Green supplier selection has recently become one of the key strategic considerations in green supply chain management, due to regulatory requirements and market trends. It can be regarded as a multi-criteria group decision-making (MCGDM) problem, in which a set of alternatives are evaluated with respect to multiple criteria. MCGDM methods based on Analytic Hierarchy Process (AHP) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) are widely used in solving green supplier selection problems. However, the classic AHP must conduct large amounts of pairwise comparisons to derive a consistent result due to its complex structure. Meanwhile, the classic TOPSIS only considers one single negative idea solution in selecting suppliers, which is insufficiently cautious. In this study, an improved TOPSIS integrated with Best-Worst Method (BWM) is developed to solve MCGDM problems with intuitionistic fuzzy information in the context of green supplier selection. The BWM is investigated to derive criterion weights, and the improved TOPSIS method is proposed to obtain decision makers’ weights in terms of different criteria. Moreover, the developed TOPSIS-based coefficient is used to rank alternatives. Finally, a green supplier selection problem in the agri-food industry is presented to validate the proposed approach followed by sensitivity and comparative analyses.
In recent years, governments and industries have been attempting to decouple economic growth from commensurate environmental burdens (Vazquez-Brust and Sarkis,
Green suppliers are located upstream of the entire supply chain; thus, they can effectively help enterprises move towards a green supply chain design (Blome
The present work attempts to remedy the limitations of existing studies and develops a hybrid MCGDM method for green supplier selection within the context of intuitionistic fuzzy sets (IFSs). The innovation and contribution of this study are three-fold. Firstly, IFSs (Atanassov,
The remainder of this study is organized as follows. Section
In real life, DMs frequently disagree when expressing their ideas in assessment. Fuzzy sets (Zadeh,
TOPSIS developed by Hwang and Yoon (
The BWM proposed by Rezaei (
Numerous researchers have studied the criteria and decision models involved in the process of selecting a suitable supplier (Chai
Recently, large numbers of green supplier evaluation and selection approaches have been developed, ranging from a single method to hybrid methods that are integrated with multiple techniques (Govindan
Summary of studies using decision-making methods for green supplier selection.
Category | Method | MCGDM | Industry | Literature |
Optimization model | DEA | Dobos and Vorosmarty ( |
||
Bi-objective programming | Automotive industry | Vahidi |
||
Fuzzy clustering | Fuzzy c-means and VIKOR | Automotive industry | Akman ( |
|
MCDM model | ANP and GRA; fuzzy NGT and VIKOR; fuzzy ANP, DEMATEL and TOPSIS; fuzzy TODIM; fuzzy QUALIFLEX | Yes | Automotive industry | Hashemi |
ANP, DEMATEL and VIKOR; AHP, entropy and TOPSIS; fuzzy TOPSIS | Yes | Electronic industry | Kuo |
|
Delphi and DEA; fuzzy TOPSIS, VIKOR and GRA | Yes | Food industry | Banaeian |
|
ANP and GRA | Pivot irrigation equipment industry | Dou |
||
Fuzzy axiomatic design | Engineering plastic material industry | Kannan |
||
Fuzzy WASPAS | Yes | Ghorabaee |
||
DEMATEL, ANP and PROMETHEE | Yes | Polariser industry | Tsui |
|
Fuzzy AHP and TOPSIS | Yes | Fashion industry | Wang and Chan ( |
|
Fuzzy AHP, ARAS and MSGP | Yes | Light industrial machinery industry | Liao |
However, in green supplier evaluation and selection processes, some criteria are often precisely unknown, especially for environmental factors, such as easy recycling and reuse capability. Under this environment, fuzzy set theory can be regarded as an effective tool for addressing uncertainty. Kannan
As shown in Table
This section introduces the methodology used in this study for solving green supplier selection problems. Some concepts of IFSs are presented, followed by the developed methodology and steps.
Let
For an IFS
Let
Let If If If If
Let
Let
The Euclidean distance between two intuitionistic fuzzy matrices can be defined as follows: (See Yue,
This subsection presents an integrated methodology for green supplier selection on the basis of BWM and improved TOPSIS. Figure
For convenience, let
Let
Assessment framework of the proposed approach.
The focus is how to rank alternatives on the basis of individual decision matrices
Define the overall goal, criteria, sub-criteria and associated alternatives for decision-making problems, and then establish the hierarchy of the considered problem.
Design and select the evaluation scale of IFS.
The study by Aloini
Rating alternatives with linguistic terms (Aloini
Linguistic terms
IFNs
Absolutely good (AG)/absolutely high (AH)
Very good (VG)/very high (VH)
Good (G)/high (H)
Medium good (MG)/medium high (MH)
Fair (F)/medium (M)
Medium poor (MP)/medium low (ML)
Poor (P)/low (L)
Very poor (VP)/very low (VL)
Absolutely poor (AP)/absolutely low (AL)
Determine the weight vectors of criteria and sub-criteria.
In accordance with the principle of BWM developed by Rezaei (
Secondly, DMs determine the preferences of the best criterion over all the other criteria by using a number from 1 to 9 (1 means equally important and 9 signifies extremely important). The result is presented as a ‘best-to-others (BO)’ vector as follows:
Thirdly, DMs determine the preferences of the other criteria over the worst criterion by using a number from 1 to 9 (1 means equally important and 9 signifies extremely important). The result is presented as an ‘others-to worst (OW)’ vector as follows:
Lastly, establish a mathematical model and derive the optimal weights
Here, Model (4) can be transformed into the following linear programming model:
The optimal weights
A comparison is fully consistent when
Consistency index of BWM (Rezaei,
1
2
3
4
5
6
7
8
9
Consistency index
0.00
0.44
1.00
1.63
2.33
3.00
3.73
4.47
5.23
The consistency ratio (CR) of the BWM can be calculated, combining the obtained
Determine DMs’ weights with respect to different criteria.
As every DM is skilled in only some specific fields, it is more appropriate to allocate different weight values of each DM on different criteria.
For each criterion
In accordance with the previous analysis,
(1) Calculate the closeness coefficient on the basis of the improved TOPSIS.
Determine the positive ideal decision (PID) vector
The PID vector
Determine all the NID vectors on criterion
The NID vectors consist of the individual negative ideal decision (INID) vector, left individual negative ideal decision (LINID) vector and right individual negative ideal decision (RINID) vector. The INID, LINID and RINID vectors on criterion
Calculate distances
Subsequently, an extended closeness coefficient of each individual decision vector
(2) Calculate the average proximity degree on the basis of distance measure.
The proximity degree between
Furthermore, on the basis of Eq. (
(3) Derive the weights of DMs with respect to different criteria.
To comprehensively consider the closeness coefficient and proximity degree, a control parameter
The unified criterion weight
The unified criterion weights
Let
Rank all the alternatives and select the optimal one (s).
In the following, the target is to rank all the alternatives on the basis of the improved TOPSIS method.
(1) Obtain the group decision matrix with respect to criteria.
For each alternative
(2) Determine the alternatives’ PID vector
Similar to the procedures in Step 4, let
Similar to the individual NID decision vectors, the alternatives’ NID vector should have maximum separation from the alternatives’ PID vector
Moreover, the following alternatives’ decision vector also shows the maximum separation from the alternatives’ PID vector
(3) Calculate the TOPSIS-based index
The distances between each alternative’s decision value
Furthermore, an improved TOPSIS-based index is developed to measure the discrimination of
The improved TOPSIS-based index
Significantly, the closer the alternatives’ decision value
This section presents the result of an empirical case study conducted on a well-known agri-food process company in China.
Agriculture plays an important role in China as China consumes a large number of agriculture products. Agri-food production significantly contributes to the consumption of resources and presents remarkable environmental impacts. Company ABC, located in East China, is one of the leading manufacturers of processed vegetable, edible vegetable oils and condiments in China. With 26 large manufacturing facilities, company ABC has paid a major contribution to the economy and growth in the food sector. Recently, China’s government has paid considerable attention on sustainable development, which can push company ABC to incorporate the green concept into its management and administration. Company ABC is certified by ISO 14000 and uses the related guidelines to perform environmental duties, including encouraging its suppliers to improve their environmental practices and performance continuously. Company ABC needs to complete a supplier selection analysis. Under these circumstances, a decision committee consisting of three members, namely, the chief executive officer (
The detailed procedures for evaluating and selecting the most appropriate green supplier are shown as follows.
A conventional and green supplier evaluation standard is identified on the basis of an extensive review of green supplier evaluation literature in the agri-food industry (Banaeian
Hierarchical structure for green supplier evaluation (Banaeian
Financial (
Capital and financial power of supplier company (
Delivery and service (
Communication system (willingness to trade, attitude, acceptance of procedures and flexibility) (
Qualitative (
Quality (suppliers’ ability to access quality characteristics) (
EMS (
Environmental prerequisite (environmental staff training) (
In the decision process, DMs use the 9 scale linguistic terms to evaluate the performance of suppliers in terms of each criterion. Furthermore, the linguistic evaluation values are transformed into IFNs (see Table
Linguistic evaluation information for alternatives.
FG | FG | M | M | M | G | FG | FG | M | FG | G | FG | G | FG | M | ||
a |
VG | VG | FG | M | M | FG | M | M | G | M | FG | M | FG | M | FG | |
a |
VG | FG | G | FG | M | M | FG | M | M | FG | M | M | M | FG | VG | |
a |
G | G | FG | VG | FG | G | G | G | G | VG | G | VG | G | FG | G | |
G | M | G | G | VG | G | VG | M | G | FG | G | VG | FG | VG | G | ||
a |
VG | VG | G | G | FG | FG | M | FG | FG | FG | FG | FG | FG | M | FG | |
a |
G | M | FG | M | FP | FP | M | M | FG | G | M | M | M | FG | M | |
a |
G | VG | G | G | M | G | FG | M | G | G | VG | G | FG | G | M | |
FG | G | VG | G | FG | FG | VG | G | FG | VG | FG | VG | FG | FG | FG | ||
a |
G | VG | FG | FG | M | G | M | FG | FG | FG | FG | G | G | FG | G | |
a |
M | M | FG | M | FG | M | FG | M | G | G | FG | FG | M | M | M | |
a |
G | VG | G | M | G | FG | G | M | G | FG | VG | M | FG | M | FG |
BO and OW pairwise comparison vectors of criteria provided by DMs.
BO pairwise comparison vector |
OW pairwise comparison vector |
|||||
Main criteria ( |
(1,3,1,5) | (2,2,1,5) | (4,5,1,3) | (5,2,4,1) |
(3,2,5,1) |
(1,1,5,2) |
Sub-criteria ( |
(3,5,1) | (2,6,1) | (1,5,2) | (2,1,5 |
(4,1,6) |
(5,1,2) |
Sub-criteria ( |
(5,1,3,3) | (5,1,2,2) | (6,2,1,4) | (1,5,2,2) |
(1,5,2,2) |
(1,4,6,2) |
Sub-criteria ( |
(1,4,2,2) | (1,5,2,2) | (1,5,1,2) | (4,1,2,2) |
(5,1,3,2) |
(5,1,4,2) |
Sub-criteria ( |
(1,2,2,5) | (1,1,2,6) | (1,2,4,5) | (5,3,2,1) |
(5,6,4,1) |
(5,3,1,1) |
In accordance with the principle of BWM developed by Rezaei (
For the main criteria (
The optimal weights
Similarly, the other results can be derived, as shown in Table
Weight values and CRs for the main criteria.
Weights | CRs | Weights | CRs | Weights | CRs | |
0.418 | 0.087 | 0.254 | 0.097 | 0.133 | 0.087 | |
0.150 | 0.203 | 0.111 | ||||
0.349 | 0.452 | 0.558 | ||||
0.083 | 0.091 | 0.198 |
Weight values and CRs for the sub-criteria.
Weights | CRs | Weights | CRs | Weights | CRs | Final weights ( |
|||
0.229 | 0.075 | 0.337 | 0.099 | 0.601 | 0.064 | 0.096 | 0.085 | 0.080 | |
0.125 | 0.091 | 0.125 | 0.052 | 0.023 | 0.017 | ||||
0.646 | 0.572 | 0.274 | 0.271 | 0.145 | 0.036 | ||||
0.102 | 0.075 | 0.098 | 0.064 | 0.079 | 0.099 | 0.015 | 0.020 | 0.009 | |
0.526 | 0.472 | 0.291 | 0.079 | 0.096 | 0.032 | ||||
0.186 | 0.215 | 0.496 | 0.028 | 0.044 | 0.055 | ||||
0.186 | 0.215 | 0.134 | 0.028 | 0.044 | 0.015 | ||||
0.444 | 0.076 | 0.452 | 0.097 | 0.397 | 0.084 | 0.155 | 0.204 | 0.221 | |
0.112 | 0.091 | 0.083 | 0.039 | 0.041 | 0.046 | ||||
0.222 | 0.254 | 0.339 | 0.078 | 0.115 | 0.189 | ||||
0.222 | 0.203 | 0.181 | 0.078 | 0.092 | 0.101 | ||||
0.452 | 0.097 | 0.315 | 0.099 | 0.501 | 0.087 | 0.038 | 0.029 | 0.100 | |
0.254 | 0.392 | 0.279 | 0.021 | 0.036 | 0.056 | ||||
0.203 | 0.231 | 0.119 | 0.017 | 0.021 | 0.024 | ||||
0.091 | 0.062 | 0.101 | 0.008 | 0.006 | 0.020 |
The weight
(1) Calculate the closeness coefficient
Use Eq. (
Similarly, use Eqs. (
Use Eq. (
(2) Calculate the proximity degree
Use Eqs. (
Furthermore, use Eq. (
(3) Derive the weight
Use Eq. (
Analogously, the other results can be calculated, as shown in Table
Closeness coefficients, proximity degrees and criterion weights of DMs.
0.931 | 0.949 | 0.840 | 0.922 | 0.921 | 0.893 | 0.926 | 0.935 | 0.866 | 0.340 | 0.343 | 0.317 | |
0.912 | 0.908 | 0.931 | 0.913 | 0.926 | 0.930 | 0.913 | 0.917 | 0.931 | 0.331 | 0.332 | 0.337 | |
0.826 | 0.940 | 0.922 | 0.868 | 0.909 | 0.909 | 0.847 | 0.924 | 0.915 | 0.315 | 0.344 | 0.341 | |
0.836 | 0.922 | 0.846 | 0.811 | 0.873 | 0.856 | 0.823 | 0.897 | 0.851 | 0.320 | 0.349 | 0.331 | |
0.841 | 0.838 | 0.878 | 0.870 | 0.820 | 0.859 | 0.855 | 0.829 | 0.869 | 0.335 | 0.325 | 0.340 | |
0.958 | 0.929 | 0.877 | 0.952 | 0.941 | 0.914 | 0.955 | 0.935 | 0.896 | 0.343 | 0.335 | 0.322 | |
0.865 | 0.895 | 0.958 | 0.921 | 0.917 | 0.946 | 0.893 | 0.906 | 0.952 | 0.325 | 0.329 | 0.346 | |
0.828 | 0.842 | 0.890 | 0.881 | 0.910 | 0.914 | 0.854 | 0.876 | 0.902 | 0.325 | 0.332 | 0.343 | |
0.849 | 0.921 | 0.921 | 0.885 | 0.917 | 0.917 | 0.867 | 0.919 | 0.919 | 0.320 | 0.340 | 0.340 | |
0.882 | 0.943 | 0.884 | 0.879 | 0.921 | 0.883 | 0.881 | 0.932 | 0.884 | 0.327 | 0.345 | 0.328 | |
0.923 | 0.962 | 0.899 | 0.946 | 0.958 | 0.929 | 0.934 | 0.960 | 0.914 | 0.333 | 0.341 | 0.326 | |
0.857 | 0.964 | 0.853 | 0.835 | 0.888 | 0.831 | 0.846 | 0.926 | 0.842 | 0.324 | 0.354 | 0.322 | |
0.898 | 0.940 | 0.914 | 0.938 | 0.963 | 0.950 | 0.918 | 0.951 | 0.932 | 0.328 | 0.340 | 0.332 | |
0.925 | 0.876 | 0.822 | 0.913 | 0.876 | 0.864 | 0.919 | 0.876 | 0.843 | 0.348 | 0.332 | 0.320 | |
0.838 | 0.857 | 0.896 | 0.819 | 0.860 | 0.876 | 0.828 | 0.858 | 0.886 | 0.322 | 0.334 | 0.344 |
In the following, the target is to rank all the alternatives on the basis of the improved TOPSIS method.
(1) Obtain the group decision matrix with respect to criteria.
Weighteddecision information (
0.267 | 0.664 | 0.338 | 0.576 | 0.252 | 0.682 | 0.421 | 0.458 | 0.424 | 0.454 | 0.318 | 0.600 | |
0.261 | 0.672 | 0.180 | 0.738 | 0.334 | 0.581 | 0.413 | 0.467 | 0.414 | 0.465 | 0.419 | 0.460 | |
0.172 | 0.749 | 0.339 | 0.575 | 0.422 | 0.456 | 0.251 | 0.684 | 0.339 | 0.575 | 0.268 | 0.664 | |
0.174 | 0.746 | 0.343 | 0.570 | 0.329 | 0.587 | 0.174 | 0.746 | 0.343 | 0.570 | 0.262 | 0.671 | |
0.182 | 0.736 | 0.407 | 0.474 | 0.268 | 0.664 | 0.182 | 0.736 | 0.257 | 0.676 | 0.184 | 0.732 | |
0.338 | 0.576 | 0.332 | 0.583 | 0.255 | 0.679 | 0.270 | 0.662 | 0.265 | 0.668 | 0.321 | 0.596 | |
0.257 | 0.677 | 0.411 | 0.468 | 0.427 | 0.451 | 0.176 | 0.743 | 0.179 | 0.740 | 0.187 | 0.728 | |
0.257 | 0.677 | 0.180 | 0.737 | 0.338 | 0.576 | 0.176 | 0.743 | 0.263 | 0.670 | 0.269 | 0.662 | |
0.174 | 0.746 | 0.336 | 0.579 | 0.268 | 0.664 | 0.320 | 0.597 | 0.268 | 0.664 | 0.268 | 0.664 | |
0.259 | 0.675 | 0.271 | 0.660 | 0.410 | 0.470 | 0.177 | 0.741 | 0.271 | 0.660 | 0.259 | 0.674 | |
0.330 | 0.585 | 0.337 | 0.577 | 0.258 | 0.676 | 0.263 | 0.670 | 0.269 | 0.663 | 0.258 | 0.676 | |
0.257 | 0.677 | 0.435 | 0.442 | 0.405 | 0.476 | 0.176 | 0.743 | 0.277 | 0.653 | 0.321 | 0.595 | |
0.326 | 0.590 | 0.267 | 0.664 | 0.263 | 0.670 | 0.259 | 0.674 | 0.267 | 0.664 | 0.330 | 0.585 | |
0.273 | 0.657 | 0.414 | 0.466 | 0.254 | 0.681 | 0.188 | 0.727 | 0.180 | 0.738 | 0.254 | 0.681 | |
0.175 | 0.745 | 0.331 | 0.585 | 0.271 | 0.661 | 0.255 | 0.679 | 0.263 | 0.669 | 0.339 | 0.574 |
Weighted decision information (
0.421 | 0.458 | 0.338 | 0.576 | 0.173 | 0.748 | 0.336 | 0.579 | 0.338 | 0.576 | 0.318 | 0.600 | |
0.261 | 0.672 | 0.180 | 0.738 | 0.183 | 0.734 | 0.328 | 0.587 | 0.414 | 0.465 | 0.419 | 0.460 | |
0.316 | 0.602 | 0.270 | 0.661 | 0.268 | 0.664 | 0.251 | 0.684 | 0.339 | 0.575 | 0.336 | 0.578 | |
0.254 | 0.680 | 0.188 | 0.726 | 0.180 | 0.738 | 0.403 | 0.479 | 0.343 | 0.570 | 0.180 | 0.738 | |
0.182 | 0.736 | 0.153 | 0.798 | 0.268 | 0.664 | 0.264 | 0.668 | 0.176 | 0.743 | 0.336 | 0.578 | |
0.185 | 0.730 | 0.158 | 0.792 | 0.175 | 0.745 | 0.338 | 0.576 | 0.332 | 0.583 | 0.255 | 0.679 | |
0.257 | 0.677 | 0.179 | 0.740 | 0.272 | 0.659 | 0.323 | 0.593 | 0.260 | 0.673 | 0.341 | 0.573 | |
0.176 | 0.743 | 0.180 | 0.737 | 0.185 | 0.731 | 0.323 | 0.593 | 0.180 | 0.737 | 0.185 | 0.731 | |
0.174 | 0.746 | 0.268 | 0.664 | 0.336 | 0.579 | 0.320 | 0.597 | 0.336 | 0.579 | 0.336 | 0.579 | |
0.259 | 0.675 | 0.340 | 0.573 | 0.326 | 0.590 | 0.409 | 0.471 | 0.340 | 0.573 | 0.259 | 0.674 | |
0.180 | 0.737 | 0.185 | 0.731 | 0.258 | 0.676 | 0.330 | 0.585 | 0.423 | 0.455 | 0.408 | 0.473 | |
0.176 | 0.743 | 0.191 | 0.723 | 0.256 | 0.679 | 0.406 | 0.475 | 0.347 | 0.565 | 0.175 | 0.744 | |
0.178 | 0.741 | 0.184 | 0.733 | 0.180 | 0.737 | 0.326 | 0.590 | 0.267 | 0.664 | 0.263 | 0.670 | |
0.273 | 0.657 | 0.262 | 0.670 | 0.174 | 0.746 | 0.273 | 0.657 | 0.330 | 0.586 | 0.174 | 0.746 | |
0.404 | 0.476 | 0.181 | 0.737 | 0.186 | 0.729 | 0.321 | 0.596 | 0.181 | 0.737 | 0.271 | 0.661 |
Use Eq. (
(2) Determine the alternatives’ PID vector
The alternatives’ PID vector
Use Eqs. (
(3) Calculate the TOPSIS-based index
Use Eq. (
Similarly, the other TOPSIS-based indices can be obtained. Then, use Eq. (
Descend the comprehensive TOPSIS-based indices. And the ranking of all the alternatives is
This section presents the analysis of the influence of varying
In the existing methods (Yue,
Comprehensive TOPSIS-based indices with different
0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | |
0.8483 | 0.8484 | 0.8485 | 0.8486 | 0.8487 | 0.8488 | 0.8489 | 0.8490 | 0.8491 | 0.8492 | 0.8493 | |
0.8136 | 0.8136 | 0.8137 | 0.8137 | 0.8138 | 0.8139 | 0.8139 | 0.8140 | 0.8140 | 0.8141 | 0.8141 | |
0.7555 | 0.7554 | 0.7553 | 0.7552 | 0.7550 | 0.7549 | 0.7548 | 0.7547 | 0.7545 | 0.7544 | 0.7542 | |
0.8488 | 0.8487 | 0.8486 | 0.8485 | 0.8484 | 0.8484 | 0.8483 | 0.8482 | 0.8481 | 0.8480 | 0.8479 |
Ranking orders of alternatives with varying
Furthermore, this study inherits the idea of Yue (
Results with different methods.
IF-TOPSIS method | IF-VIKOR method | Proposed approach | ||||||
Ranking result | Ranking result | CI( |
Ranking result | |||||
0.688 | 2 | 0.225 | 0.087 | 0.079 | 0.849 | 1 | ||
0.408 | 3 | 0.581 | 0.144 | 0.583 | 0.814 | 3 | ||
0.138 | 4 | 0.859 | 0.193 | 1 | 0.755 | 4 | ||
0.755 | 1 | 0.248 | 0.067 | 0.018 | 0.848 | 2 |
The proposed approach is compared with two other distance-based methods, namely, the integrated AHP and IF-TOPSIS method (Buyukozkan and Guleryuz,
Furthermore, the three methods are used to solve the same green supplier selection problem. Firstly, assume that the parameter
Performances of alternatives with respect to criteria.
The green supplier selection problem is one of the most significant issues in green supply chain management. Particularly, in China’s agri-food industry, green practices play an important role in leading the society towards green economy. This work develops a novel MCGDM method for solving green supplier selection problems. The proposed MCGDM model contributes to the evaluation and selection of green suppliers. This study provides the following conclusions.
A new way to derive criterion weights by using BWM, which requires less comparison data, but leads to more consistent comparisons than traditional AHP, is presented.
The familiarity of DMs with respect to different criteria is considered, and an improved TOPSIS structure integrated with a proximity measure is provided to calculate the DMs’ weights in terms of criteria. Moreover, a comprehensive TOPSIS-based index is utilized to describe the performances of alternatives cautiously.
The developed methodology is applied to address the green supplier selection problem in the agri-food industry. The sensitivity and comparative analyses demonstrate the priority and effectiveness of the proposed method.
However, some limitations are present in this study. The calculation process of the proposed approach is more complex than that of the traditional fuzzy method, such as simple arithmetic average, IF-TOPSIS and IF-VIKOR. Moreover, the consensus reaching process is not considered in the proposed MCGDM. In the future, the proposed method can be further improved by designing effective algorithms to reduce the complexity and overcome the limitation of rank reversal (Aouadni