Hesitant Trapezoidal Fuzzy QUALIFLEX Method and Its Application in the Evaluation of Green Supply Chain Initiatives
Abstract
:1. Introduction
2. Preliminaries
2.1. Some Useful Concepts
2.2. New Concept of Hesitant Trapezoidal Fuzzy Sets
- (1)
- ;
- (2)
- ;
- (3)
- ;
- (4)
- .
- (1)
- ;
- (2)
- ;
- (3)
- ;
- (4)
- ;
- (5)
- ;
- (6)
- .
- (1)
- if , then ;
- (2)
- if , then ;
- (3)
- if , then .
3. Hesitant Trapezoidal Fuzzy QUALIFLEX Analysis Method
3.1. Description of the Hierarchical MCDM Problem with HTrFNs
3.2. The Proposed Method
3.3. The Proposed Algorithm
4. A Case Study for the Evaluation of Green Supply Chain Initiatives
4.1. Decision Context and the Analysis Process
4.2. Comparative Analysis
4.2.1. Comparative Analysis with the TOPSIS
4.2.2. Comparative Analysis with the ELECTRE
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Ratings | Abbreviation | TrFNs |
---|---|---|
s0: Very poor | VP | T (0.0, 0.0, 0.1, 0.2) |
s1: Poor | P | T (0.1, 0.2, 0.2, 0.3) |
s2: Medium poor | MP | T (0.2, 0.3, 0.4, 0.5) |
s3: Fair | F | T (0.4, 0.5, 0.5, 0.6) |
s4: Medium good | MG | T (0.5, 0.6, 0.7, 0.8) |
s5: Good | G | T (0.7, 0.8, 0.8, 0.9) |
s6: Very good | VG | T (0.8, 0.9,1.0, 1.0) |
Main Criteria | Weights of Main Criteria | Sub-Criteria | Weights of Sub-Criteria | Alternative Initiatives |
---|---|---|---|---|
C1 Manufacturing | 0.285 | C1(1) Processes | 0.269 | A1 Implement Now |
C1(2) Technical capability | 0.121 | |||
C1(3) Innovation capability | 0.193 | |||
C1(4) Production capacity | 0.417 | |||
C2 Purchasing | 0.163 | C2(1) Raw material availability | 0.423 | A2 Implement in 6 months |
C2(2) Suppliers | 0.227 | |||
C2(3) Inventory level | 0.123 | |||
C2(4) Assurance of supply | 0.227 | |||
C3 Logistics | 0.184 | C3(1) Inbound logistics | 0.110 | A3 Implement in 12 months |
C3(2) Outbound logistics | 0.230 | |||
C3(3) Packaging | 0.302 | |||
C3(4) Shipment accuracy | 0.358 | |||
C4 Marketing | 0.368 | C4(1) Salability | 0.372 | |
C4(2) Growth | 0.237 | |||
C4(3) Marketability | 0.278 | |||
C4(4) Customer service | 0.113 |
Sub-Criteria | Alternatives | ||
---|---|---|---|
A1 | A2 | A3 | |
C1(1) | MP | Between P and MP | At most MP |
C1(2) | Between MG and G | MG | At least G |
C1(3) | MP | Between MP and F | MP |
C1(4) | At least MG | G | MG |
C2(1) | Between P and MP | MG | P |
C2(2) | G | Between MP and F | At least G |
C2(3) | P | Between P and MP | Between MP and F |
C2(4) | F | G | MG |
C3(1) | MP | F | MP |
C3(2) | P | MP | At most P |
C3(3) | F | At least MG | F |
C3(4) | At most MP | MP | Between P and MP |
C4(1) | MG | MG | At least MG |
C4(2) | MG | G | At least G |
C4(3) | MP | F | F |
C4(4) | Between F and G | At least MG | F |
Sub-Criteria | Alternatives | ||
---|---|---|---|
A1 | A2 | A3 | |
C1(1) | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.2, 0.3, 0.4, 0.5)} | {T (0.0, 0.0, 0.1, 0.2), T (0.1, 0.2, 0.2, 0.3), T (0.2, 0.3, 0.4, 0.5)} |
C1(2) | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.7, 0.8, 0.8, 0.9)} | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} |
C1(3) | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.4, 0.5, 0.5, 0.6)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} |
C1(4) | {T (0.5, 0.6, 0.7, 0.8), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9)} | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} |
C2(1) | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.2, 0.3, 0.4, 0.5)} | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3)} |
C2(2) | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.4, 0.5, 0.5, 0.6)} | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} |
C2(3) | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3)} | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.2, 0.3, 0.4, 0.5)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.4, 0.5, 0.5, 0.6)} |
C2(4) | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9)} | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} |
C3(1) | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} |
C3(2) | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} | {T (0.0, 0.0, 0.1, 0.2), T (0.0, 0.0, 0.1, 0.2), T (0.1, 0.2, 0.2, 0.3)} |
C3(3) | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} | {T (0.5, 0.6, 0.7, 0.8), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} |
C3(4) | {T (0.0, 0.0, 0.1, 0.2), T (0.1, 0.2, 0.2, 0.3), T (0.2, 0.3, 0.4, 0.5)} | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} | {T (0.1, 0.2, 0.2, 0.3), T (0.1, 0.2, 0.2, 0.3), T (0.2, 0.3, 0.4, 0.5)} |
C4(1) | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} | {T (0.5, 0.6, 0.7, 0.8), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} |
C4(2) | {T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8), T (0.5, 0.6, 0.7, 0.8)} | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9)} | {T (0.7, 0.8, 0.8, 0.9), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} |
C4(3) | {T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5), T (0.2, 0.3, 0.4, 0.5)} | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} |
C4(4) | {T (0.4, 0.5, 0.5, 0.6), T (0.5, 0.6, 0.7, 0.8), T (0.7, 0.8, 0.8, 0.9)} | {T (0.5, 0.6, 0.7, 0.8), T (0.7, 0.8, 0.8, 0.9), T (0.8, 0.9, 1.0, 1.0)} | {T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6), T (0.4, 0.5, 0.5, 0.6)} |
C1(1) | 0.05 | 0.1444 | 0.0694 | C1(1) | 0.1444 | 0.05 | −0.0694 |
C1(2) | 0.0833 | −0.1333 | −0.2167 | C1(2) | −0.1333 | 0.0833 | 0.2167 |
C1(3) | −0.075 | 0 | −0.075 | C1(3) | 0 | −0.075 | 0.075 |
C1(4) | −0.0056 | 0.1445 | 0.15 | C1(4) | 0.1445 | −0.0056 | −0.15 |
C2(1) | −0.375 | 0.075 | 0.45 | C2(1) | 0.075 | −0.375 | −0.45 |
C2(2) | 0.375 | −0.0667 | −0.4417 | C2(2) | −0.0667 | 0.375 | 0.4417 |
C2(3) | −0.075 | −0.225 | −0.15 | C2(3) | −0.225 | −0.075 | 0.15 |
C2(4) | −0.3 | −0.15 | 0.15 | C2(4) | −0.15 | −0.3 | −0.15 |
C3(1) | −0.15 | 0 | 0.15 | C3(1) | 0 | −0.15 | −0.15 |
C3(2) | −0.15 | 0.067 | 0.2167 | C3(2) | 0.067 | −0.15 | −0.2167 |
C3(3) | −0.2945 | 0 | 0.2945 | C3(3) | 0 | −0.2945 | −0.2945 |
C3(4) | −0.14445 | −0.06945 | 0.075 | C3(4) | −0.06945 | −0.14445 | −0.075 |
C4(1) | 0 | −0.1444 | −0.1444 | C4(1) | −0.1444 | 0 | 0.1444 |
C4(2) | −0.15 | −0.2167 | −0.0667 | C4(2) | −0.2167 | −0.15 | 0.0667 |
C4(3) | −0.15 | −0.15 | 0 | C4(3) | −0.15 | −0.15 | 0 |
C4(4) | −0.1444 | 0.15 | 0.2945 | C4(4) | 0.15 | −0.1444 | −0.2945 |
C1(1) | −0.05 | 0.0694 | 0.1444 | C1(1) | 0.0694 | −0.05 | −0.1444 |
C1(2) | −0.0833 | −0.2167 | −0.1333 | C1(2) | −0.2167 | −0.0833 | 0.1333 |
C1(3) | 0.075 | −0.075 | 0 | C1(3) | −0.075 | 0.075 | 0 |
C1(4) | 0.0056 | 0.15 | 0.1445 | C1(4) | 0.15 | 0.0056 | −0.1445 |
C2(1) | 0.375 | 0.45 | 0.075 | C2(1) | 0.45 | 0.375 | −0.075 |
C2(2) | −0.375 | −0.4417 | −0.0667 | C2(2) | −0.4417 | −0.375 | 0.0667 |
C2(3) | 0.075 | −0.15 | −0.225 | C2(3) | −0.15 | 0.075 | 0.225 |
C2(4) | 0.3 | 0.15 | −0.15 | C2(4) | 0.15 | 0.3 | 0.15 |
C3(1) | 0.15 | 0.15 | 0 | C3(1) | 0.15 | 0.15 | 0 |
C3(2) | 0.15 | 0.2167 | 0.067 | C3(2) | 0.2167 | 0.15 | −0.067 |
C3(3) | 0.2945 | 0.2945 | 0 | C3(3) | 0.2945 | 0.2945 | 0 |
C3(4) | 0.14445 | 0.075 | −0.06945 | C3(4) | 0.075 | 0.14445 | 0.06945 |
C4(1) | 0 | −0.1444 | −0.1444 | C4(1) | −0.1444 | 0 | 0.1444 |
C4(2) | 0.15 | −0.0667 | −0.2167 | C4(2) | −0.0667 | 0.15 | 0.2167 |
C4(3) | 0.15 | 0 | −0.15 | C4(3) | 0 | 0.15 | 0.15 |
C4(4) | 0.1444 | 0.2945 | 0.15 | C4(4) | 0.2945 | 0.1444 | −0.15 |
C1(1) | −0.1444 | −0.0694 | 0.05 | C1(1) | −0.0694 | −0.1444 | −0.05 |
C1(2) | 0.1333 | 0.2167 | 0.0833 | C1(2) | 0.2167 | 0.1333 | −0.0833 |
C1(3) | 0 | 0.075 | −0.075 | C1(3) | 0.075 | 0 | 0.075 |
C1(4) | −0.1445 | −0.15 | −0.0056 | C1(4) | −0.15 | −0.1445 | 0.0056 |
C2(1) | −0.075 | −0.45 | −0.375 | C2(1) | −0.45 | −0.075 | 0.375 |
C2(2) | 0.0667 | 0.4417 | 0.375 | C2(2) | 0.4417 | 0.0667 | −0.375 |
C2(3) | 0.225 | 0.15 | −0.075 | C2(3) | 0.15 | 0.225 | 0.075 |
C2(4) | 0.15 | −0.15 | −0.3 | C2(4) | −0.15 | 0.15 | 0.3 |
C3(1) | 0 | −0.15 | −0.15 | C3(1) | −0.15 | 0 | 0.15 |
C3(2) | −0.067 | −0.2167 | −0.15 | C3(2) | −0.2167 | −0.067 | 0.15 |
C3(3) | 0 | −0.2945 | −0.2945 | C3(3) | −0.2945 | 0 | 0.2945 |
C3(4) | 0.06945 | −0.075 | −0.14445 | C3(4) | −0.075 | 0.06945 | 0.14445 |
C4(1) | 0.1444 | 0.1444 | 0 | C4(1) | 0.1444 | 0.1444 | 0 |
C4(2) | 0.2167 | 0.0667 | −0.15 | C4(2) | 0.0667 | 0.2167 | 0.15 |
C4(3) | 0.15 | 0 | −0.15 | C4(3) | 0 | 0.15 | 0.15 |
C4(4) | −0.15 | −0.2945 | −0.1444 | C4(4) | −0.2945 | −0.15 | 0.1444 |
Ranking | ||||
---|---|---|---|---|
A1 | 0.5222 | 0.5324 | 0.5048 | 3 |
A2 | 0.4794 | 0.5709 | 0.5436 | 1 |
A3 | 0.4902 | 0.5655 | 0.5357 | 2 |
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Zhang, X.; Xu, Z.; Liu, M. Hesitant Trapezoidal Fuzzy QUALIFLEX Method and Its Application in the Evaluation of Green Supply Chain Initiatives. Sustainability 2016, 8, 952. https://doi.org/10.3390/su8090952
Zhang X, Xu Z, Liu M. Hesitant Trapezoidal Fuzzy QUALIFLEX Method and Its Application in the Evaluation of Green Supply Chain Initiatives. Sustainability. 2016; 8(9):952. https://doi.org/10.3390/su8090952
Chicago/Turabian StyleZhang, Xiaolu, Zeshui Xu, and Manfeng Liu. 2016. "Hesitant Trapezoidal Fuzzy QUALIFLEX Method and Its Application in the Evaluation of Green Supply Chain Initiatives" Sustainability 8, no. 9: 952. https://doi.org/10.3390/su8090952