNs is the sum of the delay caused by the relay nodes. The value of latency which normally relates to the packet size and baud rate is measured by millisecond (ms). Concretely, based on our tests, the latency is changing from 90 ms to 280 ms for one hop according to the packet

3.3.3. Fuzzy rules and the fuzzy inference In our proposed IT2FLS-based TPA strategy, three important factors are regarded as the input variables and each of them has three linguistic variables. Therefore, the fuzzy rule base is composed of 33 = 27 IF-THEN fuzzy rules. The complete fuzzy rules of the proposed TPA strategy are listed in Table 1. In fact, some fuzzy rules will not be fired 5

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

Fig. 5. MFs for the input and output variables: (a) MFs for the latency, (b) MFs for the residual energy, (c) MFs for the distance, (d) MFs for the transmission power, (e) MFs for the communication radius. Table 2 Simulation parameters.

in the real multi-hops WSNs environment, such as fuzzy rules numbered as 3, 10, 16, 21, 25 and 27 (marked by red color in Table 1), since some parameters exist strong mutual exclusion properties. Hence, the number of complete fuzzy rules can reduce to be 21 according to the expertise and measurement experiences. The fuzzy inference processes characterized by Eqs. (10)–(12) in Section 2 are adopted to combine the fuzzy rules and the input variables. Then, with the COS type-reducer, the output processing in Section 2 is utilized to generate the final crisp outputs for the transmission power and the communication radius. The final outputs for the output variables can be obtained as 𝑦𝑖,𝑙 (𝑥) + 𝑦𝑖,𝑟 (𝑥)

Value

Available trans. power Energy consumption Communication radius Available initial energy Data size Baud rate

−1 dB, 0 dB, 10 dB, 13 dB, 17 dB 16 mA, 20 mA, 33 mA, 45 mA, 95 mA 5 m, 10 m, 20 m, 30 m, 45 m 10 J, 30 J, 70 J 64 Byte 19.2 kbps

only be relayed one by one from the source node to the sink as shown in Fig. 6(a). On the contrast, the data can be directly (or be relayed just by fewer nodes, which are mostly close to the sink) transmitted to the sink, as shown in Fig. 6(c). The other important simulation parameters are listed in Table 2. The simulations will end when the energy in most of the nodes are exhausted, and the network cannot successfully transmit data. In the simulations, both the minimum total energy (MTE) algorithm (Rodoplu and Meng, 1999) and the flow augmentation (FA) algorithm (Chang and Tassiulas, 2004) are selected for comparison. Then, the IT2FLS(0.7) and IT2FLS(0.2), the heights of whose lower MFs are respectively set to be 0.7 and 0.2, are also applied for comparison. Moreover, In order to further verify the advantages of our proposed IT2FLS-based TPA strategy, the T1FLS with the same number of input variables and fuzzy rules is also given for comparison. In the T1FLS, triangular MFs are taken as the linguistic variables for the inputs and outputs. The detailed type-1 MFs are shown in Fig. 7.

(24) 2 where 𝑖 = 1, 2. When 𝑖 = 1, 𝑦1 (𝑥) is the output for the transmission power. When 𝑖 = 2, 𝑦2 (𝑥) is the output for the communication radius. 𝑦𝑖 (𝑥) =

Parameters

4. Performance evaluation In this section, the effectiveness of the proposed TPA strategy will be evaluated through simulations firstly. Concretely, the simulation performance of the proposed IT2FLS-based TPA strategy will be evaluated according to the average latency, the energy consumption and the network lifetime. Then, some experiments will be conducted on our real-world hardware platform. In the experiments, both the lifetime and the energy consumption of the proposed TPA strategy will be tested. And, in order to further verify the advantages of the proposed IT2FL-based TPA strategy, it will be compared with some other strategies.

4.1.2. Simulation results The comparison results of the five different strategies under different topologies are respectively shown in Figs. 8–10, in which the 𝑥-axis represents the traffic rate. The larger the traffic rate is, the more data will be sent in an unit time. The results in Fig. 8(a)–(c) are respectively corresponding to the topologies shown in Fig. 6(a)–(c). From these figures, it is clearly observed that they have the similar trends. Both Fig. 8(b) and (c) are better than Fig. 8(a), since the routing is diverse of the former two, especially closing to the sink. The MTE algorithm is similar to the greedy algorithm and always selects the minimum energy routes. From Fig. 8(a)–(c), the network lifetime of MTE is consequently shorter than others, because the relay nodes on the selected route are always used for forwarding data. Hence, they consume the energy more quickly and becomes dead much faster. This leads the network lifetime of MTE

4.1. Simulations In this subsection, detailed simulations will be provided, and comprehensive comparisons will be given. 4.1.1. Simulation setting In our simulations, 30 nodes from (𝑥 = 0, 𝑦 = 0) to (𝑥 = 50, 𝑦 = 50) are deployed and their topology is random. Fig. 6(a)–(c) show three different topologies randomly created under different parameters (different communication radius). As shown in these figures, the longer the communication radius is, the more complex the topology will be, because the nodes have more routing options when they transmit/relay data. Therefore, when the communication radius is short, the data can 6

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

Fig. 6. Three different network topologies in simulations: (a) maximum communication radius is set to be 20 m, (b) maximum communication radius is set to be 25 m, (c) maximum communication radius is set to be 30 m.

Fig. 7. MFs for input and output variables of the T1FLS based TPA strategy: (a) MFs for the Latency, (b) MFs for the residual energy, (c) MFs for the distance, (d) MFs for the transmission power, (e) MFs for the communication radius.

algorithm to be the shortest. For the FA algorithm, it selects the relay node through considering the residual energy and the transmission power simultaneously. The selection chance of the node with higher residual energy is higher than the other nodes. Consequently, the node with higher energy could be always selected for data forwarding, that may cause ‘hot node’ problem which will shorten the network lifetime. Therefore, the network lifetime of FA gradually decline with the increase of the traffic rate. Both the T1FLS and the IT2FLS-based TPA strategies (IT2FLS(0.2) and IT2FLS(0.7)) adaptively select the nodes and adjust the transmission power according to the residual energy, the data latency and the distance between nodes. Since the FOU of IT2FLS provides more degrees of freedom than T1FLS, the proposed IT2FLSbased TPA strategy can describe the variables with more flexibility and can achieve better performance. As shown in these figures, the higher the FOU is, the better performance will be. Hence, the proposed IT2FLSbased TPA strategies can effectively avoid the ‘hot node’ problem which generally have over load and large data latency. Moreover, the adaptive transmission power adjustment effectively reduces the unnecessary transmission energy dissipation and prolongs the network lifetime. Fig. 9(a)–(c) demonstrate the performance on the average data latency. It can be clearly observed that the latency of MTE is lower at beginning and then becomes obviously larger than those of the other strategies. The most important reason for this phenomenon is that the energy of node is exhausted very quickly with the increasing of the traffic rate. In this case, some nodes will be isolated, then, the number of the available relay nodes reduce rapidly, and finally, there will be none available routing. Hence, the data latency of MTE

increases very fast. The latency of FA is larger than that of T1FLS and IT2FLS (IT2FLS(0.7) and IT2FLS(0.2)), because the ‘hot nodes’ will cause the network congestion and will reduce the successful transmission rate. With the same reason (the FOU of IT2FLS provides more degrees of freedom than T1FLS), the performance of proposed IT2FLS (both IT2FLS(0.2) and IT2FLS(0.7)) are better than that of T1FLS. The proposed IT2FLS (IT2FLS(0.7) and IT2FLS(0.2)) is latency-aware and can dynamically adjust the transmission power and the communication radius. Hence, the latency increasing trend of the IT2FLS strategies, especially the IT2FLS(0.7), changes slower than the other strategies. The results on the energy consumption performance are shown in Fig. 10(a)–(c). Being similar to the latency, the energy consumption of MTE is lower at beginning, then increases rapidly. The reason for this is that the quick reduction of relay nodes makes the node cost much more energy to search the available routing for data forwarding. For the FA algorithm, the ‘hot nodes’ problem declines the successful transmission rate, and then causes much more retransmission and energy consumption. The energy consumptions of both IT2FLS (IT2FLS(0.7) and IT2FLS(0.2)) and T1FLS gradually grow when the traffic rate increases. The IT2FLS strategies, especially the IT2FLS(0.7), have much less energy consumption than the T1FLS strategy under the same traffic rate. In conclusion, according to the performance results under different topologies, including the network lifetime, the network latency and the energy consumptions, the IT2FLS(0.7) strategy > the IT2FLS(0.2) strategy > the T1FLS strategy > the MTE algorithm > the FA method, where ‘‘>’’ means ‘‘performs better than’’. 7

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

Fig. 8. Result of network lifetime under different topologies.

Fig. 9. Result of network latency under different topologies.

Fig. 10. Result of network consumption under different topologies.

The base station connects to a PC, which runs an monitoring software to collect the real-time data, including the residual energy of the source nodes, the distance between nodes, the delay of the packets, and the transmission power used by the source nodes, etc. Fig. 11(b) shows the deployment of the nodes in the experimental scenarios of our laboratory. Six sensor nodes are randomly deployed in the room and/or corridor. The base station is located at the room in the lower and right corner of our laboratory. The abstracted topology of the deployment is shown in Fig. 11(c). For convenience, six sensor nodes are respectively denoted as 𝑎, 𝑏, 𝑐, 𝑑, 𝑒, 𝑓 and are classified according to their number of hops. As shown in Fig. 11(c), 𝑑, 𝑒 and 𝑓 are the three-hops nodes, 𝑐 is the two-hops node, while 𝑎 and 𝑏 are the one-hop nodes. In order to show the effectiveness of the proposed IT2FLS-based TPA strategy, the experiment without TPA strategy is also done. In the experiment without TPA strategy, the transmission power and the

4.2. Experiments In this subsection, we use one real-world application to evaluate the effectiveness of the proposed IT2FLS-based TPA strategy. 4.2.1. Experimental setting The experiment is implemented on our WSNs testing platform as shown in Fig. 11. In this platform, each node integrates the Semtech SX1231 transceiver and a 32-bit ARM-CortexTM M3 microprocessor STM32 F103VET6. Besides, two mini USB interfaces are equipped in each node for easily observing the useful debug information and the real-time operation system FreeRTOS (2011) is ported in order to coordinate multiple tasks. The node supports four RF transceivers at most, but only one of them is used in our experiments. Fig. 11(a) shows the hardware of the sensor nodes and the base station in our experiments. 8

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

Fig. 11. Hardware platform (a), experimental scenarios in our laboratory (b), corresponded metaphysical topology (c).

Fig. 12. Final topologies in the two experiments.

• In the first experiment (without TPA strategy), all the data sent by the three-hops nodes can only be delivered by the node 𝑐, thus the energy consumption of 𝑐 is higher and this node will becomes the ‘‘dead node’’ quickly. Then, the three-hops nodes, i.e. the nodes 𝑑, 𝑒 and 𝑓 , become the disconnected nodes. • In the second experiment (with the proposed IT2FLS-based TPA strategy), once node 𝑐 detects that the energy consumption is high and the residual energy is low, then it will reduce the transmission power according to the IT2FLS-based TPA strategy. The data latency of the three-hops nodes is large, because node 𝑐 must delivers all the data at beginning and the channel will be

communication radius are fixed. In both experiments, each node sends data to the base station through multi-hops according to a certain frequency. One node will become ‘‘dead node’’ if the residual energy is less than the given threshold. Each node in the experiments runs for 3500 s, and their energy consumptions are recorded. 4.2.2. Experimental results The final results are shown in Figs. 12–14, respectively. Fig. 12 shows the final topologies in the two different experiments, i.e., without TPA strategy and with the proposed IT2FLS-based TPA strategy. The reason for obtaining these final topologies are as follows: 9

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

first experiment. The reason for this is that node 𝑐 in the first experiment transmits too much data and becomes dead quickly. The energy consumption depicted in Fig. 14 shows that the energy consumption of node 𝑐 in the first experiment declines sharply to zero at 2000 s when it comes to be dead. Owing to the death of node 𝑐 in the first experiment, the nodes 𝑑, 𝑒 and 𝑓 in this case become disconnected. As a result, the retransmission load leads the lifetime in this case to be shorter and the energy consumption to be higher compared with the second experiment. Again, in the first experiment, due to the death of node 𝑐, the transmitted data of nodes 𝑎 and 𝑏 will become less than before. Thus, the life times and energy consumptions of nodes 𝑎 and 𝑏 respectively become longer and lower than the other nodes. The proposed IT2FLS-based TPA strategy can tune the node 𝑐 to reduce its transmission power, hence its energy consumption becomes lower and its lifetime comes to be longer than those in the first experiment. 5. Conclusions In WSNs, the data latency, energy consumption and communication distance are usually impacted by the deployed environment leading to high levels of uncertainties. Such uncertainties caused serious energy waste and network performance degradation. In order to deal with the high levels of uncertainties and to further improve the network performance, this study applied the IT2FLS to solve the lifetime maximization problem of WSNs. In this paper, the relationship between the transmission power and the network lifetime was firstly explored, and the network lifetime enhancing issue was converted into one TPA problem. Then, the estimation models of the data latency, the residual energy and the distances of the inter nodes were given. Furthermore, the IT2FLSbased TPA strategy was proposed to efficiently use the limited energy and to prolong the network lifetime. This TPA strategy adopted the data latency, the residual energy and the distance between nodes as input variables while using the transmission power and communication radius as output variables. Finally, the performance of the proposed IT2FLS-based TPA strategy was evaluated through simulations and experiments. Simulation and experimental results indicated that the

Fig. 13. Lifetimes of the six nodes in the two experiments.

congested. As a result, the nodes 𝑑 and 𝑒 adjust their transmission power and become the higher power nodes. At the same time, they change themselves from the three-hops nodes to the twohops nodes. Thus the data can be delivered by node 𝑐, 𝑑 or 𝑒. The data latency will be balanced in the nodes. For the two experiments, the corresponding lifetime and energy consumption are shown in Figs. 13 and 14 respectively. From both figures, we can observe that the second experiment has much better performance than the first experiment. This verified the effectiveness of the proposed IT2FLS-based TPA strategy. From Fig. 13, we can also clearly observe that the node 𝑐 has the shortest lifetime in the

Fig. 14. The energy consumption of the six nodes in the two experiments (the 𝑋-axis is experimental time in seconds while the 𝑌 -axis is the energy consumption of each node).

10

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Engineering Applications of Artificial Intelligence 87 (2020) 103269

proposed IT2FLS-based TPA strategy could effectively improve the network performance and enhance the network lifetime. In our future work, more experimental tests will be provided aiming at further evaluation of the proposed TPA strategy network performances, such as the throughput, the data transmission rate, etc. Moreover, in order to further optimize the proposed IT2FLS, some advanced evolutionary algorithms, including differential evolution algorithm, particle swarm optimization and so on, will be considered for training the consequent weights of the fuzzy rules.

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