# An Integrated CoCoSo-CRITIC-Based Decision-Making Framework for Quality Evaluation of Innovation and Entrepreneurship Education in Vocational Colleges with Intuitionistic Fuzzy Information

Authors: Chang Gou
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

This paper proposes a multiattribute group decision-making (MAGDM) based on the CoCoSo method under the intuitionistic fuzzy sets (IFSs) environment for quality evaluation of innovation and entrepreneurship education (IEE) in vocational colleges. First of all, this paper extends the CoCoSo to the IFSs environment. Second, a new MAGDM model for quality evaluation of IEE in vocational colleges based on the CoCoSo algorithm is built. In this algorithm, the attribute weight is derived by subjective weight and objective weight, and the objective weights are defined by using the CRITIC method. At the end of this given study, some comparisons are given to verify the decision effectiveness of the algorithm.


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## Body

## 1. Introduction

Along with daily growing decision complications and ambiguity and things’ fuzziness of contemporary human subjective information cognition, there are new and increasingly arduous for DMs to offer real exact assessments [1–3]. So as to derive a better decision choice of MADM which depicted qualitative decision choice [4, 5], Zadeh [6] built the fuzzy sets (FSs) to study not exact information [7, 8]. Furthermore, the intuitionistic fuzzy sets (IFSs) [9] were built. The most common intuitionistic fuzzy decision methods are the GRA method [10], TOPSIS method [11], EDAS method [12], and so on. Different from the above methods, there are three different aggregation strategies to derive better results in the CoCoSo method [13]. In addition, each strategy will give a score index and then get a complete ranking through the score of each data [13]. Zavadskas et al. [14] studied new operational research technologies and MADM tools. No one has adopted the CoCoSo method to solve the decision-making of TPD. Consequently, the CoCoSo method was employed in this study. This study presents a given MAGDM model which determines the objective of the criteria weight through improved CRITIC and selects the most suitable public charging service sections by the CoCoSo. This study proposes three contributions as follows: This paper presents a new MAGDM with the CoCoSo method and CRITIC methods under IFSs. Both the weights of subjective information of experts and objective information of schemes are considered in the operator. The attributes of the decision scheme and their weights can be changed. This model is still applicable if the decision-maker’s preference for the scheme changes with the change in time and development trend. The new MAGDM model for quality evaluation of IEE in vocational colleges based on the IF-CoCoSo algorithm is built.The whole studies thread is as follows: Section2 gives a literature review; Section 3 introduces the IFSs; Section 4 builds the MAGDM based on the CoCoSo method under IFSs; Section 5 illustrates a fresh example for quality evaluation of IEE in vocational colleges to prove the decision practicability; Section 6 gives the comparison analysis.


## 2. Literature Review

### 2.1. IFSs

Zadeh [15] designed the FSs. Atanassov [9] proposed the IFSs. The IFSs represented the membership, nonmembership, and hesitation [16–19]. Gou et al. [20] proposed the exponential algorithm for IFSs and proved its effectiveness. Based on the Dombi operations, Liu et al. [21] extended the BM operator and then obtained some feasible intuitionistic fuzzy operators. Gupta et al. [22] extended entropy to the intuitionistic fuzzy environment and demonstrated the importance of parameter alpha to the conclusion. Zhang and He [23] defined the t-norm and the corresponding t-conorm to explain the concept of geometric interactive aggregation operators under IFSs. He et al. [24] applied the power decision operators to IFSs environments. Li and Wu [25] put forward cross entropy decision distance and the GRA method under IFSs. Bao et al. [26] studied the evidential reasoning and prospect theory in the IFSs context. Chen et al. [27] extended the TOPSIS and similarity measurement decision for the MCDM method in IFSs. Gan and Luo [28] used the IFSs and DEMATEL to test whether there is a significant causal relationship. Gupta et al. [29] amended the SIR method in the context of IFSs. Rouyendegh [30] innovatively applied the ELECTRE decision method to the IFSs environment. Phochanikorn and Tan [31] incorporated DEMATE-VIKOR under IFSs. Krishankumar et al. [32] first proposed PROMETHEE under IFSs.


### 2.2. CoCoSo

The CoCoSo method was first suggested by Yazdani et al. [13] in 2018; it is based on a comprehensive product model of simple additive weighting and exponential weighting. The CoCoSo was generalized to many practical cases. Peng et al. [33] not only used the CoCoSo and CRITIC method to evaluate the 5G information industry but also adopted the novel q-ROF score function and CoCoSo methods [34] for financial risk evaluation. Yazdani et al. [13] utilized the CoCoSo information method to study logistics centers’ locations. Yazdani et al. [35] put forward a compromise method that combines the grey number and CoCoSo method to objectively measure supplier performance. Erceg et al. [36] proposed the interval rough CoCoSo for inventory management in storage systems. However, we still encounter some practical decision problems with complex data during the real decision process. In order to handle these complex information, the CoCoSo method is successfully proposed under the IFSs soft decision environment [37], hesitant fuzzy soft decision environment [38], and bipolar complex fuzzy sets environment [39].


## 2.1. IFSs

Zadeh [15] designed the FSs. Atanassov [9] proposed the IFSs. The IFSs represented the membership, nonmembership, and hesitation [16–19]. Gou et al. [20] proposed the exponential algorithm for IFSs and proved its effectiveness. Based on the Dombi operations, Liu et al. [21] extended the BM operator and then obtained some feasible intuitionistic fuzzy operators. Gupta et al. [22] extended entropy to the intuitionistic fuzzy environment and demonstrated the importance of parameter alpha to the conclusion. Zhang and He [23] defined the t-norm and the corresponding t-conorm to explain the concept of geometric interactive aggregation operators under IFSs. He et al. [24] applied the power decision operators to IFSs environments. Li and Wu [25] put forward cross entropy decision distance and the GRA method under IFSs. Bao et al. [26] studied the evidential reasoning and prospect theory in the IFSs context. Chen et al. [27] extended the TOPSIS and similarity measurement decision for the MCDM method in IFSs. Gan and Luo [28] used the IFSs and DEMATEL to test whether there is a significant causal relationship. Gupta et al. [29] amended the SIR method in the context of IFSs. Rouyendegh [30] innovatively applied the ELECTRE decision method to the IFSs environment. Phochanikorn and Tan [31] incorporated DEMATE-VIKOR under IFSs. Krishankumar et al. [32] first proposed PROMETHEE under IFSs.


## 2.2. CoCoSo

The CoCoSo method was first suggested by Yazdani et al. [13] in 2018; it is based on a comprehensive product model of simple additive weighting and exponential weighting. The CoCoSo was generalized to many practical cases. Peng et al. [33] not only used the CoCoSo and CRITIC method to evaluate the 5G information industry but also adopted the novel q-ROF score function and CoCoSo methods [34] for financial risk evaluation. Yazdani et al. [13] utilized the CoCoSo information method to study logistics centers’ locations. Yazdani et al. [35] put forward a compromise method that combines the grey number and CoCoSo method to objectively measure supplier performance. Erceg et al. [36] proposed the interval rough CoCoSo for inventory management in storage systems. However, we still encounter some practical decision problems with complex data during the real decision process. In order to handle these complex information, the CoCoSo method is successfully proposed under the IFSs soft decision environment [37], hesitant fuzzy soft decision environment [38], and bipolar complex fuzzy sets environment [39].


## 3. Preliminaries

### 3.1. IFSs

Atanassov [9] proposed the IFSs.Definition 1.
(see [40]). Let X be the nonempty information set; the IFS is defined as(1)A=<axi,μAaxi,vAaxi>|axi∈X,where μAaxi∈0,1 and vAaxi∈0,1 represent the membership and given nonmembership of axi∈X to A, and(2)0≤μAaxi+vAaxi≤1,axi∈X.
α=aμ,av is called the given intuitionistic fuzzy number(IFN). The πAax is named the uncertainty of x to A40:(3)πAax=1−μAax−vAax,∀ax∈X.Definition 2.
(see [41]). Let α=aμ,av be the IFN, then the defined score function is(4)SFα=2aμ+av−1,SFα∈0,1.Definition 3.
(see [42]). Let α=aμ,av be IFN, then the accuracy function is(5)AFa=aμ+av,AFa∈0,1.Definition 4.
(see [43]). α1=aμ1,av1 and α2=aμ2,av2 are two IFSs; then,(6)α1⊕α2=aμ1+aμ2−aμ1aμ2,av1av2,α1⊗α2=aμ1aμ2,av1+av2−av1av2,λα=1−1−aμλ,avλ,λ>0,αλ=aμλ,1−1−avλ,λ>0.Definition 5.
(see [44]). α1=aμ1,av1 and α2=aμ2,av2 are two IFSs; the Hamming distance is(7)HDα1,α2=12aμ1−aμ2+av1−av2+aπ1−aπ2.Definition 6.
(see [45]). Suppose that αj=aμj,avj,j=1,2,…,s; let IFWA: Qn⟶Q, then(8)IFWAxwα1,α2,…,αs=⊕j=1sxwjαj=1−∏j=1s1−aμjxwj,∏j=1savjxwj.
xw=xw1,xw2,…,xwsT is weight of αj=aμj,avj, and xwj>0,∑j=1sxwj=1.Definition 7.
(see [46]). Suppose that αj=aμj,avj,j=1,2,…,s; let IFWG: Qn⟶Q, then(9)IFWGxwα1,α2,…,αs=⊗j=1sαjxwj=∏j=1saμjxwj,1−∏j=1s1−avjxwj,xw=xw1,xw2,…,xwsT is weight of αj=aμj,avj, and xwj>0,∑j=1sxwj=1.


## 3.1. IFSs

Atanassov [9] proposed the IFSs.Definition 1.
(see [40]). Let X be the nonempty information set; the IFS is defined as(1)A=<axi,μAaxi,vAaxi>|axi∈X,where μAaxi∈0,1 and vAaxi∈0,1 represent the membership and given nonmembership of axi∈X to A, and(2)0≤μAaxi+vAaxi≤1,axi∈X.
α=aμ,av is called the given intuitionistic fuzzy number(IFN). The πAax is named the uncertainty of x to A40:(3)πAax=1−μAax−vAax,∀ax∈X.Definition 2.
(see [41]). Let α=aμ,av be the IFN, then the defined score function is(4)SFα=2aμ+av−1,SFα∈0,1.Definition 3.
(see [42]). Let α=aμ,av be IFN, then the accuracy function is(5)AFa=aμ+av,AFa∈0,1.Definition 4.
(see [43]). α1=aμ1,av1 and α2=aμ2,av2 are two IFSs; then,(6)α1⊕α2=aμ1+aμ2−aμ1aμ2,av1av2,α1⊗α2=aμ1aμ2,av1+av2−av1av2,λα=1−1−aμλ,avλ,λ>0,αλ=aμλ,1−1−avλ,λ>0.Definition 5.
(see [44]). α1=aμ1,av1 and α2=aμ2,av2 are two IFSs; the Hamming distance is(7)HDα1,α2=12aμ1−aμ2+av1−av2+aπ1−aπ2.Definition 6.
(see [45]). Suppose that αj=aμj,avj,j=1,2,…,s; let IFWA: Qn⟶Q, then(8)IFWAxwα1,α2,…,αs=⊕j=1sxwjαj=1−∏j=1s1−aμjxwj,∏j=1savjxwj.
xw=xw1,xw2,…,xwsT is weight of αj=aμj,avj, and xwj>0,∑j=1sxwj=1.Definition 7.
(see [46]). Suppose that αj=aμj,avj,j=1,2,…,s; let IFWG: Qn⟶Q, then(9)IFWGxwα1,α2,…,αs=⊗j=1sαjxwj=∏j=1saμjxwj,1−∏j=1s1−avjxwj,xw=xw1,xw2,…,xwsT is weight of αj=aμj,avj, and xwj>0,∑j=1sxwj=1.


## 4. Approach to the Intuitionistic Fuzzy MAGDM-Based CoCoSo Method with CRITIC

LetXA=XA1,XA2,…,XAm be the alternatives set, XT=XT1,XT2,…,XTn the chosen attributes set with corresponding weight xw=xw1,xw2,…,xwn, where xwj∈0,1, ∑j=1nxwj=1 and a experts group XE=XE1,XE2,…,XEq with weight vector xω=xω1,xω2,…,xωt, where xωk∈0,1, ∑k=1txωk=1. Assume that decision matrix Ak=aαijkm×n, aαijk=aμijk,aνijkm×ni=1,2,…,m,j=1,2,…,n,k=1,2,…,t. The IF-CoCoSo method is used to solve MAGDM problems, which includes the following steps:Step 1.
The matrix under IFSs is described:(10)Ak=aα11k…aα1nk⋮⋱⋮aαm1k…aαmnk=aαijkm×n.Step 2.
Calculate the overall matrixX=xxijm×n, xxij=aμij,aυijm×n by the IFWA operator.(11)xxij=IFWAωaαij1,aαij2,…,aαijt=1−∏k=1t1−aμijkωk,∏k=1tavijkωk.Step 3.
Normalize the defined overall matrixX=xxijm×n to NX=nxijm×n.(12)nxij=aμij,avij,XTjis a benefit criterion,avij,aμij,XTjis a cost criterion.Step 4.
Calculate the defined weight through the CRITIC method.
The CRITIC is usually used to obtain the objective weight [47]. Mukhametzyanov [48] studied specific character for determining weights. Žižović et al. [49] studied the objective weight coefficients. The initial matrix is(13)NX=nx11…nx1n⋮⋱⋮nxm1⋯nxmn=nxijm×n=aμij,aυijm×n.(1)
Depending on the NX, the score function is defined.(14)SFnxij=2aμij+avij−1.(2)
Calculate the defined correlation coefficientρjk:(15)nx¯j=1m∑i=1mSFnxij,ρjk=∑i=1mSFnxij−nx¯jSFnxik−nx¯k∑i=1mSFnxij−nx¯j2∑i=1mSFnxik−nx¯k2.(3)
Obtain the built standard deviation (σj) and the index (C) for given attributes:(16)σj=1m−1∑i=1mSFnxij−nx¯j2,Cj=σj∑k=1n1−ρjk.(4)
Obtain the objective weight:(17)xwj=Cj∑j=1nCj;j=1,…,n.Step 5.
Obtain the weighted comparability sequenceIFSi.(18)IFSi=∑j=1nxwj×SFnxij.Step 6.
The sum of weights of comparability seriesIFPi.(19)IFPi=∑j=1nSFnxijxwj.Step 7.
The three aggregation modes are utilized to comprehensively calculate the given relative importance by the following equations(20)IFKAi=IFPi+IFSi∑i=1mIFPi+IFSi.(21)IFKBi=IFSiminiIFSi+IFPiminIFPi.(22)IFKCi=λIFSi+1−λIFPiλmaxiIFSi+1−λmaxIFPi,0≤λ≤1,where IFKAi is the given arithmetic mean, IFKBi is the sum of the given relative scores, and IFKCi is the given balanced compromise.Step 8.
Obtain the assessment valueIFKi by the following equation.(23)IFKi=IFKAiIFKBiIFKBi3+IFKAi+IFKBi+IFKBi3.Step 9.
Sort the designed alternatives throughIFKi, and the higher the IFKi, the better the designed alternative is.


## 5. Numerical Example and Some Comparative Studies

### 5.1. Numerical Example

Nowadays, many higher vocational colleges have many outstanding problems in the process of carrying out IEE, which seriously affect the effectiveness of IEE. The main reason for these problems is that in some higher vocational colleges still insufficient attention has been paid to the given development of IEE, the popularity of IEE is not high, and a good cultural atmosphere of innovation and entrepreneurship has not yet been formed. In addition, the concept of IEE in some higher vocational colleges lags behind slightly, and IEE has not been integrated into the talent training system of higher vocational colleges. The links are out of touch, resulting in the lack of continuity and systematization of the entire educational practice. There are also some higher vocational colleges whose IEE activities are mere formalities. The lack of teachers and the lack of IEE awareness and educational ability have also led to the failure of higher vocational colleges to form a good innovation and entrepreneurship system. The key to the root cause of this problem is that higher vocational colleges lack a feasible evaluation index system for innovation and entrepreneurship quality, so they cannot guide the development direction of IEE in vocational colleges and cannot guarantee the quality of IEE in higher vocational colleges. This is because education evaluation itself is an effective way to control the quality of IEE. Only through scientific and reasonable education evaluation work can we timely find out whether the IEE work in vocational colleges deviates from the actual development direction so as to give corrective measures in a timely manner. To ensure that all IEE activities are always centered on the expected educational goals, while improving the effectiveness of IEE activities in higher vocational colleges, it also promotes the healthy and stable development of IEE in higher vocational colleges. A point in case that the quality evaluation of IEE in vocational colleges under IFNs is used to depict the built methods. There are five vocational collegesVCii=1,2,3,4,5 to choose from. The experts found four selected attributes to depict these vocational colleges: XT1 represents course teaching quality; XT2 means practical teaching; XT3 represents the quality of the teaching staff; and XT4 means the IEE achievements. The quality evaluation of IEE in vocational colleges is evaluated with IFNs (whose weight xw=0.35,0.40,0.25); the five vocational colleges is evaluated by four DMs XEk (expert’s weight xωk=0.18,0.34,0.26,0.22T) using four criteria in the context of IFSs.Then, we employ the developed algorithm (λ=0.5) to choose outstanding vocational colleges under IFSs. The specific calculation steps are given.Step 10.
The assessed matrixAk=αijk5×4 is shown in Tables 1–3.Table 1
The assessed matrix through the first DM.
AlternativesXT1XT2XT3XT4VC1(0.5, 0.3)(0.7, 0.1)(0.7, 0.3)(0.4, 0.5)VC2(0.7, 0.2)(0.5, 0.3)(0.6, 0.2)(0.6, 0.4)VC3(0.8, 0.1)(0.6, 0.4)(0.6, 0.3)(0.8, 0.1)VC4(0.6, 0.4)(0.6, 0.2)(0.5, 0.5)(0.5, 0.3)VC5(0.8, 0.1)(0.8, 0.2)(0.8, 0.1)(0.3, 0.6)Table 2
The assessed matrix through the second DM.
AlternativesXT1XT2XT3XT4VC1(0.6, 0.3)(0.8, 0.1)(0.8, 0.1)(0.7, 0.2)VC2(0.7, 0.2)(0.7, 0.2)(0.7, 0.2)(0.6, 0.4)VC3(0.8, 0.1)(0.6, 0.3)(0.6, 0.3)(0.5, 0.5)VC4(0.7, 0.1)(0.5, 0.4)(0.5, 0.4)(0.7, 0.2)VC5(0.6, 0.3)(0.7, 0.3)(0.7, 0.3)(0.6, 0.3)Table 3
The assessed matrix through the third DM.
AlternativesXT1XT2XT3XT4VC1(0.7, 0.2)(0.6, 0.2)(0.5, 0.3)(0.6, 0.4)VC2(0.8, 0.1)(0.6, 0.4)(0.4, 0.5)(0.7, 0.1)VC3(0.9, 0.1)(0.8, 0.1)(0.6, 0.3)(0.8, 0.1)VC4(0.6, 0.3)(0.7, 0.2)(0.8, 0.1)(0.5, 0.4)VC5(0.7, 0.3)(0.7, 0.2)(0.7, 0.3)(0.7, 0.2)Step 11.
Calculate the overall information matrix (Table4) by equation (12).Table 4
The overall matrix.
AlternativesXT1XT2XT3XT4VC1(0.72, 0.21)(0.72, 0.14)(0.69, 0.21)(0.24, 0.51)VC2(0.71, 0.19)(0.62, 0.28)(0.53, 0.46)(0.37, 0.57)VC3(0.80, 0.14)(0.71, 0.22)(0.59, 0.47)(0.29, 0.60)VC4(0.64, 0.17)(0.62, 0.28)(0.68, 0.28)(0.37, 0.59)VC5(0.69, 0.25)(0.70, 0.25)(0.69, 0.32)(0.47, 0.53)Step 12.
The given cost attributes are transformed into given benefit attributes (Table5).Table 5
The normalized matrixNX.
AlternativesXT1XT2XT3XT4VC1(0.72, 0.21)(0.72, 0.14)(0.69, 0.21)(0.51, 0.24)VC2(0.71, 0.19)(0.62, 0.28)(0.53, 0.46)(0.57, 0.37)VC3(0.80, 0.14)(0.71, 0.22)(0.59, 0.47)(0.60, 0.29)VC4(0.64, 0.17)(0.62, 0.28)(0.68, 0.28)(0.59, 0.37)VC5(0.69, 0.25)(0.70, 0.25)(0.69, 0.32)(0.53, 0.47)Step 13.
The normalized score information are given in Table6.Table 6
The normalized score matrix.
AlternativesXT1XT2XT3XT4VC10.640.580.580.00VC20.620.530.520.31VC30.730.640.660.17VC40.450.530.650.32VC50.630.660.710.48Step 14.
The definedρjk is(24)ρij=1.000.68−0.04−0.320.681.000.690.14−0.420.691.000.460.310.140.461.00.Step 15.
The defined standard deviation is(25)σ1=0.10,σ2=0.06,σ3=0.07,σ4=0.18.
The C is determined:C1=0.25,C2=0.09,C3=0.13,C4=0.49.Step 16.
The final weight is calculated.(26)xw1=0.258,xw2=0.096,xw3=0.139,xw4=0.507.Step 17.
TheIFSi is obtained.(27)IFS1=0.30,IFS2=0.44,IFS3=0.43,IFS4=0.42,IFS5=0.57.Step 18.
TheIFPi is obtained.(28)IFP1=2.79,IFP2=3.29,IFP3=3.23,IFP4=3.25,IFP5=3.49.Step 19.
TheIFKAi,IFKBi,IFKBi are obtained (Table 7).Table 7
TheIFKAi,IFKBi,IFKBi.
IFKAiIFKBiIFKCiVC10.172.000.76VC20.202.640.92VC30.202.570.90VC40.202.550.90VC50.223.141.00Step 20.
TheIFKi is obtained.(29)IFK1=1.61,IFK2=2.05,IFK3=2.00,IFK4=1.99,IFK5=2.34.Step 21.
The ranking of alternatives is as follows (the higher theIFKi, the better the alternative i).(30)VC5≻VC4≻VC2≻VC3≻VC1.


### 5.2. Comparative Analyses

For this research, five college stadiums are selected to assess. This paper applied the IF-CoCoSo method to solve MAGDM. In order to certify the superiority of the IF-CoCoSo method more efficiently, we employed some previous decision methods (the IFWA operator [45], IFWG operator [46], IF-TOPSIS method [50], IF-GRA method [51], and IF-taxonomy method [52]). The ranking of given alternatives was recorded and is given in Table 8.Table 8
Alternative ranking under existing methods.
MethodsRankingIFWA operator [45]VC5≻VC4≻VC3≻VC2≻VC1IFWG operator [46]VC5≻VC4≻VC2≻VC3≻VC1IF-TOPSIS method [50]VC5≻VC4≻VC2≻VC3≻VC1IF-GRA method [51]VC5≻VC2≻VC3≻VC4≻VC1IF-taxonomy methodVC5≻VC2≻VC4≻VC3≻VC1Compared with the result of the CoCoSo method to other methods, consequently, Table8 shows that the results of the five application methods are basically consistent with the IF-CoCoSo algorithm.


## 5.1. Numerical Example

Nowadays, many higher vocational colleges have many outstanding problems in the process of carrying out IEE, which seriously affect the effectiveness of IEE. The main reason for these problems is that in some higher vocational colleges still insufficient attention has been paid to the given development of IEE, the popularity of IEE is not high, and a good cultural atmosphere of innovation and entrepreneurship has not yet been formed. In addition, the concept of IEE in some higher vocational colleges lags behind slightly, and IEE has not been integrated into the talent training system of higher vocational colleges. The links are out of touch, resulting in the lack of continuity and systematization of the entire educational practice. There are also some higher vocational colleges whose IEE activities are mere formalities. The lack of teachers and the lack of IEE awareness and educational ability have also led to the failure of higher vocational colleges to form a good innovation and entrepreneurship system. The key to the root cause of this problem is that higher vocational colleges lack a feasible evaluation index system for innovation and entrepreneurship quality, so they cannot guide the development direction of IEE in vocational colleges and cannot guarantee the quality of IEE in higher vocational colleges. This is because education evaluation itself is an effective way to control the quality of IEE. Only through scientific and reasonable education evaluation work can we timely find out whether the IEE work in vocational colleges deviates from the actual development direction so as to give corrective measures in a timely manner. To ensure that all IEE activities are always centered on the expected educational goals, while improving the effectiveness of IEE activities in higher vocational colleges, it also promotes the healthy and stable development of IEE in higher vocational colleges. A point in case that the quality evaluation of IEE in vocational colleges under IFNs is used to depict the built methods. There are five vocational collegesVCii=1,2,3,4,5 to choose from. The experts found four selected attributes to depict these vocational colleges: XT1 represents course teaching quality; XT2 means practical teaching; XT3 represents the quality of the teaching staff; and XT4 means the IEE achievements. The quality evaluation of IEE in vocational colleges is evaluated with IFNs (whose weight xw=0.35,0.40,0.25); the five vocational colleges is evaluated by four DMs XEk (expert’s weight xωk=0.18,0.34,0.26,0.22T) using four criteria in the context of IFSs.Then, we employ the developed algorithm (λ=0.5) to choose outstanding vocational colleges under IFSs. The specific calculation steps are given.Step 10.
The assessed matrixAk=αijk5×4 is shown in Tables 1–3.Table 1
The assessed matrix through the first DM.
AlternativesXT1XT2XT3XT4VC1(0.5, 0.3)(0.7, 0.1)(0.7, 0.3)(0.4, 0.5)VC2(0.7, 0.2)(0.5, 0.3)(0.6, 0.2)(0.6, 0.4)VC3(0.8, 0.1)(0.6, 0.4)(0.6, 0.3)(0.8, 0.1)VC4(0.6, 0.4)(0.6, 0.2)(0.5, 0.5)(0.5, 0.3)VC5(0.8, 0.1)(0.8, 0.2)(0.8, 0.1)(0.3, 0.6)Table 2
The assessed matrix through the second DM.
AlternativesXT1XT2XT3XT4VC1(0.6, 0.3)(0.8, 0.1)(0.8, 0.1)(0.7, 0.2)VC2(0.7, 0.2)(0.7, 0.2)(0.7, 0.2)(0.6, 0.4)VC3(0.8, 0.1)(0.6, 0.3)(0.6, 0.3)(0.5, 0.5)VC4(0.7, 0.1)(0.5, 0.4)(0.5, 0.4)(0.7, 0.2)VC5(0.6, 0.3)(0.7, 0.3)(0.7, 0.3)(0.6, 0.3)Table 3
The assessed matrix through the third DM.
AlternativesXT1XT2XT3XT4VC1(0.7, 0.2)(0.6, 0.2)(0.5, 0.3)(0.6, 0.4)VC2(0.8, 0.1)(0.6, 0.4)(0.4, 0.5)(0.7, 0.1)VC3(0.9, 0.1)(0.8, 0.1)(0.6, 0.3)(0.8, 0.1)VC4(0.6, 0.3)(0.7, 0.2)(0.8, 0.1)(0.5, 0.4)VC5(0.7, 0.3)(0.7, 0.2)(0.7, 0.3)(0.7, 0.2)Step 11.
Calculate the overall information matrix (Table4) by equation (12).Table 4
The overall matrix.
AlternativesXT1XT2XT3XT4VC1(0.72, 0.21)(0.72, 0.14)(0.69, 0.21)(0.24, 0.51)VC2(0.71, 0.19)(0.62, 0.28)(0.53, 0.46)(0.37, 0.57)VC3(0.80, 0.14)(0.71, 0.22)(0.59, 0.47)(0.29, 0.60)VC4(0.64, 0.17)(0.62, 0.28)(0.68, 0.28)(0.37, 0.59)VC5(0.69, 0.25)(0.70, 0.25)(0.69, 0.32)(0.47, 0.53)Step 12.
The given cost attributes are transformed into given benefit attributes (Table5).Table 5
The normalized matrixNX.
AlternativesXT1XT2XT3XT4VC1(0.72, 0.21)(0.72, 0.14)(0.69, 0.21)(0.51, 0.24)VC2(0.71, 0.19)(0.62, 0.28)(0.53, 0.46)(0.57, 0.37)VC3(0.80, 0.14)(0.71, 0.22)(0.59, 0.47)(0.60, 0.29)VC4(0.64, 0.17)(0.62, 0.28)(0.68, 0.28)(0.59, 0.37)VC5(0.69, 0.25)(0.70, 0.25)(0.69, 0.32)(0.53, 0.47)Step 13.
The normalized score information are given in Table6.Table 6
The normalized score matrix.
AlternativesXT1XT2XT3XT4VC10.640.580.580.00VC20.620.530.520.31VC30.730.640.660.17VC40.450.530.650.32VC50.630.660.710.48Step 14.
The definedρjk is(24)ρij=1.000.68−0.04−0.320.681.000.690.14−0.420.691.000.460.310.140.461.00.Step 15.
The defined standard deviation is(25)σ1=0.10,σ2=0.06,σ3=0.07,σ4=0.18.
The C is determined:C1=0.25,C2=0.09,C3=0.13,C4=0.49.Step 16.
The final weight is calculated.(26)xw1=0.258,xw2=0.096,xw3=0.139,xw4=0.507.Step 17.
TheIFSi is obtained.(27)IFS1=0.30,IFS2=0.44,IFS3=0.43,IFS4=0.42,IFS5=0.57.Step 18.
TheIFPi is obtained.(28)IFP1=2.79,IFP2=3.29,IFP3=3.23,IFP4=3.25,IFP5=3.49.Step 19.
TheIFKAi,IFKBi,IFKBi are obtained (Table 7).Table 7
TheIFKAi,IFKBi,IFKBi.
IFKAiIFKBiIFKCiVC10.172.000.76VC20.202.640.92VC30.202.570.90VC40.202.550.90VC50.223.141.00Step 20.
TheIFKi is obtained.(29)IFK1=1.61,IFK2=2.05,IFK3=2.00,IFK4=1.99,IFK5=2.34.Step 21.
The ranking of alternatives is as follows (the higher theIFKi, the better the alternative i).(30)VC5≻VC4≻VC2≻VC3≻VC1.


## 5.2. Comparative Analyses

For this research, five college stadiums are selected to assess. This paper applied the IF-CoCoSo method to solve MAGDM. In order to certify the superiority of the IF-CoCoSo method more efficiently, we employed some previous decision methods (the IFWA operator [45], IFWG operator [46], IF-TOPSIS method [50], IF-GRA method [51], and IF-taxonomy method [52]). The ranking of given alternatives was recorded and is given in Table 8.Table 8
Alternative ranking under existing methods.
MethodsRankingIFWA operator [45]VC5≻VC4≻VC3≻VC2≻VC1IFWG operator [46]VC5≻VC4≻VC2≻VC3≻VC1IF-TOPSIS method [50]VC5≻VC4≻VC2≻VC3≻VC1IF-GRA method [51]VC5≻VC2≻VC3≻VC4≻VC1IF-taxonomy methodVC5≻VC2≻VC4≻VC3≻VC1Compared with the result of the CoCoSo method to other methods, consequently, Table8 shows that the results of the five application methods are basically consistent with the IF-CoCoSo algorithm.


## 6. Conclusion

Deepening the IEE in higher vocational colleges is not only an urgent important need to really improve the quality of our country’s market economy but also a powerful measure to really promote higher education reform and improve graduates’ entrepreneurship. Therefore, major higher vocational colleges need to proceed from the actual situation, further strengthen the design of the school’s IEE quality evaluation information system, timely correct and improve inappropriate codes of conduct, and ensure that the IEE can always focus on education. The goal is to provide effective services for improving the effectiveness of IEE activities and to ensure the healthy development of IEE. The quality evaluation of IEE in vocational colleges is looked as MAGDM. Thus, in this paper, the IF-CoCoSo method is proposed to solve MADM problems for quality evaluation of IEE in vocational colleges.In the future, the IF-CoCoSo method will be expanded to some other existing fuzzy environment, such as the Q-rung orthopair fuzzy set, Pythagorean fuzzy set, and interval-valued IFSs, or expanded to study some other existing decision-making issues [53–56]. At the same time, the novel logarithm method of additive weights [57] shall be our future works for uncertain MAGDM problems.



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*Source: 6071276-2022-09-10.xml*