# Research on Evaluating Algorithms for the Service Quality of Wireless Sensor Networks Based on Interval-Valued Intuitionistic Fuzzy EDAS and CRITIC Methods

Authors: Shihui Li; Bo Wang
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

Wireless sensor networks play an important role in economic production and social life. However, in recent years, the number of wireless sensor network vulnerabilities has been increasing rapidly, which makes wireless sensor networks face more and more severe challenges. It is of great significance to realize the quantitative evaluation of wireless sensor networks in order to maintain the service quality of wireless sensor networks more effectively. The evaluating problem of the service quality of wireless sensor networks is a kind of multiple attribute group decision-making (MAGDM) problem. In this paper, depending on the classical EDAS method, the EDAS method will be extended to interval-valued intuitionistic fuzzy sets (IVIFSs) to address some MAGDM issues. At first, some essential concepts of IVIFSs are briefly reviewed. Subsequently, relying on the CRITIC method, the attributes’ weights are decided. Furthermore, integrating the EDAS method with IVIFSs, IVIF-EDAS method is established, and all calculating procedures are depicted. Finally, an empirical application for evaluating the service quality of wireless sensor networks is given to demonstrate this novel algorithm, and some comparative analyses are made to confirm the merits of the designed method.


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## Body

## 1. Introduction

In order to improve the accuracy of real-life decision-making, Zadeh [1] initially designed the fuzzy sets (FSs). Atanassov [2] designed the intuitionistic fuzzy sets (IFSs), which could be a generalization of FSs. In IFSs, there are three mathematical functions expressing the degrees of membership, nonmembership, and hesitancy. And they must satisfy the only condition that their sum of three degrees cannot exceed one. Gou et al. [3] pointed out a novel exponential operational law about IFNs and offered a method which was utilized to aggregate intuitionistic fuzzy information. He et al. [4] integrated the power averaging operators with IFSs and defined several intuitionistic fuzzy power interaction aggregation operators. Zhang and He [5] defined the extensions of intuitionistic fuzzy geometric interaction operators by using the t-norm and the corresponding t-conorm means. Li and Wu [6] presented the intuitionistic fuzzy cross-entropy distance and the GRA. Liang et al. [7] extended the MABAC method to IFSs by utilizing the novel distance measures. Khan and Lohani [8] put forward a novel similarity measure about IFNs depending on the distance measure of the double sequence of bounded variation. Chen et al. [9] developed the novel MCDM method based on the TOPSIS method and similarity measures in the context of IFSs. Li et al. [10] developed a grey target decision-making method in the form of IFNs on the basis of grey relational analysis [11]. Garg [12] developed some intuitionistic fuzzy averaging operators by taking the degrees of hesitation between the membership mathematical functions into consideration. Gupta et al. [13] extended the fuzzy entropy [14] to IFSs with axiomatic justification and proposed the importance of parameter alpha. Bao et al. [15] put forward the prospect theory and the evidential reasoning method under IFSs. Gan and Luo [16] employed a hybrid method on the basis of DEMATEL and IFSs. Gupta et al. [17] modified the superiority and inferiority ranking (SIR) method and combined it under IFSs. Krishankumar et al. [18] developed IFSP (intuitionistic fuzzy set-based PROMETHEE) which was a novel ranking method. Luo and Wang [19] combined IFSs with the VIKOR method relying on a novel distance measure by taking the IFSs into consideration. Hao et al. [20] presented the novel intuitionistic fuzzy MADM method depending on the decision theory. Zhang et al. [21] defined the intuitionistic fuzzy TOPSIS method based on CVPIFRS models with an application to biomedical problems. Garg [22] developed the generalized intuitionistic fuzzy entropy-based approach for solving multiattribute decision-making problems with unknown attribute weights. Liu et al. [23] presented some novel intuitionistic fuzzy operators by extending the BM operator on the basis of the Dombi operations [24] and designed some MAGDM methods. Jin et al. [25] developed two group decision-making (GDM) methods which could obtain the normalized intuitionistic fuzzy priority weights from the designed IFPRs on the basis of the order consistency and the multiplicative consistency. Wu et al. [26] gave VIKOR algorithms for assessing the financing risk about rural tourism projects under IVIFSs. Wu et al. [27] designed the algorithms for evaluating the competitiveness of tourist destination with some IVIF Hamy mean operators. Wu et al. [28] proposed some IVIF Dombi Heronian mean operators for evaluating the ecological tourism value. Chen and Kuo [29] presented the novel MADM method using the nonlinear programming (NLP) model with hyperbolic tangent function and IVIFSs. Lu and Wei [30] proposed the TODIM method for social-integration-based rural performance appraisal under IVIFSs and integrated the ELECTRE method with IFSs to tackle some MCDM issues. Garg and Kumar [31] defined the group decision-making approach based on possibility degree measures and the linguistic intuitionistic fuzzy aggregation operators using Einstein norm operations. Garg and Arora [32] proposed the generalized intuitionistic fuzzy soft power aggregation operator based on the t-norm and its application in multicriteria decision-making.Keshavarz Ghorabaee et al. [33] designed the evaluation based on distance from average solution (EDAS) to solve multicriteria inventory classification (MCIC) issues. In recent years, this method was enriched by the related extensions. For example, Ghorabaee et al. [34] modified such an EDAS method to tackle supplier selection issues. Keshavarz Ghorabaee et al. [35] presented the EDAS method with normal distribution to tackle stochastic issues. Peng and Liu [36] designed the neutrosophic soft MADM algorithms on the basis of EDAS and defined the similarity measure. Kahraman et al. [37] integrated the EDAS method with IFSs to select the solid waste disposal site. He et al. [38] designed the EDAS model for MAGDM with PULTSs. Keshavarz Ghorabaee et al. [39] made some comparative analyses about the phenomenon of order reversal depending on EDAS and TOPSIS. Wang et al. [40] proposed the EDAS model for MAGDM under the 2-tuple linguistic neutrosophic environment. Li et al. [41] defined the EDAS for MAGDM issues under the q-rung orthopair fuzzy environment. Feng et al. [42] integrated the EDAS with the extended hesitant fuzzy linguistic environment. Karasan and Kahraman [43] designed the interval-valued neutrosophic EDAS to decision-making issues.Unfortunately, we failed to find the work of the EDAS method based on the CRITIC method with IVIFSs in the existing literature. So, investigating the EDAS method with IVIFSs is essential. The fundamental objective of our research is to develop an original method which can be more effectively to address some MAGDM issues in the context of the EDAS method and IVIFSs. Hence, the highlights of this work are illustrated subsequently. Above all, the EDAS method is extended to the IVIFSs. In addition, because the DMs are restrained by their knowledge, it is tricky to assign the criteria weights directly. Hence, the CRITIC method is utilized to decide each attribute’s weight. Last but not the least, an empirical application is offered to demonstrate this novel approach, and several comparative analyses are offered to demonstrate some merits of the novel approach.However, there are no studies on the EDAS method for MAGDM under IVIFSs in the existing literature. Therefore, it is necessary to pay attention to this issue. The innovativeness of the paper can be summarized as follows: (1) the EDAS method is modified by IVIFSs; (2) the interval-valued intuitionistic fuzzy EDAS (IVIF-EDAS) method is designed to solve the MAGDM issues with IVIFSs; (3) a case study for evaluating the service quality of wireless sensor networks is designed to prove the developed method; and (4) some comparative studies are given to verify the rationality of the IVIF-EDAS method.The reminder of our essay proceeds as follows. Some fundamental knowledge of IVIFSs is concisely reviewed in Section2. The extended EDAS method is integrated with IVIFSs, and the calculating procedures are simply depicted in Section 3. An empirical application for assessing the service quality of wireless sensor networks is given to show the superiority of this approach, and some comparative analyses are offered to prove some merits of such a method in Section 4. At last, we make an overall conclusion of such a work in Section 5.


## 2. Preliminaries

Definition 1.
(see [2]). The interval-valued IFSs (IVIFSs) on X are the object of the form(1)I=x,μ˜Ix,ν˜Ixx∈X,where μ˜Ix⊂0,1 is the “membership degree of I” and ν˜Ix⊂0,1 is named the “nonmembership degree of I,” and μ˜Ix and ν˜Ix meet the mathematical condition: 0≤supμ˜Ix+supν˜Ix≤1, ∀x∈X. For convenience, we call I=μL,μR,νL,νR as an IVIFN.Definition 2.
(see [44]). Let I1=μ1L,μ1R,ν1L,ν1R and I2=μ2L,μ2R,ν2L,ν2R be two IVIFNs; the operation formula of them can be defined as follows:(2)I1⊕I2=μ1L+μ2L−μ1Lμ2L,μ1R+μ2R−μ1Rμ2R,ν1Lν2L,ν1Rν2R,(3)I1⊗I2=μ1Lμ2L,μ1Rμ2R,ν1L+ν2L−ν1Lν2L,ν1R+ν2R−ν1Rν2R,(4)λI1=1−1−μ1Lλ,1−1−μ1Rλ,ν1Lλ,ν1Rλ,λ>0,(5)I1λ=μ1Lλ,μ1Rλ,1−1−λ1Lλ,1−1−λ1Rλ,λ>0.
Derived from Definition2, the following properties of the operation laws can be obtained:(1)
I1⊕I2=I2⊕I1,I1⊗I2=I2⊗I1,I1λ1λ2=I1λ1λ2(2)
λI1⊕I2=λI1⊕λI2,I1⊗I2λ=I1λ⊗I2λ(3)
λ1I1⊕λ2I1=λ1+λ2I1,I1λ1⊗I1λ2=I1λ1+λ2Definition 3.
(see [45]). Let I1=μ1L,μ1R,ν1L,ν1R and I2=μ2L,μ2R,ν2L,ν2R be IVIFNs; the score and accuracy values of I1 and I2 can be defined as follows:(6)SI1=μ1L+μ1L1−μ1L−ν1L+μ1R+μ1R1−μ1R−ν1R2,SI2=μ2L+μ2L1−μ2L−ν2L+μ2R+μ2R1−μ2R−ν2R2,(7)HI1=μ1L+ν1L+μ1R+ν1R2,HI2=μ2L+ν2L+μ2R+ν2R2.
For two IFNsI1 and I2, regarding Definition 3,(1)
IfsI1<sI2, then I1<I2(2)
IfsI1>sI2, then I1>I2(3)
IfsI1=sI2 and hI1<hI2, then I1<I2(4)
IfsI1=sI2 and hI1>hI2, then I1>I2(5)
IfsI1=sI2 and hI1=hI2, then I1=I2
Under the context of the IVIFNs, some aggregation operators will be introduced in this chapter, including the interval-valued intuitionistic fuzzy WA (IVIFWA) operator and the interval-valued intuitionistic fuzzy WG (IVIFWG) operator.Definition 4.
(see [44]). Let Ij=μIj,νIjj=1,2,…,n be a set of IVIFNs; the IVIFWA operator is defined as(8)IVIFWAωI1,I2,…,In=⊕j=1nωjIj,where ω=ω1,ω2,…,ωnT is the weight vector of Ijj=1,2,…,n and ωj>0,∑j=1nωj=1.
Derived from Definition4, the subsequent result can be obtained:Theorem 1.
The fused value by the IVIFWA operator could also be an IVIFN, where(9)IVIFWAωI1,I2,…,In=⊕j=1nωjIj=1−∏j=1n1−μIjLωj,1−∏j=1n1−μIjRωj,∏j=1nνIjLωj,∏j=1nνIjRωj,where ω=ω1,ω2,…,ωnT is the weight vector of Ijj=1,2,…,n and ωj>0,∑j=1nωj=1.Definition 5.
(see [44]). Let Ijj=1,2,…,n be a set of IVIFNs; the IVIFWG operator can be given as(10)IVIFWGωI1,I2,…,In=⊗j=1nIjωj,where ω=ω1,ω2,...,ωnT is the weight vector of Ijj=1,2,…,n and ωj>0,∑j=1nωj=1.
Derived from Definition5, the detailed result can be obtained.Theorem 2.
The fused value by using the IVIFWG operator could also be an IVIFN, where(11)IVIFWGωI1,I2,…,In=⊗j=1nIjωj=∏j=1nμIjLωj,∏j=1nμIjRωj,1−∏j=1n1−νIjLωj,1−∏j=1n1−νIjRωj,where ω=ω1,ω2,...,ωnT is the weight vector of Ijj=1,2,…,n and ωj>0,∑j=1nωj=1.


## 3. The EDAS Method with IVIFNs

Integrating the EDAS method with IVIFSs, we build the IVIF-EDAS method in which the assessment values are given by IVIFNs. The calculating procedures of the developed method can be described subsequently.LetZ=Z1,Z2,…,Zn be the attribute set and z=z1,z2,…,zn be the attribute weight Zj, where zj∈0,1,j=1,2,…,n,∑j=1nzj=1. Assume D=D1,D2,…,Dl is a set of decision makers that have a significant degree of d=d1,d2,…,dl, where dk∈0,1, k=1,2,…,l., ∑k=1ldk=1. Let Y=Y1,Y2,…,Ym be a discrete collection of alternatives. And Q=qijm×n is the overall IVIFN decision matrix; qij means the value of alternative Yi regarding attribute Zj. Subsequently, the specific calculating procedures will be depicted.Step 1: set up each decision maker’s IVIFN decision matrixQk=qijkm×n, and calculate the overall IVIFN decision matrix Q=qijm×n:(12)Qk=qijkm×n=q11kq12k⋯q1nkq21kq22k⋯q2nk⋮⋮⋮⋮qm1kqm2k⋯qmnk,(13)Q=qijm×n=q11q12⋯q1nq21q22⋯q2n⋮⋮⋮⋮qm1qm2⋯qmn,(14)qij=1−∏k=1l1−μqijkLdk,1−∏k=1l1−μqijkRdk,∏k=1lνqijkLdk,∏k=1lνqijkRdk,whereqijk is the assessment value of alternative Yii=1,2,…,m on the basis of the attribute Zjj=1,2,…,n and the decision maker Dkk=1,2,…,l.Step 2: normalize the overall IVIFN decision matrixQ=qijm×n to QN=qijNm×n:(15)qijN=μijL,μijR,νijL,νijR,Zjis a benefit criterion,νijL,νijR,μijL,μijR,Zjis a cost criterion.Step 3: utilize the CRITIC method to determine the weighting matrix of attributes.CRiteria Importance through Intercriteria Correlation (CRITIC) method will be designed in this part which is utilized to decide attributes’ weights. This method was initially put forward by Diakoulaki et al. [46] which took the correlations between attributes into consideration. Subsequently, the calculating procedures of this method will be presented:(1)
Depending on the normalized overall IVIFN decision matrixQN=qijNm×n, the correlation coefficient between attributes can be calculated:(16)ICjt=∑i=1mSqijN−SqjNSqitN−SqtN∑i=1mSqijN−SqjN2∑i=1mSqitN−SqtN2,j,t=1,2,…,n,whereqjN=1/m∑i=1mSqijN and qtN=1/m∑i=1mSqitN.(2)
Calculate attributes’ standard deviation:(17)ISj=1m−1∑i=1mSqijN−SqjN2,j=1,2,…,n,whereqjN=1/m∑i=1mSqijN.(3)
Calculate the attributes’ weights:(18)zj=ISj∑t=1n1−ICjt∑j=1nISj∑t=1n1−ICjt,j=1,2,…,n,wherezj∈0,1 and ∑j=1nzj=1.Step 4: calculate the average solution (AV) regarding all designed attributes:(19)AV=AVj1×n=∑i=1mq^ijNm1×n,(20)AVj1×n=∑i=1mq^ijNm1×n=1−∏i=1m1−μijNL1/m,1−∏i=1m1−μijNR1/m∏i=1mνijNL1/m,∏i=1mνijNR1/m1×n.Step 5: depending on the AV’s results, the positive distance from average (PDA) and negative distance from average (NDA) can be defined:(21)PDAij=PDAijm×n=max0,sqijN−sAVjsAVj,(22)NDAij=NDAijm×n=max0,sAVj−sqijNsAVj.Step 6: calculateSPi and SNi which express the weighted sum of PDA and NDA:(23)SPi=∑j=1nzj⋅PDAij,NPi=∑j=1nzj⋅NDAij.Step 7: depending on the above calculated results,SPi and SNi can be normalized as(24)NSPi=SPimaxiSPi,NSNi=1−SNimaxiSNi.Step 8: calculate the appraisal scoreASi regarding every alternative’s NSPi and NSNi:(25)ASi=12NSPi+NSNi.Step 9: according toASi, all the alternatives can be ranked. The higher the value of ASi is, the optimal alternative will be selected.


## 4. The Empirical Example and Comparative Analysis

### 4.1. An Empirical Example

With the development of research on wireless technique and other related techniques, wireless sensor networks (WSNs) have been widely used in various applications which involve diverse working environments, monitoring objects, and data conditions. Different applications require different quality of service (QoS) for data collection and data transmission. Thus, it is essential to provide QoS guarantee mechanisms in WSNs to achieve good performance in various applications. Accordingly, it is of great significance to study the QoS guarantee mechanisms in WSNs. In general terms, the QoS of WSNs focuses on timeliness and reliability of data transmission, as well as coverage and connectivity of the network topology for data collection. The QoS guarantee implementation relies on different mechanisms in WSNs. Although many methods and techniques have been proposed in the existing literature, the QoS guarantee mechanism is still faced with the following challenges in complex applications: (1) there exist several types of data traffic which have different QoS requirements. Therefore, a multiple-level QoS guarantee mechanism is in great demand. (2) There could be multiple QoS requirements for one data traffic. Thus, it is necessary to provide multiple-QoS guarantee mechanisms for theses traffics. (3) Since the traffic distributes are nonuniform in space and time, a method for the efficient transmission in a dynamic traffic is required. (4) There exists nonuniform replacement of the nodes as well as dynamic and changeful topology in many applications of the WSN. It is necessary to provide an efficient deployment method to satisfy the requirement of effectively covering. In this chapter, an empirical example for evaluating the service quality of wireless sensor networks which considered the complex MAGDM issues [47–54] will be provided by making use of the IVIF-EDAS method. Thus, in such a section, we present a numerical example to assess computer network systems with IVIFNs in order to show the designed method. There are five wireless sensor networks Aii=1,2,3,4,5 to select. The expert group selects four attributes to evaluate these five wireless sensor networks: ① G1 is the product quality factor; ② G2 is the technology factor; ③ G3 is the delivery factor; and ④ G4 is the price factor. Taking its own business development into consideration, a company wants to choose a wireless sensor network. There are five potential wireless sensor networks Yii=1,2,3,4,5. In order to select the optimal wireless sensor network, the expert group invites five experts D=D1,D2,D3,D4,D5 (expert’s weight d=1/5,1/5,1/5,1/5,1/5) to assess these wireless sensor networks. All experts give their assessment information depending on the four subsequently attributes: ① Z1 is the traffic convenience; ② Z2 is the product price; ③ Z3 is the green environmental protection ability; and ④ Z4 is the service quality. Evidently, Z2 is the g cost attribute, while Z1, Z3, and Z4 are the benefit attributes. To obtain the optimal wireless sensor network, the calculating procedures are involved:Step 1: set up each decision maker’s IVIFN evaluation matrixQk=qijkm×ni=1,2,…,m,j=1,2,…,n as in Tables 1–5. Derived from these tables and equations (12)–(14), the overall IVIFN decision matrix could be calculated. The results are recorded in Table 6.Table 1
IVIFN evaluation information byD1.
Z1Z2Z3Z4Y1([0.35, 0.38], [0.58, 0.62])([0.21, 0.31], [0.33, 0.69])([0.24, 0.33], [0.41, 0.66])([0.32, 0.43] [0.45, 0.57)Y2([0.29, 0.39] [0.44, 0.61])([0.28, 0.34], [0.46, 0.64])([0.11, 0.25], [0.32, 0.75])([0.39, 0.44], [0.52, 0.61])Y3([0.40, 0.49], [0.51, 0.60])([0.33, 0.51], [0.53, 0.67])([0.44, 0.50], [0.52, 0.56])([0.28, 0.39], [0.61, 0.72])Y4([0.33, 0.48], [0.54, 0.67])([0.42, 0.49], [0.51, 0.58])([0.41, 0.44], [0.46, 0.59])([0.41, 0.46], [0.49, 0.53])Y5([0.26, 0.48], [0.61, 0.74])([0.42, 0.47], [0.52, 0.58])([0.41, 0.48], [0.51, 0.59])([0.38, 0.53], [0.55, 0.62])Table 2
IVIFN evaluation information byD2.
Z1Z2Z3Z4Y1([0.38, 0.42], [0.55, 0.62])([0.43, 0.49], [0.51, 0.57])([0.29, 0.39], [0.59, 0.71])([0.45, 0.48], [0.50, 0.55])Y2([0.37, 0.48], [0.56, 0.63])([0.34, 0.44], [0.51, 0.66])([0.46, 0.50], [0.52, 0.54])([0.39, 0.48], [0.50, 0.61])Y3([0.37, 0.50], [0.54, 0.63])([0.27, 0.39], [0.67, 0.73])([0.41, 0.52], [0.54, 0.59])([0.16, 0.33], [0.72, 0.84])Y4([0.46, 0.49], [0.52, 0.54])([0.32, 0.38], [0.56, 0.68])([0.37, 0.43], [0.47, 0.63])([0.29, 0.34], [0.68, 0.71])Y5([0.40, 0.48], [0.52, 0.60])([0.46, 0.49], [0.51, 0.54])([0.42, 0.47], [0.55, 0.58])([0.33, 0.38], [0.62, 0.67])Table 3
IVIFN evaluation information byD3.
Z1Z2Z3Z4Y1([0.44, 0.48], [0.52, 0.56])([0.38, 0.42], [0.48, 0.62])([0.31, 0.42], [0.59, 0.69])([0.40, 0.49], [0.58, 0.60])Y2([0.38, 0.42], [0.59, 0.62])([0.35, 0.43], [0.58, 0.65])([0.42, 0.48], [0.52, 0.58])([0.26, 0.33], [0.59, 0.74)Y3([0.35, 0.42], [0.59, 0.65])([0.48, 0.50], [0.51, 0.52])([0.18, 0.36], [0.64, 0.82])([0.38, 0.43], [0.56, 0.62])Y4([0.27, 0.34], [0.59, 0.73])([0.26, 0.43], [0.62, 0.74])([0.38, 0.46], [0.52, 0.62])([0.31, 0.45], [0.62, 0.69])Y5([0.46, 0.51], [0.52, 0.54])([0.44, 0.51], [0.52, 0.56])([0.34, 0.45], [0.62, 0.66])([0.35, 0.45], [0.55, 0.65])Table 4
IVIFN evaluation information byD4.
Z1Z2Z3Z4Y1([0.42, 0.48], [0.51, 0.58])([0.37, 0.44], [0.59, 0.63])([0.25, 0.37], [0.68, 0.75])([0.22, 0.35], [0.67, 0.78])Y2([0.41, 0.49], [0.52, 0.59])([0.36, 0.39], [0.49, 0.64])([0.27, 0.43], [0.65, 0.73])([0.42, 0.45], [0.52, 0.58])Y3([0.43, 0.48], [0.52, 0.57])([0.42, 0.48], [0.52, 0.58])([0.41, 0.48], [0.54, 0.59])([0.34, 0.49], [0.58, 0.66])Y4([0.32, 0.43], [0.64, 0.67])([0.32, 0.43], [0.59, 0.68])([0.36, 0.39], [0.58, 0.64])([0.15, 0.39], [0.64, 0.85])Y5([0.37, 0.45], [0.56, 0.63])([0.36, 0.45], [0.55, 0.64])([0.42, 0.50] [0.52, 0.58])([0.27, 0.45], [0.65, 0.73])Table 5
IVIFN evaluation information byD5.
Z1Z2Z3Z4Y1([0.63, 0.66], [0.69, 0.37])([0.45, 0.46], [0.48, 0.55])([0.39, 0.45], [0.59, 0.61])([0.43, 0.47], [0.54, 0.57])Y2([0.43, 0.47], [0.52, 0.57])([0.37, 0.43], [0.59, 0.63])([0.40, 0.50], [0.52, 0.60])([0.41, 0.48], [0.52, 0.59])Y3([0.47, 0.49], [0.51, 0.53])([0.29, 0.35], [0.65, 0.71])([0.42, 0.48], [0.53, 0.58])([0.27, 0.43], [0.67, 0.73])Y4([0.41, 0.49], [0.52, 0.59])([0.43, 0.47], [0.52, 0.57])([0.46, 0.48], [0.52, 0.54])([0.19, 0.38], [0.67, 0.81])Y5([0.33, 0.45], [0.64, 0.67])([0.48, 0.50], [0.51, 0.52])([0.44, 0.46], [0.53, 0.56])([0.21, 0.37], [0.68, 0.79])Table 6
Overall IVIFN evaluation information.
Z1Z2Z3Z4Y1([0.4341, 0.4442], [0.5051, 0.5233])([0.4722, 0.4833], [0.4901, 0.5189])([0.2798, 0.2980], [0.6087, 0.6455])([0.4376, 0.4521], [0.5475, 0.5499])Y2([0.5341, 0.5365], [0.4152, 0.42532)([0.5502, 0.5708], [0.4209, 0.4429])([0.6432, 0.6679], [0.3807, 0.3988])([0.5908, 0.6213], [0.3216, 0.4453])Y3([0.4325, 0.4365], [0.5472, 0.5711])([0.4029, 0.4233], [0.5120, 0.5431])([0.4458, 0.4687], [0.4897, 0.4988])([0.3246, 0.4362], [0.2109, 0.4907])Y4([0.5231, 0.5433], [0.4761, 0.4866])([0.4877, 0.4902], [0.4211, 0.4766])([0.5765, 0.5870], [0.4211, 0.4465])([0.3287, 0.4309], [0.4870, 0.4998])Y5([0.4168, 0.4561], [0.5232, 0.5690])([0.4907, 0.5142], [0.4606, 0.4980])([0.4755, 0.5219], [0.4658, 0.4785])([0.4598, 0.4622], [0.1121, 0.2366])Step 2: normalize the evaluation matrixQ=qijm×n to QN=qijNm×n (see Table 7).Table 7
The normalized IVIFN evaluation information.
Z1Z2Z3Z4Y1([0.4341, 0.4442], [0.5051, 0.5233])([0.4901, 0.5189], [0.4722, 0.4833])([0.2798, 0.2980], [0.6087, 0.6455)])([0.4376, 0.4521], [0.5475, 0.5499])Y2([0.5341, 0.5365], [0.4152, 0.42532])([0.4209, 0.4429], [0.5502, 0.5708])([0.6432, 0.6679], [0.3807, 0.3988])([0.5908, 0.6213], [0.3216, 0.4453])Y3([0.4325, 0.4365] [0.5472, 0.5711)([0.5120, 0.5431], [0.4029, 0.4233])([0.4458, 0.4687], [0.4897, 0.4988]([0.3246, 0.4362], [0.2109, 0.4907])Y4([0.5231, 0.5433], [0.4761, 0.4866])([0.4211, 0.4766], [0.4877, 0.4902])([0.5765, 0.5870], [0.4211, 0.4465])([0.3287, 0.4309], [0.4870, 0.4998])Y5([0.4168, 0.4561], [0.5232, 0.5690])([0.4606, 0.4980], [0.4907, 0.5142])([0.4755, 0.5219], [0.4658, 0.4785])([0.4598, 0.4622], [0.1121, 0.2366])Step 3: decide the attribute weightszjj=1,2,…,n by making use of the CRITIC method as recorded in Table 8.Table 8
The attribute weightszj.
Z1Z2Z3Z4Zj0.13110.21620.22330.4094Step 4: depending on the calculated results of Table8, the value of average solution (AV) can be obtained on the basis of all proposed attributes by equations (19) and (20) (see Table 9).Table 9
The value of average solution.
Average solutionZ1([0.4286, 0.4782], [0.4784, 0.5231])Z2([0.5219, 0.5690], [0.4221, 0.4410])Z3([0.4522, 0.4897], [0.4588, 0.5099])Z4([0.4308, 0.4906], [0.3265, 0.4128])Step 5: relying on the results of AV, the PDA and NDA can be calculated by utilizing equations (21) and (22) (see Tables 10 and 11).Table 10
The results ofPDAij.
Z1Z2Z3Z4Y10.00000.00540.00000.0000Y20.12360.00000.28330.3164Y30.00000.14360.00000.0000Y40.09290.00000.15650.0000Y50.00000.00000.00000.0000Table 11
The results ofNDAij.
Z1Z2Z3Z4Y10.00840.00000.38750.0288Y20.00000.14770.00000.0000Y30.09380.00000.12520.0245Y40.00000.00380.00000.3567Y50.12930.03680.03590.0046Step 6: on the basis of equation (23) and attribute weighting vector ω=0.1311,0.2162,0.2233,0.4094, the values of SPi and SNi can be calculated:(26)SP1=0.0018,SP2=0.2063,SP3=0.0375,SP4=0.0659,SP5=0.0000,SN1=0.1379,SN2=0.0356,SN3=0.0689,SN4=0.1052,SN5=0.0338.Step 7: the results of Step 6 could be normalized by equation (24):(27)NSP1=0.0063,NSP2=1.0000,NSP3=0.1200,NSP4=0.3037,NSP5=0.0000,NSN1=0.0000,NSN2=0.7528,NSN3=0.5462,NSN4=0.1982,NSN5=0.7361.Step 8: o n the basis of each alternative’sNSPi and NSNi, the values of AS are calculated:(28)AS1=0.0038,AS2=0.8715,AS3=0.3581,AS4=0.2613,AS5=0.3732.Step 9: according to the AS, all the alternatives can be ranked; the higher the value of AS is, the optimal alternative will be selected. Evidently, the rank of these five alternatives isY2>Y5>Y3>Y4>Y1, and Y2 is the best wireless sensor network.Table 12
Evaluation results of dissimilar methods.
MethodsRanking orderThe optimal alternativeThe worst alternativeIVIFWAY2>Y4>Y3>Y5>Y1Y2Y1IVIFWGY2>Y3>Y5>Y4>Y1Y2Y1The modified VIKORY2>Y3>Y4>Y5>Y1Y2Y1The GRA methodY2>Y4>Y5>Y1>Y3Y2Y3The developed methodY2>Y5>Y3>Y4>Y1Y2Y1


### 4.2. Comparative Analysis

In this part, our developed method is compared with some other methods to illustrate its superiority.First of all, our presented method is compared with IVIFWA and IVIFWG operators [44]. For the IVIFWA operator, the calculated result is SY1=0.4364, SY2=0.5806, SY3=0.4852, SY4=0.4941, and SY5=0.4752. Thus, the ranking order is Y2>Y4>Y3>Y5>Y1. For the IVIFWG operator, the calculated result is SY1=0.4197, SY2=0.5708, SY3=0.4762, SY4=0.4673, and SY5=0.4733. So, the ranking order is Y2>Y3>Y5>Y4>Y1.Furthermore, our presented method is compared with the modified VIKOR method with IVIFSs [55]. Then, we can obtain the calculation result. The closest ideal score values are determined as CI∗Y1=1.0000, CI∗Y2=0.1705, CI∗Y3=0.3404, CI∗Y4=0.6723, and CI∗Y5=0.4065. And the farthest worst score values are determined as CI−Y1=0.0000, CI−Y2=0.5103, CI−Y3=0.7247, CI−Y4=0.1856, and CI−Y5=0.1139. Then, each alternative’s relative closeness is calculated as DRC1=1.0000, DRC2=0.2652, DRC3=0.3265, DRC4=0.7982, and DRC5=0.8077. Hence, the ranking order of alternatives is Y2>Y3>Y4>Y5>Y1.In the end, our presented method is compared with GRA-based IVIFSs [56]. Then, we can obtain the calculation result. The grey relational grades of each alternative are calculated as γ1=0.8398, γ2=1.0000, γ3=0.8307, γ4=0.8821, and γ5=0.8672. Therefore, the ranking order of alternatives is Y2>Y4>Y5>Y1>Y3.Eventually, the results of dissimilar methods are recorded in Table12.Derived from Table12, it is evident that the optimal wireless sensor network is Y2 in the mentioned methods, while the worst choice is Y1 in most situations. In other words, these methods’ ranking results are slightly different. Different methods could effectively tackle MAGDM issues from different kinds of angles. IVIFWA and IVIFWG operators emphasize to aggregate evaluation information. The modified VIKOR method with IVIFSs emphasizes the closest to the ideal solution and the farthest to the worst solution. The GRA-based IVIFSs emphasize the degree of similarity or difference between two sequences on the basis of the relation. However, our developed method emphasizes to calculate the expected function from the average solution. Compared with the aforementioned methods, it is more practical and effective since the procedures of calculation are simpler, and it is more convenient to apply to the practical situations.


## 4.1. An Empirical Example

With the development of research on wireless technique and other related techniques, wireless sensor networks (WSNs) have been widely used in various applications which involve diverse working environments, monitoring objects, and data conditions. Different applications require different quality of service (QoS) for data collection and data transmission. Thus, it is essential to provide QoS guarantee mechanisms in WSNs to achieve good performance in various applications. Accordingly, it is of great significance to study the QoS guarantee mechanisms in WSNs. In general terms, the QoS of WSNs focuses on timeliness and reliability of data transmission, as well as coverage and connectivity of the network topology for data collection. The QoS guarantee implementation relies on different mechanisms in WSNs. Although many methods and techniques have been proposed in the existing literature, the QoS guarantee mechanism is still faced with the following challenges in complex applications: (1) there exist several types of data traffic which have different QoS requirements. Therefore, a multiple-level QoS guarantee mechanism is in great demand. (2) There could be multiple QoS requirements for one data traffic. Thus, it is necessary to provide multiple-QoS guarantee mechanisms for theses traffics. (3) Since the traffic distributes are nonuniform in space and time, a method for the efficient transmission in a dynamic traffic is required. (4) There exists nonuniform replacement of the nodes as well as dynamic and changeful topology in many applications of the WSN. It is necessary to provide an efficient deployment method to satisfy the requirement of effectively covering. In this chapter, an empirical example for evaluating the service quality of wireless sensor networks which considered the complex MAGDM issues [47–54] will be provided by making use of the IVIF-EDAS method. Thus, in such a section, we present a numerical example to assess computer network systems with IVIFNs in order to show the designed method. There are five wireless sensor networks Aii=1,2,3,4,5 to select. The expert group selects four attributes to evaluate these five wireless sensor networks: ① G1 is the product quality factor; ② G2 is the technology factor; ③ G3 is the delivery factor; and ④ G4 is the price factor. Taking its own business development into consideration, a company wants to choose a wireless sensor network. There are five potential wireless sensor networks Yii=1,2,3,4,5. In order to select the optimal wireless sensor network, the expert group invites five experts D=D1,D2,D3,D4,D5 (expert’s weight d=1/5,1/5,1/5,1/5,1/5) to assess these wireless sensor networks. All experts give their assessment information depending on the four subsequently attributes: ① Z1 is the traffic convenience; ② Z2 is the product price; ③ Z3 is the green environmental protection ability; and ④ Z4 is the service quality. Evidently, Z2 is the g cost attribute, while Z1, Z3, and Z4 are the benefit attributes. To obtain the optimal wireless sensor network, the calculating procedures are involved:Step 1: set up each decision maker’s IVIFN evaluation matrixQk=qijkm×ni=1,2,…,m,j=1,2,…,n as in Tables 1–5. Derived from these tables and equations (12)–(14), the overall IVIFN decision matrix could be calculated. The results are recorded in Table 6.Table 1
IVIFN evaluation information byD1.
Z1Z2Z3Z4Y1([0.35, 0.38], [0.58, 0.62])([0.21, 0.31], [0.33, 0.69])([0.24, 0.33], [0.41, 0.66])([0.32, 0.43] [0.45, 0.57)Y2([0.29, 0.39] [0.44, 0.61])([0.28, 0.34], [0.46, 0.64])([0.11, 0.25], [0.32, 0.75])([0.39, 0.44], [0.52, 0.61])Y3([0.40, 0.49], [0.51, 0.60])([0.33, 0.51], [0.53, 0.67])([0.44, 0.50], [0.52, 0.56])([0.28, 0.39], [0.61, 0.72])Y4([0.33, 0.48], [0.54, 0.67])([0.42, 0.49], [0.51, 0.58])([0.41, 0.44], [0.46, 0.59])([0.41, 0.46], [0.49, 0.53])Y5([0.26, 0.48], [0.61, 0.74])([0.42, 0.47], [0.52, 0.58])([0.41, 0.48], [0.51, 0.59])([0.38, 0.53], [0.55, 0.62])Table 2
IVIFN evaluation information byD2.
Z1Z2Z3Z4Y1([0.38, 0.42], [0.55, 0.62])([0.43, 0.49], [0.51, 0.57])([0.29, 0.39], [0.59, 0.71])([0.45, 0.48], [0.50, 0.55])Y2([0.37, 0.48], [0.56, 0.63])([0.34, 0.44], [0.51, 0.66])([0.46, 0.50], [0.52, 0.54])([0.39, 0.48], [0.50, 0.61])Y3([0.37, 0.50], [0.54, 0.63])([0.27, 0.39], [0.67, 0.73])([0.41, 0.52], [0.54, 0.59])([0.16, 0.33], [0.72, 0.84])Y4([0.46, 0.49], [0.52, 0.54])([0.32, 0.38], [0.56, 0.68])([0.37, 0.43], [0.47, 0.63])([0.29, 0.34], [0.68, 0.71])Y5([0.40, 0.48], [0.52, 0.60])([0.46, 0.49], [0.51, 0.54])([0.42, 0.47], [0.55, 0.58])([0.33, 0.38], [0.62, 0.67])Table 3
IVIFN evaluation information byD3.
Z1Z2Z3Z4Y1([0.44, 0.48], [0.52, 0.56])([0.38, 0.42], [0.48, 0.62])([0.31, 0.42], [0.59, 0.69])([0.40, 0.49], [0.58, 0.60])Y2([0.38, 0.42], [0.59, 0.62])([0.35, 0.43], [0.58, 0.65])([0.42, 0.48], [0.52, 0.58])([0.26, 0.33], [0.59, 0.74)Y3([0.35, 0.42], [0.59, 0.65])([0.48, 0.50], [0.51, 0.52])([0.18, 0.36], [0.64, 0.82])([0.38, 0.43], [0.56, 0.62])Y4([0.27, 0.34], [0.59, 0.73])([0.26, 0.43], [0.62, 0.74])([0.38, 0.46], [0.52, 0.62])([0.31, 0.45], [0.62, 0.69])Y5([0.46, 0.51], [0.52, 0.54])([0.44, 0.51], [0.52, 0.56])([0.34, 0.45], [0.62, 0.66])([0.35, 0.45], [0.55, 0.65])Table 4
IVIFN evaluation information byD4.
Z1Z2Z3Z4Y1([0.42, 0.48], [0.51, 0.58])([0.37, 0.44], [0.59, 0.63])([0.25, 0.37], [0.68, 0.75])([0.22, 0.35], [0.67, 0.78])Y2([0.41, 0.49], [0.52, 0.59])([0.36, 0.39], [0.49, 0.64])([0.27, 0.43], [0.65, 0.73])([0.42, 0.45], [0.52, 0.58])Y3([0.43, 0.48], [0.52, 0.57])([0.42, 0.48], [0.52, 0.58])([0.41, 0.48], [0.54, 0.59])([0.34, 0.49], [0.58, 0.66])Y4([0.32, 0.43], [0.64, 0.67])([0.32, 0.43], [0.59, 0.68])([0.36, 0.39], [0.58, 0.64])([0.15, 0.39], [0.64, 0.85])Y5([0.37, 0.45], [0.56, 0.63])([0.36, 0.45], [0.55, 0.64])([0.42, 0.50] [0.52, 0.58])([0.27, 0.45], [0.65, 0.73])Table 5
IVIFN evaluation information byD5.
Z1Z2Z3Z4Y1([0.63, 0.66], [0.69, 0.37])([0.45, 0.46], [0.48, 0.55])([0.39, 0.45], [0.59, 0.61])([0.43, 0.47], [0.54, 0.57])Y2([0.43, 0.47], [0.52, 0.57])([0.37, 0.43], [0.59, 0.63])([0.40, 0.50], [0.52, 0.60])([0.41, 0.48], [0.52, 0.59])Y3([0.47, 0.49], [0.51, 0.53])([0.29, 0.35], [0.65, 0.71])([0.42, 0.48], [0.53, 0.58])([0.27, 0.43], [0.67, 0.73])Y4([0.41, 0.49], [0.52, 0.59])([0.43, 0.47], [0.52, 0.57])([0.46, 0.48], [0.52, 0.54])([0.19, 0.38], [0.67, 0.81])Y5([0.33, 0.45], [0.64, 0.67])([0.48, 0.50], [0.51, 0.52])([0.44, 0.46], [0.53, 0.56])([0.21, 0.37], [0.68, 0.79])Table 6
Overall IVIFN evaluation information.
Z1Z2Z3Z4Y1([0.4341, 0.4442], [0.5051, 0.5233])([0.4722, 0.4833], [0.4901, 0.5189])([0.2798, 0.2980], [0.6087, 0.6455])([0.4376, 0.4521], [0.5475, 0.5499])Y2([0.5341, 0.5365], [0.4152, 0.42532)([0.5502, 0.5708], [0.4209, 0.4429])([0.6432, 0.6679], [0.3807, 0.3988])([0.5908, 0.6213], [0.3216, 0.4453])Y3([0.4325, 0.4365], [0.5472, 0.5711])([0.4029, 0.4233], [0.5120, 0.5431])([0.4458, 0.4687], [0.4897, 0.4988])([0.3246, 0.4362], [0.2109, 0.4907])Y4([0.5231, 0.5433], [0.4761, 0.4866])([0.4877, 0.4902], [0.4211, 0.4766])([0.5765, 0.5870], [0.4211, 0.4465])([0.3287, 0.4309], [0.4870, 0.4998])Y5([0.4168, 0.4561], [0.5232, 0.5690])([0.4907, 0.5142], [0.4606, 0.4980])([0.4755, 0.5219], [0.4658, 0.4785])([0.4598, 0.4622], [0.1121, 0.2366])Step 2: normalize the evaluation matrixQ=qijm×n to QN=qijNm×n (see Table 7).Table 7
The normalized IVIFN evaluation information.
Z1Z2Z3Z4Y1([0.4341, 0.4442], [0.5051, 0.5233])([0.4901, 0.5189], [0.4722, 0.4833])([0.2798, 0.2980], [0.6087, 0.6455)])([0.4376, 0.4521], [0.5475, 0.5499])Y2([0.5341, 0.5365], [0.4152, 0.42532])([0.4209, 0.4429], [0.5502, 0.5708])([0.6432, 0.6679], [0.3807, 0.3988])([0.5908, 0.6213], [0.3216, 0.4453])Y3([0.4325, 0.4365] [0.5472, 0.5711)([0.5120, 0.5431], [0.4029, 0.4233])([0.4458, 0.4687], [0.4897, 0.4988]([0.3246, 0.4362], [0.2109, 0.4907])Y4([0.5231, 0.5433], [0.4761, 0.4866])([0.4211, 0.4766], [0.4877, 0.4902])([0.5765, 0.5870], [0.4211, 0.4465])([0.3287, 0.4309], [0.4870, 0.4998])Y5([0.4168, 0.4561], [0.5232, 0.5690])([0.4606, 0.4980], [0.4907, 0.5142])([0.4755, 0.5219], [0.4658, 0.4785])([0.4598, 0.4622], [0.1121, 0.2366])Step 3: decide the attribute weightszjj=1,2,…,n by making use of the CRITIC method as recorded in Table 8.Table 8
The attribute weightszj.
Z1Z2Z3Z4Zj0.13110.21620.22330.4094Step 4: depending on the calculated results of Table8, the value of average solution (AV) can be obtained on the basis of all proposed attributes by equations (19) and (20) (see Table 9).Table 9
The value of average solution.
Average solutionZ1([0.4286, 0.4782], [0.4784, 0.5231])Z2([0.5219, 0.5690], [0.4221, 0.4410])Z3([0.4522, 0.4897], [0.4588, 0.5099])Z4([0.4308, 0.4906], [0.3265, 0.4128])Step 5: relying on the results of AV, the PDA and NDA can be calculated by utilizing equations (21) and (22) (see Tables 10 and 11).Table 10
The results ofPDAij.
Z1Z2Z3Z4Y10.00000.00540.00000.0000Y20.12360.00000.28330.3164Y30.00000.14360.00000.0000Y40.09290.00000.15650.0000Y50.00000.00000.00000.0000Table 11
The results ofNDAij.
Z1Z2Z3Z4Y10.00840.00000.38750.0288Y20.00000.14770.00000.0000Y30.09380.00000.12520.0245Y40.00000.00380.00000.3567Y50.12930.03680.03590.0046Step 6: on the basis of equation (23) and attribute weighting vector ω=0.1311,0.2162,0.2233,0.4094, the values of SPi and SNi can be calculated:(26)SP1=0.0018,SP2=0.2063,SP3=0.0375,SP4=0.0659,SP5=0.0000,SN1=0.1379,SN2=0.0356,SN3=0.0689,SN4=0.1052,SN5=0.0338.Step 7: the results of Step 6 could be normalized by equation (24):(27)NSP1=0.0063,NSP2=1.0000,NSP3=0.1200,NSP4=0.3037,NSP5=0.0000,NSN1=0.0000,NSN2=0.7528,NSN3=0.5462,NSN4=0.1982,NSN5=0.7361.Step 8: o n the basis of each alternative’sNSPi and NSNi, the values of AS are calculated:(28)AS1=0.0038,AS2=0.8715,AS3=0.3581,AS4=0.2613,AS5=0.3732.Step 9: according to the AS, all the alternatives can be ranked; the higher the value of AS is, the optimal alternative will be selected. Evidently, the rank of these five alternatives isY2>Y5>Y3>Y4>Y1, and Y2 is the best wireless sensor network.Table 12
Evaluation results of dissimilar methods.
MethodsRanking orderThe optimal alternativeThe worst alternativeIVIFWAY2>Y4>Y3>Y5>Y1Y2Y1IVIFWGY2>Y3>Y5>Y4>Y1Y2Y1The modified VIKORY2>Y3>Y4>Y5>Y1Y2Y1The GRA methodY2>Y4>Y5>Y1>Y3Y2Y3The developed methodY2>Y5>Y3>Y4>Y1Y2Y1


## 4.2. Comparative Analysis

In this part, our developed method is compared with some other methods to illustrate its superiority.First of all, our presented method is compared with IVIFWA and IVIFWG operators [44]. For the IVIFWA operator, the calculated result is SY1=0.4364, SY2=0.5806, SY3=0.4852, SY4=0.4941, and SY5=0.4752. Thus, the ranking order is Y2>Y4>Y3>Y5>Y1. For the IVIFWG operator, the calculated result is SY1=0.4197, SY2=0.5708, SY3=0.4762, SY4=0.4673, and SY5=0.4733. So, the ranking order is Y2>Y3>Y5>Y4>Y1.Furthermore, our presented method is compared with the modified VIKOR method with IVIFSs [55]. Then, we can obtain the calculation result. The closest ideal score values are determined as CI∗Y1=1.0000, CI∗Y2=0.1705, CI∗Y3=0.3404, CI∗Y4=0.6723, and CI∗Y5=0.4065. And the farthest worst score values are determined as CI−Y1=0.0000, CI−Y2=0.5103, CI−Y3=0.7247, CI−Y4=0.1856, and CI−Y5=0.1139. Then, each alternative’s relative closeness is calculated as DRC1=1.0000, DRC2=0.2652, DRC3=0.3265, DRC4=0.7982, and DRC5=0.8077. Hence, the ranking order of alternatives is Y2>Y3>Y4>Y5>Y1.In the end, our presented method is compared with GRA-based IVIFSs [56]. Then, we can obtain the calculation result. The grey relational grades of each alternative are calculated as γ1=0.8398, γ2=1.0000, γ3=0.8307, γ4=0.8821, and γ5=0.8672. Therefore, the ranking order of alternatives is Y2>Y4>Y5>Y1>Y3.Eventually, the results of dissimilar methods are recorded in Table12.Derived from Table12, it is evident that the optimal wireless sensor network is Y2 in the mentioned methods, while the worst choice is Y1 in most situations. In other words, these methods’ ranking results are slightly different. Different methods could effectively tackle MAGDM issues from different kinds of angles. IVIFWA and IVIFWG operators emphasize to aggregate evaluation information. The modified VIKOR method with IVIFSs emphasizes the closest to the ideal solution and the farthest to the worst solution. The GRA-based IVIFSs emphasize the degree of similarity or difference between two sequences on the basis of the relation. However, our developed method emphasizes to calculate the expected function from the average solution. Compared with the aforementioned methods, it is more practical and effective since the procedures of calculation are simpler, and it is more convenient to apply to the practical situations.


## 5. Conclusion

In this paper, IVIF-EDAS method is developed to tackle the MAGDM issues based on the description of the EDAS method and some fundamental notions of IVIFSs. To begin with, the fundamental information of IVIFSs is simply introduced. After that, the IVIFWA and IVIFWG operators are utilized to integrate the IVIFNs. Subsequently, relying on the CRITIC method, the attributes’ weights are decided. In addition, applying the EDAS method to the IVIFSs, a new method is designed, and the calculating procedures are listed in detail. Finally, an application for assessing the service quality of wireless sensor networks has been given to show the superiority of this novel method, and comparative analysis between the IVIF-EDAS method and some other methods could also be made to further verify some merits of such a method. In our future works, the EDAS method and the CRITIC method will be extensively applied in different uncertain and ambiguous environments [57–67].



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*Source: 5391940-2020-07-22.xml*