# GRA and CRITIC Method for Intuitionistic Fuzzy Multiattribute Group Decision Making and Application to Development Potentiality Evaluation of Cultural and Creative Garden

Authors: Quan-Song Qi
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

In recent years, cultural and creative industry park is becoming a kind of hot industry to promote industrial restructuring and to improve the quality of urban space. For this reason, cultural and creative industrial parks are planning to build across the country. Currently, cultural and creative industrial parks that develop better than others thank to the government’s overall planning, construction, marketing, and management. At the same time, the new cultural and creative industry parks face enormous challenges, such as how to have together the cultural and creative industries and related groups or how to have area cultural creativity. And it is frequently regarded as a multiattribute group decision-making (MAGDM) process. Thus, a novel MAGDM process is needed to tackle it. Depending on the conventional grey relational analysis (GRA) method and intuitionistic fuzzy sets (IFSs), this paper designs a novel intuitive distance-based IF-GRA method for development potentiality evaluation of cultural and creative garden. First of all, some necessary theories related to IFSs are briefly reviewed. In addition, since subjective randomness frequently exists in determining criteria weights, the weights of criteria are decided objectively by utilizing the CRITIC method. Afterwards, relying on novel distance measures between IFSs, the GRA method is extended to the IFSs to calculate assessment score of each alternative. Eventually, an application about development potentiality evaluation of cultural and creative garden and some comparative analysis is given. The results think that the designed method is useful for development potentiality evaluation of cultural and creative garden.


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## Body

## 1. Introduction

In reality, decision-making information is often given uncertainly due to the complexity of the objective world [1–6], as well as the uncertainty of the ambiguity of human thinking [7–12], which makes the uncertainty in decision-making theory, methodology, and application of the decision-making a focus for researchers [13–17]. In order to depict uncertain information, Zadeh [18] firstly defined the basic decision theory of fuzzy sets (FSs). Atanassov [19] presented the novel definition of IFSs. Gou et al. [20] defined some exponential operational law for IFNs. Gupta et al. [21] defined the fuzzy entropy under IFSs. Li and Wu [22] presented the intuitionistic fuzzy cross entropy distance. Khan et al. [23] defined similarity measure about IFNs. Li et al. [24] gave a novel grey MADM with IFNs. Liu et al. [25] built some BM fused operators under IFSs with Dombi operations. Su et al. [26] built the induced generalized OWA operator under IFSs. Garg [27] presented a method related to MAGDM on the basis of IFS preference. Chen et al. [28] developed TOPSIS method and similarity measures under IFSs. Gan and Luo [29] used the hybrid method with DEMATEL and IFSs. Krishankumar et al. [30] integrated AHP under IFSs to design a GDM model. Gupta et al. [31] modified the SIR method under IFSs. Bao et al. [32] defined prospect theory and evidential reasoning algorithms under the IFSs. Hao et al. [33] presented a theory of decision field for IFSs. Jin et al. [34] defined two GDM methods with IFPRs, defined the MABAC model to IFSs through distance measures, and defined the VIKOR method under IFSs. Cali and Balaman [35] proposed ELECTRE I with the VIKOR method under IFSs to reflect the decision makers’ preferences. Rouyendegh [36] used the ELECTRE method in IFSs to deal with some MADM process. Liang [37] defined EDAS process for MAGDM under IFSs. Xiao et al. [38] defined the intuitionistic fuzzy taxonomy approach. Ju et al. [39] built the divergence-based distance measure for IFSs. Jiang et al. [40] proposed the adjustable approach for IF-MADM. Zeshui Xu [41] developed an interactive decision method for IF-MADM. Krohling et al. [42] defined the IF-TODIM for MADM. Wang et al. [43] proposed the IF-MADM based on the based on evidential reasoning. He et al. [44] defined the generalized geometric interaction operators under IFSs. Zhao et al. [45] extended the CPT-TODIM method for interval-valued intuitionistic fuzzy MAGDM.GRA was initially developed by Deng [46] to solve MAGDM issues. Compared with other MAGDM, the GRA method can consider the shape similarity of every alternative from PIS and NIS. Chen [47] connected the IF-GRA method with entropy-TOPSIS process for choosing building materials supplier. Tan et al. [48] defined the GRA process with AHP. Alptekin et al. [49] solved the MADM process with the GRA method. Yazdani et al. [50] provided the QFD method and GRA method in dealing with supply chain drivers. Malek et al. [51] built the hybrid GRA method for green supply. Zhu et al. [52] aimed at choosing the carbon market with GRA algorithms and EMD. Chiang [53] used the GRA model through dependent criteria MADM process. Kung and Wen [54] used GRA to solve the grey-MADM issues. Wan et al. [55] defined the intuitionistic fuzzy programming method for group decision making with interval-valued fuzzy preference relations. Wan et al. [56] defined the intuitionistic fuzzy programming method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations. Wan et al. [57] proposed the three-phase method for group decision making with interval-valued intuitionistic fuzzy preference relations. Xui et al. [58] studied the MADM with triangular intuitionistic fuzzy numbers based on the zero-sum game model.The innovativeness of such paper can be summarized as follows: (1) the CRITIC method is built is to derive the weight information of the attribute under IFSs; (2) this paper employs a novel combined distance measures; (3) this paper designs a novel intuitive distance-based IF-GRA method for MAGDM based on the CRITIC method; (4) a case study for development potentiality evaluation of cultural and creative garden is given to show the developed approach; and (4) some comparative studies are provided with the existing methods.In order to do so, the remainder of this paper is arranged in the following way. Some concept of IFSs is introduced in Section2. The improved GRA process is defined under IFNs, and the calculating steps are listed in Section 3. An empirical application about development potentiality evaluation of cultural and creative garden is given to depict the superiority of such designed method, and some comparative analysis is given to prove the merits of such method in Section 4. At last, we make the useful conclusion of such work in Section 5.


## 2. Preliminaries

### 2.1. IFSs

Definition 1.
(see [19]). An IFS on X is defined as follows:(1)I=x,μIx,νIx|x∈X,where μIx∈0,1 is named as the membership of Iand νIx∈0,1 is named as the nonmembership of I, and μIx and νIx meet such condition: 0≤μIx+νIx≤1, ∀x∈X.Definition 2.
(see [59]). Let I1=μ1,ν1 and I2=μ2,ν2 be two IFNs, and the operation formula is as follows:(2)I1⊕I2=μ1+μ2−μ1μ2,ν1ν2,(3)I1⊗I2=μ1μ2,ν1+ν2−ν1ν2,(4)λI1=1−1−μ1λ,ν1λ,λ>0,(5)I1λ=μ1λ,1−1−ν1λ,λ>0.Definition 3.
(see [60]). Let I1=μ1,ν1 and I2=μ2,ν2 be IFNs, and the score and accuracy functions of I1 and I2 are as follows:(6)SI1=μ1+μ11−μ1−ν1,SI2=μ2+μ21−μ2−ν2,(7)HI1=μ1+ν1,HI2=μ2+ν2,
For two IFNsI1 and I2, regarding Definition 3, (1)
IfsI1<sI2,thenI1<I2(2)
IfsI1=sI2,hI1<hI2,thenI1<I2(3)
IfsI1=sI2,hI1=hI2,thenI1=I2Definition 4.
(see [61]). Let I1=μ1,ν1 and I2=μ2,ν2 be IFNs, and the novel Euclidean distances between two IFNs can be defined as follows:(8)IFEDI1,I2=16ℓ12+ℓ22+ℓ32,where ℓ1=μ1−μ2+ν1−ν2+μ1+1−ν1−μ2+1−ν2/2, ℓ2=π1+π2/2, and ℓ3=maxμ1−μ2,ν1−ν2,π1−π2/2


### 2.2. Intuitionistic Fuzzy Aggregation Operators

Under the IFSs, some fused operators will be introduced, including IFWA fused operator and IFWG fused operator.Definition 5.
(see [59]). Let Ij=μIj,νIjj=1,2,…,n be a group of IFNs, and the IFWA operator is as follows:(9)IFWAωI1,I2,…,In=⊕j=1nωjIj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.
From Definition5, the result could be derived.Theorem 1.
The fused value by IFWA is an IFN, where(10)IFWAωI1,I2,…,In=⊕j=1nωjIj=1−∏j=1n1−μIjωj,∏j=1nνIjωj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.Definition 6.
(see [59]). Let Ijj=1,2,…,n be a set of IFNs, and the IFWG operator is as follows:(11)IFWGωI1,I2,…,In=⊗j=1nIjωj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.
From Definition6, the result could be derived.Theorem 2.
The fused value by IFWG is an IFN.(12)IFWGωI1,I2,…,In=⊗j=1nIjωj=∏j=1nμIjωj,1−∏j=1n1−νIjωj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.


## 2.1. IFSs

Definition 1.
(see [19]). An IFS on X is defined as follows:(1)I=x,μIx,νIx|x∈X,where μIx∈0,1 is named as the membership of Iand νIx∈0,1 is named as the nonmembership of I, and μIx and νIx meet such condition: 0≤μIx+νIx≤1, ∀x∈X.Definition 2.
(see [59]). Let I1=μ1,ν1 and I2=μ2,ν2 be two IFNs, and the operation formula is as follows:(2)I1⊕I2=μ1+μ2−μ1μ2,ν1ν2,(3)I1⊗I2=μ1μ2,ν1+ν2−ν1ν2,(4)λI1=1−1−μ1λ,ν1λ,λ>0,(5)I1λ=μ1λ,1−1−ν1λ,λ>0.Definition 3.
(see [60]). Let I1=μ1,ν1 and I2=μ2,ν2 be IFNs, and the score and accuracy functions of I1 and I2 are as follows:(6)SI1=μ1+μ11−μ1−ν1,SI2=μ2+μ21−μ2−ν2,(7)HI1=μ1+ν1,HI2=μ2+ν2,
For two IFNsI1 and I2, regarding Definition 3, (1)
IfsI1<sI2,thenI1<I2(2)
IfsI1=sI2,hI1<hI2,thenI1<I2(3)
IfsI1=sI2,hI1=hI2,thenI1=I2Definition 4.
(see [61]). Let I1=μ1,ν1 and I2=μ2,ν2 be IFNs, and the novel Euclidean distances between two IFNs can be defined as follows:(8)IFEDI1,I2=16ℓ12+ℓ22+ℓ32,where ℓ1=μ1−μ2+ν1−ν2+μ1+1−ν1−μ2+1−ν2/2, ℓ2=π1+π2/2, and ℓ3=maxμ1−μ2,ν1−ν2,π1−π2/2


## 2.2. Intuitionistic Fuzzy Aggregation Operators

Under the IFSs, some fused operators will be introduced, including IFWA fused operator and IFWG fused operator.Definition 5.
(see [59]). Let Ij=μIj,νIjj=1,2,…,n be a group of IFNs, and the IFWA operator is as follows:(9)IFWAωI1,I2,…,In=⊕j=1nωjIj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.
From Definition5, the result could be derived.Theorem 1.
The fused value by IFWA is an IFN, where(10)IFWAωI1,I2,…,In=⊕j=1nωjIj=1−∏j=1n1−μIjωj,∏j=1nνIjωj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.Definition 6.
(see [59]). Let Ijj=1,2,…,n be a set of IFNs, and the IFWG operator is as follows:(11)IFWGωI1,I2,…,In=⊗j=1nIjωj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.
From Definition6, the result could be derived.Theorem 2.
The fused value by IFWG is an IFN.(12)IFWGωI1,I2,…,In=⊗j=1nIjωj=∏j=1nμIjωj,1−∏j=1n1−νIjωj,where ω=ω1,ω2,…,ωnT be the weight of Ijj=1,2,…,n, ωj>0,∑j=1nωj=1.


## 3. GRA Method for MAGDM with IFNs

In such section, we build the IF-GRA process for MAGDM. The calculating steps of the defined process could be depicted subsequently. LetR=R1,R2,…,Rn be the group of attributes and r=r1,r2,…,rn be the weight of Rj, where rj∈0,1,j=1,2,…,n,∑j=1nrj=1. Assume H=H1,H2,…,Hl be a set of DMs that have degree of h=h1,h2,…,hl, where hk∈0,1,k=1,2,…,l∑k=1lhk=1. Let F=F1,F2,…,Fm be a set of alternatives. And Q=qijm×n is the matrix with IFNs, where qij means the Fi for Rj. Subsequently, the specific calculating steps will be depicted.Step 1. Get each DM’s matrix Qk=qijkm×n with IFNs and derive the overall IF-matrix Q=qijm×n.(13)Qk=qijkm×n=q11kq12k…q1nkq21kq22k…q2nk⋮⋮⋮⋮qm1kqm2k…qmnk,(14)Q=qijm×n=q11q12…q1nq21q22…q2n⋮⋮⋮⋮qm1qm2…qmn,(15)qij=1−∏k=1l1−μqijkhk,∏k=1lνqijkhk,whereqijk is the value of Fii=1,2,…,mRjj=1,2,…,n and the Hkk=1,2,…,l.Step 2. Normalize the matrix Q=qijm×n with IFNs to QN=qijNm×n.(16)qijN=μij,νij,Rjis a benefit,criterion,νij,μij,Rjis a cost criterion.Step 3. Employ CRITIC process to derive the weight of attributes.The CRITIC method is proposed to decide attributes’ weights. This method was initially defined by Diakoulaki et al. [62]. Then, the calculating steps of such method are presented.(1)
Depending on the normalized overall matrixQN=qijNm×n with IFNs, the correlation coefficient between attributes can be defined.(17)IFCCjt=∑i=1mSqijN−SqjNSqitN−SqtN∑i=1mSqijN−SqjN2∑i=1mSqitN−SqtN2,j,t=1,2,…,n,whereSqjN=1/m∑i=1mSqijN and SqtN=1/m∑i=1mSqitN.(2)
Attributes’ standard deviation is obtained.(18)IFSDj=1m−1∑i=1mSqijN−SqjN2,j=1,2,…,n.whereSqjN=1/m∑i=1mSqijN.(3)
The attributes’ weights are defined.(19)rj=IFSDj∑t=1n1−IFCCjt∑j=1nIFSDj∑t=1n1−IFCCjt,j=1,2…,n.whererj∈0,1 and ∑j=1nrj=1.Step 4. Define the intuitionistic fuzzy PIS (IFPIS) Aj+ and the intuitionistic fuzzy NIS (IFNIS) Aj− as follows:(20)Aj+=maxiqijN=maxiμijN,miniνijN,(21)Aj−=miniqijN=miniμijN,maxiνijN.whereqijN denotes the normalized IFNs.Step 5. Compute the grey relational coefficient (GRC) of every alternative between each alternative and IFPIS and the GRC between each alternative and IFPIS as follows:(22)IFPISξij=min1≤i≤mmin1≤j≤nIFEDqijN,Aj++ρmax1≤i≤mmax1≤j≤nIFEDqijN,Aj+IFEDqijN,Aj++ρmax1≤i≤mmax1≤j≤nIFEDqijN,Aj+,IFNISξij=min1≤i≤mmin1≤j≤nIFEDqijN,Aj−+ρmax1≤i≤mmax1≤j≤nIFEDqijN,Aj−IFEDqijN,Aj−+ρmax1≤i≤mmax1≤j≤nIFEDqijN,Aj−,i=1,2,…,m,j=1,2,…,n.Step 6. Derive the degree of GRC of all alternatives from IFPIS and IFNIS as follows:(23)IFPISξi=∑j=1nrjIFPISξij,i=1,2,…,m,(24)IFNISξi=∑j=1nrjIFNISξij,i=1,2,…,m.Step 7. Compute each alternative’s intuitionistic fuzzy relative relational degree (IFRRD) of all alternatives from IFPIS as follows:(25)IFRRDi=IFNISξiIFNISξi+IFPISξi,i=1,2,…,m.Step 8. According to the IFRRDii=1,2,…,m, the largest value of IFRRDii=1,2,…,m is, the optimal alternative is.


## 4. Numerical Example and Comparative Analysis

### 4.1. Numerical Example

Traditional culture is the essence of Chinese history of civilization; considering the intangible cultural heritage as an important part of traditional culture, the development of China’s history of civilization progress and the social economy has a far-reaching influence. In China, cultural creative industry is an emerging industry, showing a good momentum of development. The cultural resources of China’s rich heritage provided plenty of cultural capital for development of creative industry and, at the same time, put forward the theory and practice of cultural and creative industry park, provideing the material basis for the development of creative industries. Many cities have many categories of intangible cultural heritage items, and government and groups are working to contribute the protection and inheritance of intangible cultural heritage actively. However, in the background of new era, the traditional protection measures have been unable to meet development requirements of the times and intangible cultural heritage protection, and inheritance work needs innovation. In this chapter, an empirical application about development potentiality evaluation of cultural and creative garden is provided through the IF-GRA method. There are five potential cultural and creative gardensFii=1,2,3,4,5 preparing to evaluate their development potentiality. In order to assess these cultural and creative gardens fairly, three experts H=H1,H2,H3 (expert’s weight h=0.35,0.32,0.33) are invited. All experts depict their information through four subsequent attributes: ① R1 is market risk; ② R2 is environmental risk; ③ R3 is risk of enterprise assets structure; and ④ R4 is cost of enterprise operation and management. Evidently, R4 is cost attribute, while R1, R2, and R3 are benefit attributes, and the decision-making matrix is depicted in Tables 1–3.Step 1. Based on the information Qk=qijkm×ni=1,2,…,m,j=1,2,…,n given in Tables 1–3 and the expert’s weight h=0.35,0.32,0.33, we can derive the overall matrix Q=qijm×ni=1,2,…,m,j=1,2,…,n according to equation (16), and the computing results are listed in Table 4.Step 2. Normalize the matrix Q=qijm×n to QN=qijNm×n (see Table 5).Step 3. Decide the attribute weights rjj=1,2,…,n by CRITIC as listed in Table 6.Step 4. Calculate the IFPISAj+ and IFNISAj− according to (20) and (21).Step 5. Compute the GRC of every alternative from IFPIS and IFNIS (Tables 7 and 8).Step 6. Derive the degree of GRC of all given alternatives from IFPIS and IFNIS (Table 9).Step 7. Derive the IFRRDξi of every alternative from IFPIS (Table 10).Step 8. Relying on the IFRRDξi, all the given alternatives could be ordered; the larger value of IFRRDξi is, the better alternative selected is. Evidently, the order is F3>F1>F5>F4>F2, and F3 is the optimal cultural and creative gardens.(26)Aj+=0.4413,0.1625,0.5054,0.2042,0.6862,0.1569,0.4924,0.2844,Aj−=0.2051,0.3945,0.3078,0.4041,0.3169,0.2763,0.1986,0.5885.Table 1
Decision-making information depicted byH1.
R1R2R3R4F1(0.1, 0.3)(0.5, 0.2)(0.5, 0.4)(0.3, 0.3)F2(0.2, 0.5)(0.4, 0.1)(0.4, 0.5)(0.2, 0.4)F3(0.3, 0.6)(0.4, 0.2)(0.6, 0.3)(0.5, 0.2)F4(0.1, 0.3)(0.7, 0.1)(0.5, 0.4)(0.2, 0.4)F5(0.5, 0.4)(0.4, 0.3)(0.8, 0.1)(0.4, 0.5)Table 2
Decision-making information given byH2.
R1R2R3R4F1(0.2, 0.5)(0.4, 0.3)(0.1, 0.1)(0.4, 0.5)F2(0.1, 0.3)(0.4, 0.5)(0.3, 0.2)(0.5, 0.2)F3(0.5, 0.1)(0.2, 0.7)(0.4, 0.2)(0.3, 0.4)F4(0.4, 0.2)(0.3, 0.3)(0.3, 0.5)(0.5, 0.1)F5(0.5, 0.1)(0.6, 0.2)(0.6, 0.2)(0.3, 0.6)Table 3
Decision-making information given byH3.
R1R2R3R4F1(0.4, 0.1)(0.3, 0.4)(0.4, 0.5)(0.2, 0.2)F2(0.3, 0.4)(0.5, 0.3)(0.5, 0.2)(0.1, 0.2)F3(0.4, 0.2)(0.3, 0.5)(0.7, 0.2)(0.8, 0.1)F4(0.5, 0.2)(0.4, 0.3)(0.4, 0.1)(0.3, 0.6)F5(0.3, 0.1)(0.5, 0.4)(0.6, 0.2)(0.2, 0.4)Table 4
Overall matrix with IFNS.
R1R2R3R4F1(0.2418, 0.2458)(0.4077, 0.2862)(0.3169, 0.2763)(0.3037, 0.3090)F2(0.2051, 0.3945)(0.4350, 0.2405)(0.4065, 0.2756)(0.2844, 0.2549)F3(0.4026, 0.2353)(0.3078, 0.4041)(0.5858, 0.2305)(0.5885, 0.1986)F4(0.3489, 0.2305)(0.5054, 0.2042)(0.4086, 0.2719)(0.3414, 0.2934)F5(0.4413, 0.1625)(0.5038, 0.2897)(0.6862, 0.1569)(0.3069, 0.4924)Table 5
The normalized matrix with IFNS.
R1R2R3R4F1(0.2418, 0.2458)(0.4077, 0.2862)(0.3169, 0.2763)(0.3090, 0.3037)F2(0.2051, 0.3945)(0.4350, 0.2405)(0.4065, 0.2756)(0.2549, 0.2844)F3(0.4026, 0.2353)(0.3078, 0.4041)(0.5858, 0.2305)(0.1986, 0.5885)F4(0.3489, 0.2305)(0.5054, 0.2042)(0.4086, 0.2719)(0.2934, 0.3414)F5(0.4413, 0.1625)(0.5038, 0.2897)(0.6862, 0.1569)(0.4924, 0.3069)Table 6
The attributes weightsrj.
R1R2R3R4rj0.26070.24220.27800.2170Table 7
GRC of every alternative from IFPIS.
AlternativesR1R2R3R4F10.68251.00000.33330.4095F20.54430.43430.41750.4943F30.70490.68251.00001.0000F40.51810.49430.43430.4831F51.00000.43430.41750.5181Table 8
GRC of every alternative from IFNIS.
AlternativesR1R2R3R4F10.51720.34880.41670.4545F20.78951.00001.00000.8333F30.44120.36590.33330.3947F41.00000.51720.71431.0000F50.42860.45450.48390.4769Table 9
IFPISξi and IFNISξi of every alternative.
AlternativesIFPISξiIFNISξiF10.56530.4146F20.47890.9398F30.85240.3746F40.48560.7449F50.62750.4866Table 10
IFRRD of each alternative from IFPIS.
AlternativesF1F2F3F4F5IFRRDξi0.58330.33480.69730.39860.5649


### 4.2. Compare Analysis

In such section, IF-GRA is made comparison with some existing methods to show their superiority.The IF-GRA model is compared with the IF-VIKOR method [63]. Then, we could derive the calculating result. The closest ideal scores are as follows: CI∗F1=0.9042, CI∗F2=0.6776, CI∗F3=0.0000, CI∗F4=0.9876, and CI∗F5=0.9563. And the farthest worst score is as follows: CI−F1=0.0122, CI−F2=0.3442, CI−F3=1.0000, CI−F4=0.0175, and CI−F5=0.0000. Then, each alternatives’ relative closeness are calculated as follows: DRC1=0.9854, DRC2=0.6465, DRC3=0.0000, DRC4=0.9764, and DRC5=1.0000. Hence, the order is F3>F2>F4>F1>F5.Furthermore, our defined method is compared with IFWA and IFWG [59]. For IFWA operator, the calculating value is as follows: SF1=0.0797,SF2=0.1416,SF3=0.3355, SF4=0.0447,andSF5=0.0409. Thus, the ranking order is F3>F2>F1>F4>F5. For the IFWG, the calculating value is SF1=−0.0106,SF2=0.1229,SF3=0.3021, SF4=0.0358,andSF5=0.0087. So, the ranking order is F3>F2>F4>F5>F1.In the end, the IF-GRA method is also compared with the IF-CODAS method [64]. Then, we can have the calculating result. The total assessment score (AS) of each alternative is calculated as follows: AS1=−0.8032, AS2=0.1435, AS3=1.4843, AS4=−0.3809, and AS5=−0.4307. Therefore, the order is F3>F2>F4>F5>F1.Obviously, the results of these existing methods are depicted in Table11.Table 11
Calculating results of these methods.
MethodsOrderThe best alternativeThe worst alternativeIFWA operatorF3>F2>F1>F4>F5F3F5IFWG operatorF3>F2>F4>F5>F1F3F1IF-VIKOR methodF3>F2>F4>F1>F5F3F5IF-CODAS methodF3>F2>F4>F5>F1F3F1The developed methodF3>F1>F5>F4>F2F3F2From Table11, it is evidently that the best alternative is F3. In other words, the ranking order is slightly different. Different methods can cope with MAGDM from different angles. IFWA and IFWG operators emphasize to fuse assessing information. The IF-VIKOR emphasizes the closest to PIS and the farthest to NIS. However, compared with the above methods, our designed method is more precise since it considers the degree of shape similarity of every alternative from PIS and NIS. Furthermore, compared with the IF-CODAS method, our designed method utilizes novel distance measures and CRITIC method. The novel distance measures can not only reflect IFSs more comprehensiveness but also take waver in IFSs into consideration and do not generate counterintuitive situations. The CRITIC method can minimize subjective randomness while the criteria weights are determined.


## 4.1. Numerical Example

Traditional culture is the essence of Chinese history of civilization; considering the intangible cultural heritage as an important part of traditional culture, the development of China’s history of civilization progress and the social economy has a far-reaching influence. In China, cultural creative industry is an emerging industry, showing a good momentum of development. The cultural resources of China’s rich heritage provided plenty of cultural capital for development of creative industry and, at the same time, put forward the theory and practice of cultural and creative industry park, provideing the material basis for the development of creative industries. Many cities have many categories of intangible cultural heritage items, and government and groups are working to contribute the protection and inheritance of intangible cultural heritage actively. However, in the background of new era, the traditional protection measures have been unable to meet development requirements of the times and intangible cultural heritage protection, and inheritance work needs innovation. In this chapter, an empirical application about development potentiality evaluation of cultural and creative garden is provided through the IF-GRA method. There are five potential cultural and creative gardensFii=1,2,3,4,5 preparing to evaluate their development potentiality. In order to assess these cultural and creative gardens fairly, three experts H=H1,H2,H3 (expert’s weight h=0.35,0.32,0.33) are invited. All experts depict their information through four subsequent attributes: ① R1 is market risk; ② R2 is environmental risk; ③ R3 is risk of enterprise assets structure; and ④ R4 is cost of enterprise operation and management. Evidently, R4 is cost attribute, while R1, R2, and R3 are benefit attributes, and the decision-making matrix is depicted in Tables 1–3.Step 1. Based on the information Qk=qijkm×ni=1,2,…,m,j=1,2,…,n given in Tables 1–3 and the expert’s weight h=0.35,0.32,0.33, we can derive the overall matrix Q=qijm×ni=1,2,…,m,j=1,2,…,n according to equation (16), and the computing results are listed in Table 4.Step 2. Normalize the matrix Q=qijm×n to QN=qijNm×n (see Table 5).Step 3. Decide the attribute weights rjj=1,2,…,n by CRITIC as listed in Table 6.Step 4. Calculate the IFPISAj+ and IFNISAj− according to (20) and (21).Step 5. Compute the GRC of every alternative from IFPIS and IFNIS (Tables 7 and 8).Step 6. Derive the degree of GRC of all given alternatives from IFPIS and IFNIS (Table 9).Step 7. Derive the IFRRDξi of every alternative from IFPIS (Table 10).Step 8. Relying on the IFRRDξi, all the given alternatives could be ordered; the larger value of IFRRDξi is, the better alternative selected is. Evidently, the order is F3>F1>F5>F4>F2, and F3 is the optimal cultural and creative gardens.(26)Aj+=0.4413,0.1625,0.5054,0.2042,0.6862,0.1569,0.4924,0.2844,Aj−=0.2051,0.3945,0.3078,0.4041,0.3169,0.2763,0.1986,0.5885.Table 1
Decision-making information depicted byH1.
R1R2R3R4F1(0.1, 0.3)(0.5, 0.2)(0.5, 0.4)(0.3, 0.3)F2(0.2, 0.5)(0.4, 0.1)(0.4, 0.5)(0.2, 0.4)F3(0.3, 0.6)(0.4, 0.2)(0.6, 0.3)(0.5, 0.2)F4(0.1, 0.3)(0.7, 0.1)(0.5, 0.4)(0.2, 0.4)F5(0.5, 0.4)(0.4, 0.3)(0.8, 0.1)(0.4, 0.5)Table 2
Decision-making information given byH2.
R1R2R3R4F1(0.2, 0.5)(0.4, 0.3)(0.1, 0.1)(0.4, 0.5)F2(0.1, 0.3)(0.4, 0.5)(0.3, 0.2)(0.5, 0.2)F3(0.5, 0.1)(0.2, 0.7)(0.4, 0.2)(0.3, 0.4)F4(0.4, 0.2)(0.3, 0.3)(0.3, 0.5)(0.5, 0.1)F5(0.5, 0.1)(0.6, 0.2)(0.6, 0.2)(0.3, 0.6)Table 3
Decision-making information given byH3.
R1R2R3R4F1(0.4, 0.1)(0.3, 0.4)(0.4, 0.5)(0.2, 0.2)F2(0.3, 0.4)(0.5, 0.3)(0.5, 0.2)(0.1, 0.2)F3(0.4, 0.2)(0.3, 0.5)(0.7, 0.2)(0.8, 0.1)F4(0.5, 0.2)(0.4, 0.3)(0.4, 0.1)(0.3, 0.6)F5(0.3, 0.1)(0.5, 0.4)(0.6, 0.2)(0.2, 0.4)Table 4
Overall matrix with IFNS.
R1R2R3R4F1(0.2418, 0.2458)(0.4077, 0.2862)(0.3169, 0.2763)(0.3037, 0.3090)F2(0.2051, 0.3945)(0.4350, 0.2405)(0.4065, 0.2756)(0.2844, 0.2549)F3(0.4026, 0.2353)(0.3078, 0.4041)(0.5858, 0.2305)(0.5885, 0.1986)F4(0.3489, 0.2305)(0.5054, 0.2042)(0.4086, 0.2719)(0.3414, 0.2934)F5(0.4413, 0.1625)(0.5038, 0.2897)(0.6862, 0.1569)(0.3069, 0.4924)Table 5
The normalized matrix with IFNS.
R1R2R3R4F1(0.2418, 0.2458)(0.4077, 0.2862)(0.3169, 0.2763)(0.3090, 0.3037)F2(0.2051, 0.3945)(0.4350, 0.2405)(0.4065, 0.2756)(0.2549, 0.2844)F3(0.4026, 0.2353)(0.3078, 0.4041)(0.5858, 0.2305)(0.1986, 0.5885)F4(0.3489, 0.2305)(0.5054, 0.2042)(0.4086, 0.2719)(0.2934, 0.3414)F5(0.4413, 0.1625)(0.5038, 0.2897)(0.6862, 0.1569)(0.4924, 0.3069)Table 6
The attributes weightsrj.
R1R2R3R4rj0.26070.24220.27800.2170Table 7
GRC of every alternative from IFPIS.
AlternativesR1R2R3R4F10.68251.00000.33330.4095F20.54430.43430.41750.4943F30.70490.68251.00001.0000F40.51810.49430.43430.4831F51.00000.43430.41750.5181Table 8
GRC of every alternative from IFNIS.
AlternativesR1R2R3R4F10.51720.34880.41670.4545F20.78951.00001.00000.8333F30.44120.36590.33330.3947F41.00000.51720.71431.0000F50.42860.45450.48390.4769Table 9
IFPISξi and IFNISξi of every alternative.
AlternativesIFPISξiIFNISξiF10.56530.4146F20.47890.9398F30.85240.3746F40.48560.7449F50.62750.4866Table 10
IFRRD of each alternative from IFPIS.
AlternativesF1F2F3F4F5IFRRDξi0.58330.33480.69730.39860.5649


## 4.2. Compare Analysis

In such section, IF-GRA is made comparison with some existing methods to show their superiority.The IF-GRA model is compared with the IF-VIKOR method [63]. Then, we could derive the calculating result. The closest ideal scores are as follows: CI∗F1=0.9042, CI∗F2=0.6776, CI∗F3=0.0000, CI∗F4=0.9876, and CI∗F5=0.9563. And the farthest worst score is as follows: CI−F1=0.0122, CI−F2=0.3442, CI−F3=1.0000, CI−F4=0.0175, and CI−F5=0.0000. Then, each alternatives’ relative closeness are calculated as follows: DRC1=0.9854, DRC2=0.6465, DRC3=0.0000, DRC4=0.9764, and DRC5=1.0000. Hence, the order is F3>F2>F4>F1>F5.Furthermore, our defined method is compared with IFWA and IFWG [59]. For IFWA operator, the calculating value is as follows: SF1=0.0797,SF2=0.1416,SF3=0.3355, SF4=0.0447,andSF5=0.0409. Thus, the ranking order is F3>F2>F1>F4>F5. For the IFWG, the calculating value is SF1=−0.0106,SF2=0.1229,SF3=0.3021, SF4=0.0358,andSF5=0.0087. So, the ranking order is F3>F2>F4>F5>F1.In the end, the IF-GRA method is also compared with the IF-CODAS method [64]. Then, we can have the calculating result. The total assessment score (AS) of each alternative is calculated as follows: AS1=−0.8032, AS2=0.1435, AS3=1.4843, AS4=−0.3809, and AS5=−0.4307. Therefore, the order is F3>F2>F4>F5>F1.Obviously, the results of these existing methods are depicted in Table11.Table 11
Calculating results of these methods.
MethodsOrderThe best alternativeThe worst alternativeIFWA operatorF3>F2>F1>F4>F5F3F5IFWG operatorF3>F2>F4>F5>F1F3F1IF-VIKOR methodF3>F2>F4>F1>F5F3F5IF-CODAS methodF3>F2>F4>F5>F1F3F1The developed methodF3>F1>F5>F4>F2F3F2From Table11, it is evidently that the best alternative is F3. In other words, the ranking order is slightly different. Different methods can cope with MAGDM from different angles. IFWA and IFWG operators emphasize to fuse assessing information. The IF-VIKOR emphasizes the closest to PIS and the farthest to NIS. However, compared with the above methods, our designed method is more precise since it considers the degree of shape similarity of every alternative from PIS and NIS. Furthermore, compared with the IF-CODAS method, our designed method utilizes novel distance measures and CRITIC method. The novel distance measures can not only reflect IFSs more comprehensiveness but also take waver in IFSs into consideration and do not generate counterintuitive situations. The CRITIC method can minimize subjective randomness while the criteria weights are determined.


## 5. Conclusion

The rapid development of science and technology, and increasingly people rising consumer demand, is characterized by “knowledge” and “culture” of cultural creative industry arises at the historic moment. Culture creative industry mainly refers to culture as the foundation, taking innovation as the core, powered by ideas, using high-tech technology in promoting cultural resources for effective integration and utilization, through constant research and development and extensive application of knowledge industry, knowledge to produce high value-added products and services of the new industry. In the modern society, the foreign and the Chinese government gives great importance to the development of cultural creative industry. Meanwhile, from the eighteenth century British industrial revolution began, the human came into the industrial revolution; but with the development of computer, electronic science, and technology industry, the traditional manufacturing industry gradually declined, there has been a major shift in urban economic structure, industrial layout, and type of economy, and many cities on a large number of industrial building heritages choose to dismantle, abandoned, or transform and face a dilemma. In this case, the sustainable development theory makes cultural creative industry become a new way to redesign of old industrial building heritages. Theory of sustainable development for urban renewal must renew the city’s overall memory and link the development of the city space and urban context inheritance (including the city’s cultural landscape), so a lot of countries under the guidance of sustainable development theory of transforming urban heritage of the old industrial buildings for the city’s cultural creative industry park realize the sustainable development of the cultural creative industrial park. Based on this, the author looked for cultural creative industrial park design development at home and abroad research, hoping to explore sustainable cultural creative industrial park for the future development in China, and promoting the cultural creative industry cluster of high speed. This paper offers the useful solution for such issue since it designs a novel intuitive distance-based IF-GRA method to build the evaluation system of development potentiality evaluation of cultural and creative garden. And then a numerical example is given to prove that such novel method is reasonable.The main contribution of this paper can be summarized as follows: (1) the CRITIC method is built to derive the weight information of the attribute under IFSs; (2) this paper employs a novel combined distance measures; (3) this paper designs a novel intuitive distance-based IF-GRA method for MAGDM based on the CRITIC method; (4) a case study for development potentiality evaluation of cultural and creative garden is given to show the developed approach; and some comparative studies are provided with the existing methods, and (5) the proposed method can also contribute to the other evaluation issues.In the future works, the designed model and algorithm could be needful and meaningful to solve other real MAGDM issues, and the designed methods could also be expanded to other uncertain setting [65–71].



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*Source: 9957505-2021-07-09.xml*