Resilient Supplier Selection in Electronic Components Procurement: An Integration of Evidence Theory and RuleBased Transformation into TOPSIS to Tackle Uncertain and Incomplete Information
Abstract
:1. Introduction
2. Literature Review
2.1. Trends in Supplier Selection
2.2. Resilient Supplier Selection
2.3. Supplier Selection in the Electronics Industry
2.4. Suggested List of Criteria for Resilient Supplier Selection in the Electronics Industry
3. Extension of TOPSIS
3.1. Evidence Theory and Generalised Decision Matrix
3.2. RuleBased Information Transformation Technique
3.2.1. RuleBased Transformation Technique for Qualitative Assessment
3.2.2. RuleBased Transformation Technique for Quantitative Assessment
3.3. Integration of a Generalised Decision Matrix Into TOPSIS
 Conduct an assessment of quantitative criteria through numerical measurement and qualitative criteria with a specified set of evaluation grades. Degrees of belief are assigned to numerical values for quantitative criteria and grades that best describe the actual situation for qualitative criteria. Note that more than one value or a grade could be assigned if the situation is uncertain, and the total degree of belief could be less than one if the supporting information is insufficient or incomplete. The results can eventually be in various forms, as defined in Table 3.
 Identify a general set of grades and construct the equivalence rules between the assessment scales of each criterion and the general grades.
 Transform the original assessment results, using the rulebased transformation technique, into the generalised belief structure $S\left({e}_{i}\left({a}_{l}\right)\right)$ for each alternative ${a}_{l}$ for each criterion ${e}_{i}$, and then draw the generalised decision matrix, as exemplified by Table 2.
 Convert the belief structures into utility intervals, and then construct the interval decision matrix, as shown in Table 5.
 Calculate the min $C{C}_{l}$ and max $C{C}_{l}$ for each alternative ${a}_{l}$ based on extended TOPSIS.
 Select the best alternative based solely on avg $CC$ or in combination with the decisionmaker’s risk attitude.
4. Application of the Proposed Methodology in a Resilient Supplier Selection Problem
 ${\beta}_{Excellent,1}=\left(0.4\times 0.5\right)=0.2$
 ${\beta}_{Good,1}=\left(0.6\times 0.5\right)+\left(0.4\times 0.5\right)=0.5$
 ${\beta}_{Fair,1}=\left(0.4\times 0.5\right)=0.2$
 ${\beta}_{Poor,1}=\left(0.2\times 0.5\right)=0.1$
 ${\beta}_{Very\text{}poor,1}=0$
 ${\beta}_{Fair,7}=\frac{76}{74}=0.333$
 ${\beta}_{Poor,7}=10.333=0.667$
 ${\beta}_{Excellent,7}={\beta}_{Good,7}={\beta}_{Very\text{}poor,7}=0$
 Although both methodologies provide a compensatory process of aggregation, they employ different approaches to derive the composite scores for each alternative. The proposed hybrid methodology is based on the principle of the TOPSIS method, which derives the score from the distances between the performance of the alternative and the best and worst values within the peer group, while the ER method conforms to conjunctive reasoning by seeking joint support from all criteria. This means that the composite score of an alternative derived by the ER method is independent of the performance of other alternatives; however, this is not the case for the TOPSISbased methodology.
 According to the different approaches described in (1), the ER method did not assign an interval to supplier 1′s composite score since the interval only reflected the incompleteness of the information which emerged solely from suppliers 2 and 3. This implies that supplier 1′s overall performance did not change whether or not the other suppliers’ performance fluctuated. On the other hand, the TOPSIS method gave an interval to supplier 1′s composite score due to the fact that the other suppliers’ performance was uncertain because of incomplete or unknown information, and the overall performance of an alternative was dependent on the changes in performance of the others. Therefore, the proposed TOPSIS methodology is more rational, and provides a more comprehensive picture for ranking and choosing alternatives. The ER method seems to be more appropriate for constructing a selfassessment model for analysing and monitoring overall performance. The performance analysis of a single element without another alternative for comparison is an obvious limitation of the TOPSISbased methodology.
 When considering minimum composite scores derived by the two methodologies, supplier 2 received a lower score than supplier 3 in the TOPSIS method, while the opposite result was obtained by the ER method. Such a difference was mainly caused by the high level of incompleteness in supplier 3′s performance (in criteria ${e}_{6}$ and ${e}_{7}$). The incompleteness means that the performance can be assigned to any value or any grade in the frame of discernment, such that its utility can range from 0 to 1. In the extended TOPSIS method, when calculating the minimum score for each alternative, its performance is assumed at the lowest level while the performance of the others is set at the highest level. This means that when calculating min $C{C}_{2}$, supplier 3′s utility was assumed at 0.7 and 1 in criteria ${e}_{6}$ and ${e}_{7}$, respectively. This considerably downgraded supplier 2′s $CC$ score due to the large distance between its minimum performance and the assumed excellent performance of supplier 3. Although the same method was applied when calculating min $C{C}_{3}$, the effects were not significant since only a short distance between supplier 3′s minimum utility and the highest utility of other suppliers was reported.
 Based on the explanation in (3), each alternative’s range derived by the proposed TOPSIS methodology is not sensitive to the incompleteness and uncertainty of its own assessment data, but to those of the other alternatives. In contrast, in the ER approach, each alternative’s range is a true reflection of the incompleteness of its own data.
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Criterion  Definition  References 

Resilience capabilities  
1. Responsiveness  The supplier’s ability and availability to quickly react or respond to customer requirements.  [1,6,7,11,13,15,38,39] 
2. Safety stock inventory  The supplier’s capacity to hold adequate amounts of essential materials and goods to support customers during disruptive events.  [1,2,4,6,7,11,13] 
3. Invulnerable location  The supplier’s location which should be in a safe area with low risk of natural disasters to minimise impacts on supply chain processes.  [4,6,14] 
4. Backup supplier contracts  The supplier’s outsourcing contracts which enable customers to overcome shortages of supply capacity in the case of disruption.  [2,6,7,13,14] 
5. Robustness  Physical protection infrastructure and safety system of the supplier’s building and facilities to minimise negative impacts of disruption, especially in the case of natural disasters.  [4,6,13,15,39] 
6. Delivery rerouting  Rerouting options (based on the supplier’s location) or the supplier’s ability to adjust transportation routes during disruptive events.  [4,6,13,14,39] 
7. Restoration  The supplier’s ability to restore damaged facilities and equipment or to resume production to a normal state of operation.  [2,6,7,13,15] 
8. Risk of production shutdown  The possibility of production shutdown, which may be caused by failure of facilities, machine breakdown, labour strikes, natural disasters, and technological problems.  [4,8,14,15,38] 
9. Risk of transportation failure  The possibility of transportation failure, which may be caused by vehicle failure, route insecurity, terrorist attacks, and natural disasters.  [4,8,14,15] 
10. Risk of communication breakdown and loss of information  The possibility of communication and transaction breakdown which may be caused by system errors and instability and insecurity of the information system.  [4,8,13,14,15,38,39,41] 
General criteria  
11. Production capacity  The volume of products that can be produced and delivered by the supplier using their current resources.  [4,7,13,23,38,39,40,41] 
12. Delivery performance  The supplier’s order cycle time, ontime delivery performance, and shipping accuracy.  [4,7,8,13,15,22,23,38,39,40,41,42] 
13. Service and support  The supplier’s ability and willingness to assist with the design process and ability to provide technical assistance and support for postsales services.  [1,8,11,15,22,23,38,40,41,42] 
14. Innovation and technology  The supplier’s innovation and technological advances.  [7,15,23,38,40,41] 
15. Firm’s image and reputation  The supplier’s profile, image, market share, and brand recognition.  [7,8,15,23,38,39,40,41,42] 
16. Product quality  Defect rate at the customer’s plant, or the supplier’s process capability.  [1,4,7,8,11,15,22,23,38,39,40,41,42] 
17. Product price  The unit price of the product.  [1,4,7,8,11,13,15,22,23,38,39,40,41,42] 
Decision Matrix M × L  w_{1}  w_{2}  …  w_{L} 

e_{1}  e_{2}  …  e_{L}  
${a}_{1}$  $S\left({e}_{1}\left({a}_{1}\right)\right)$  $S\left({e}_{2}\left({a}_{1}\right)\right)$  …  $S\left({e}_{L}\left({a}_{1}\right)\right)$ 
${a}_{2}$  $S\left({e}_{1}\left({a}_{2}\right)\right)$  $S\left({e}_{2}\left({a}_{2}\right)\right)$  …  $S\left({e}_{L}\left({a}_{2}\right)\right)$ 
…  …  …  …  … 
…  …  …  …  … 
${a}_{M}$  $S\left({e}_{1}\left({a}_{M}\right)\right)$  $S\left({e}_{2}\left({a}_{M}\right)\right)$  …  $S\left({e}_{L}\left({a}_{M}\right)\right)$ 
Assessment Results  $\mathbf{Mathematical}\text{}\mathbf{Formulations}\text{}\mathbf{(}\mathit{i}\mathbf{=}\mathbf{1}\mathbf{,}\text{}\mathbf{\dots}\mathbf{,}\text{}\mathit{L}\mathbf{,}\text{}\mathit{l}\mathbf{=}\mathbf{1}\mathbf{,}\text{}\mathbf{\dots}\mathbf{,}\text{}\mathit{M}\mathbf{)}$ 

Qualitative assessment  
(1) Precise and complete  ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n}^{i},1.0\right)\right\}$ 
(2) Uncertain but complete  ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n}^{i},{\gamma}_{n}^{i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,{N}^{i}\right\}$, $\sum}_{n=1}^{{N}^{i}}{\gamma}_{n}^{i}\left({a}_{l}\right)=1$ 
(3) Uncertain and incomplete (with a degree of ignorance)  ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n}^{i},{\gamma}_{n}^{i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,\text{}{N}^{i}\right\}$, $\sum}_{n=1}^{{N}^{i}}{\gamma}_{n}^{i}\left({a}_{l}\right)<1$ 
(4) Complete ignorance  n/a (the assessor has no information to conduct the assessment) 
Quantitative assessment  
(5) Precise and complete  ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({h}_{j}^{i},\text{}1.0\right)\right\}$ 
(6) Uncertain but complete  ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({h}_{j}^{i},\text{}{\gamma}_{j}^{i}\left({a}_{l}\right)\right),\text{}j=1,\text{}\dots ,\text{}J\right\}$, $\sum}_{j=1}^{J}{\gamma}_{j}^{i}=1$ 
(7) Uncertain and incomplete (with a degree of ignorance)  ${S}^{i}\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({h}_{j}^{i},\text{}{\gamma}_{j}^{i}\left({a}_{l}\right)\right),\text{}j=1,\text{}\dots ,\text{}J\right\}$, $\sum}_{j=1}^{J}{\gamma}_{j}^{i}<1$ 
(8) Complete ignorance  n/a 
Assessment Results  $\mathbf{Mathematical}\text{}\mathbf{Formulations}\text{}(\mathit{i}\mathbf{=}\mathbf{1}\mathbf{,}\text{}\dots \mathbf{,}\text{}\mathit{L},\text{}\mathit{l}\mathbf{=}\mathbf{1},\text{}\mathbf{\dots}\mathbf{,}\text{}\mathit{M}\mathbf{)}$ 

Qualitative assessment  
(1) Precise and complete  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,N\right\}$, $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)=1$ 
(2) Uncertain but complete  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,N\right\}$, $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)=1$ 
(3) Uncertain and incomplete (with a degree of ignorance)  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,\text{}N;\text{}\left(H,{\beta}_{H,i}\left({a}_{l}\right)\right)\right\}$, $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)<1$ and ${\beta}_{H,i}\left({a}_{l}\right)>0$ and $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)+{\beta}_{H,i}\left({a}_{l}\right)=1$ 
(4) Complete ignorance  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left(H,1.0\right)\right\}$ 
Quantitative assessment  
(5) Precise and complete  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,N\right\}$, $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)=1$ 
(6) Uncertain but complete  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,N\right\}$, $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)=1$ 
(7) Uncertain and incomplete (with a degree of ignorance)  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left({H}_{n},{\beta}_{n,i}\left({a}_{l}\right)\right),\text{}n=1,\text{}\dots ,\text{}N;\text{}\left(H,{\beta}_{H,i}\left({a}_{l}\right)\right)\right\}$, $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)<1$ and ${\beta}_{H,i}\left({a}_{l}\right)>0$ and $\sum}_{n=1}^{N}{\beta}_{n,i}\left({a}_{l}\right)+{\beta}_{H,i}\left({a}_{l}\right)=1$ 
(8) Complete ignorance  $S\left({e}_{i}\left({a}_{l}\right)\right)=\left\{\left(H,1.0\right)\right\}$ 
Decision Matrix $2\mathit{M}\mathbf{\times}\mathit{L}$  ${\mathit{w}}_{\mathbf{1}}$  ${\mathit{w}}_{\mathbf{2}}$  …  ${\mathit{w}}_{\mathit{L}}$ 

${\mathit{e}}_{1}$  ${\mathit{e}}_{2}$  …  ${\mathit{e}}_{\mathit{L}}$  
${a}_{1}$  ${U}_{min}\left({e}_{1}\left({a}_{1}\right)\right)$  ${U}_{min}\left({e}_{2}\left({a}_{1}\right)\right)$  …  ${U}_{min}\left({e}_{L}\left({a}_{1}\right)\right)$ 
${U}_{max}\left({e}_{1}\left({a}_{1}\right)\right)$  ${U}_{max}\left({e}_{2}\left({a}_{1}\right)\right)$  …  ${U}_{max}\left({e}_{L}\left({a}_{1}\right)\right)$  
${a}_{2}$  ${U}_{min}\left({e}_{1}\left({a}_{2}\right)\right)$  ${U}_{min}\left({e}_{2}\left({a}_{2}\right)\right)$  …  ${U}_{min}\left({e}_{L}\left({a}_{2}\right)\right)$ 
${U}_{max}\left({e}_{1}\left({a}_{2}\right)\right)$  ${U}_{max}\left({e}_{2}\left({a}_{2}\right)\right)$  …  ${U}_{max}\left({e}_{L}\left({a}_{2}\right)\right)$  
…  …  …  …  … 
…  …  …  …  
${a}_{M}$  ${U}_{min}\left({e}_{1}\left({a}_{M}\right)\right)$  ${U}_{min}\left({e}_{2}\left({a}_{M}\right)\right)$  …  ${U}_{min}\left({e}_{L}\left({a}_{M}\right)\right)$ 
${U}_{max}\left({e}_{1}\left({a}_{M}\right)\right)$  ${U}_{max}\left({e}_{2}\left({a}_{M}\right)\right)$  …  ${U}_{max}\left({e}_{L}\left({a}_{M}\right)\right)$ 
Criterion  Assessment Scale 

Responsiveness $({e}_{1})$  Assessment grades A–D

Backup supplier contracts $({e}_{2})$  The number of backup suppliers or partners that can supply raw materials when disruptive events occur (count data) 
Restoration $({e}_{3})$  Assessment grades A–D

Risk of losing information and communication $({e}_{4})$  The number of failures or issues regarding the supplier’s information and communication infrastructure/network during the past 12 months (count data) 
Service and support $({e}_{5})$  Assessment grades A–E

Innovation and technology $({e}_{6})$  Assessment grades A–D

Product quality $({e}_{7})$  The defect rate in the last quarter (defective parts per million: DPPM) 
Criteria  Equivalence Rules 
Responsiveness $({e}_{1})$  A $\leftrightarrow $ {(Excellent, 1)} 
B $\leftrightarrow $ {(Excellent, 0.4), (Good, 0.6)}  
C $\leftrightarrow $ {(Good, 0.4), (Fair, 0.4), (Poor, 0.2)}  
D $\leftrightarrow $ {(Very poor, 1)}  
Backup supplier contracts $({e}_{2})$  ≥4 $\leftrightarrow $ Excellent 
3 $\leftrightarrow $ Good  
2 $\leftrightarrow $ Fair  
1 $\leftrightarrow $ Poor  
0 $\leftrightarrow $ Very poor  
Restoration $({e}_{3})$  A $\leftrightarrow $ {(Excellent, 1)} 
B $\leftrightarrow $ {(Excellent, 0.4), (Good, 0.6)}  
C $\leftrightarrow $ {(Fair, 0.7), (Poor, 0.3)}  
D $\leftrightarrow $ {(Very poor, 1)}  
Risk of losing information and communication $({e}_{4})$  0 $\leftrightarrow $ Excellent 
1 $\leftrightarrow $ Good  
2 $\leftrightarrow $ Fair  
3 $\leftrightarrow $ Poor  
≥4 $\leftrightarrow $ Very poor  
Service and support $({e}_{5})$  A $\leftrightarrow $ {(Excellent, 1)} 
B $\leftrightarrow $ {(Good, 1)}  
C $\leftrightarrow $ {(Fair, 1)}  
D $\leftrightarrow $ {(Poor, 1)}  
E $\leftrightarrow $ {(Very poor, 1)}  
Innovation and technology $({e}_{6})$  A $\leftrightarrow $ {(Excellent, 1)} 
B $\leftrightarrow $ {(Good, 1)}  
C $\leftrightarrow $ {(Fair, 0.5), (Poor, 0.5)}  
D $\leftrightarrow $ {(Very poor, 1)}  
Product quality $({e}_{7})$  ≤1 $\leftrightarrow $ Excellent 
2.5 $\leftrightarrow $ Good  
4 $\leftrightarrow $ Fair  
7 $\leftrightarrow $ Poor  
≥10 $\leftrightarrow $ Very poor 
Original Decision Matrix $\mathbf{3}\mathbf{\times}\mathbf{7}$  ${\mathit{w}}_{\mathbf{1}}\mathbf{=}\mathbf{0.17}$  ${\mathit{w}}_{\mathbf{2}}\mathbf{=}\mathbf{0.14}$  ${\mathit{w}}_{\mathbf{3}}\mathbf{=}\mathbf{0.09}$  ${\mathit{w}}_{\mathbf{4}}\mathbf{=}\mathbf{0.12}$  ${\mathit{w}}_{\mathbf{5}}\mathbf{=}\mathbf{0.17}$  ${\mathit{w}}_{\mathbf{6}}\mathbf{=}\mathbf{0.14}$  ${\mathit{w}}_{\mathbf{7}}\mathbf{=}\mathbf{0.17}$ 

$\mathbf{Responsiveness}\text{}({\mathit{e}}_{\mathbf{1}})$  $\mathbf{Backup}\text{}\mathbf{Supplier}\text{}\mathbf{Contracts}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{2}}\mathbf{)}$  $\mathbf{Restoration}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{3}}\mathbf{)}$  $\mathbf{Risk}\text{}\mathbf{of}\text{}\mathbf{Losing}\text{}\mathbf{Information}\text{}\mathbf{and}\text{}\mathbf{Communication}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{4}}\mathbf{)}$  $\mathbf{Service}\text{}\mathbf{and}\text{}\mathbf{Support}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{5}}\mathbf{)}$  $\mathbf{Innovation}\text{}\mathbf{and}\text{}\mathbf{Technology}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{6}}\mathbf{)}$  $\mathbf{Product}\text{}\mathbf{Quality}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{7}}\mathbf{)}$  
Supplier 1  {(B, 0.5), (C, 0.5)}  1  {(B, 1)}  1  {(C, 0.8), (D, 0.2)}  {(B, 0.4), (C, 0.6)}  6 
Supplier 2  {(B, 1)}  0  {(A, 1)}  0  {(B, 1)}  {(B, 0.2), (C, 0.5)}  7 
Supplier 3  {(B, 1)}  0  {(B, 1)}  0  {(B, 1)}  {(B, 0.2), (C, 0.4)}  n/a 
Generalised Decision Matrix $\mathbf{3}\mathbf{\times}\mathbf{7}$  ${\mathit{w}}_{\mathbf{1}}\mathbf{=}\mathbf{0.17}$  ${\mathit{w}}_{\mathbf{2}}\mathbf{=}\mathbf{0.14}$  ${\mathit{w}}_{\mathbf{3}}\mathbf{=}\mathbf{0.09}$  ${\mathit{w}}_{\mathbf{4}}\mathbf{=}\mathbf{0.12}$  ${\mathit{w}}_{\mathbf{5}}\mathbf{=}\mathbf{0.17}$  ${\mathit{w}}_{\mathbf{6}}\mathbf{=}\mathbf{0.14}$  ${\mathit{w}}_{\mathbf{7}}\mathbf{=}\mathbf{0.17}$ 

$\mathbf{Responsiveness}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{1}}\mathbf{)}$  $\mathbf{Backup}\text{}\mathbf{Supplier}\text{}\mathbf{Contracts}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{2}}\mathbf{)}$  $\mathbf{Restoration}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{3}}\mathbf{)}$  $\mathbf{Risk}\text{}\mathbf{of}\text{}\mathbf{Losing}\text{}\mathbf{Information}\text{}\mathbf{and}\text{}\mathbf{Communication}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{4}}\mathbf{)}$  $\mathbf{Service}\text{}\mathbf{and}\text{}\mathbf{Support}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{5}}\mathbf{)}$  $\mathbf{Innovation}\text{}\mathbf{and}\text{}\mathbf{Technology}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{6}}\mathbf{)}$  $\mathbf{Product}\text{}\mathbf{Quality}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{7}}\mathbf{)}$  
Supplier 1  {(Excellent, 0.2), (Good, 0.5), (Fair, 0.2), (Poor, 0.1)}  {(Poor, 1)}  {(Excellent, 0.4), (Good, 0.6)}  {(Good, 1)}  {(Fair, 0.8), (Poor, 0.2)}  {(Good, 0.4), (Fair, 0.3), (Poor, 0.3)}  {(Fair, 0.333), (Poor, 0.667)} 
Supplier 2  {(Excellent, 0.4), (Good, 0.6)}  {(Very poor, 1)}  {(Excellent, 1)}  {(Excellent, 1)}  {(Good, 1)}  {(Good, 0.2), (Fair, 0.25), (Poor, 0.25), (H, 0.3)}  {(Poor, 1)} 
Supplier 3  {(Excellent, 0.4), (Good, 0.6)}  {(Very poor, 1)}  {(Excellent, 0.4), (Good, 0.6)}  {(Excellent, 1)}  {(Good, 1)}  {(Good, 0.2), (Fair, 0.2), (Poor, 0.2), (H, 0.4)}  {(H, 1)} 
Interval Decision Matrix $\mathbf{6}\mathbf{\times}\mathbf{7}$  ${\mathit{w}}_{\mathbf{1}}\mathbf{=}\mathbf{0.17}$  ${\mathit{w}}_{\mathbf{2}}\mathbf{=}\mathbf{0.14}$  ${\mathit{w}}_{\mathbf{3}}\mathbf{=}\mathbf{0.09}$  ${\mathit{w}}_{\mathbf{4}}\mathbf{=}\mathbf{0.12}$  ${\mathit{w}}_{\mathbf{5}}\mathbf{=}\mathbf{0.17}$  ${\mathit{w}}_{\mathbf{6}}\mathbf{=}\mathbf{0.14}$  ${\mathit{w}}_{\mathbf{7}}\mathbf{=}\mathbf{0.17}$  

$\mathbf{Responsiveness}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{1}}\mathbf{)}$  $\mathbf{Backup}\text{}\mathbf{Supplier}\text{}\mathbf{Contracts}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{2}}\mathbf{)}$  $\mathbf{Restoration}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{3}}\mathbf{)}$  $\mathbf{Risk}\text{}\mathbf{of}\text{}\mathbf{Losing}\text{}\mathbf{Information}\text{}\mathbf{and}\text{}\mathbf{Communication}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{4}}\mathbf{)}$  $\mathbf{Service}\text{}\mathbf{and}\text{}\mathbf{Support}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{5}}\mathbf{)}$  $\mathbf{Innovation}\text{}\mathbf{and}\text{}\mathbf{Technology}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{6}}\mathbf{)}$  $\mathbf{Product}\text{}\mathbf{Quality}\text{}\mathbf{(}{\mathit{e}}_{\mathbf{7}}\mathbf{)}$  
Supplier 1  ${U}_{min}$  0.7  0.25  0.85  0.75  0.45  0.525  0.33325 
${U}_{max}$  0.7  0.25  0.85  0.75  0.45  0.525  0.33325  
Supplier 2  ${U}_{min}$  0.85  0  1  1  0.75  0.3375  0.25 
${U}_{max}$  0.85  0  1  1  0.75  0.6375  0.25  
Supplier 3  ${U}_{min}$  0.85  0  0.85  1  0.75  0.3  0 
${U}_{max}$  0.85  0  0.85  1  0.75  0.7  1 
Suppliers  $\mathbf{Min}\text{}\mathit{C}{\mathit{C}}_{\mathit{l}}$  $\mathbf{Avg}\text{}\mathit{C}{\mathit{C}}_{\mathit{l}}$  $\mathbf{Max}\text{}\mathit{C}{\mathit{C}}_{\mathit{l}}$  Range (max–min) 

Supplier 1  0.217  0.371  0.526  0.309 
Supplier 2  0.318  0.514  0.711  0.393 
Supplier 3  0.441  0.624  0.806  0.365 
Suppliers  ${\mathit{U}}_{\mathit{m}\mathit{i}\mathit{n}}\left({\mathit{a}}_{\mathit{l}}\right)$  ${\mathit{U}}_{\mathit{a}\mathit{v}\mathit{g}}\left({\mathit{a}}_{\mathit{l}}\right)$  ${\mathit{U}}_{\mathit{m}\mathit{a}\mathit{x}}\left({\mathit{a}}_{\mathit{l}}\right)$  Range (max–min) 

Supplier 1  0.519  0.519  0.519  0.000 
Supplier 2  0.586  0.604  0.623  0.037 
Supplier 3  0.549  0.641  0.733  0.184 
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Sureeyatanapas, P.; Waleekhajornlert, N.; Arunyanart, S.; Niyamosoth, T. Resilient Supplier Selection in Electronic Components Procurement: An Integration of Evidence Theory and RuleBased Transformation into TOPSIS to Tackle Uncertain and Incomplete Information. Symmetry 2020, 12, 1109. https://doi.org/10.3390/sym12071109
Sureeyatanapas P, Waleekhajornlert N, Arunyanart S, Niyamosoth T. Resilient Supplier Selection in Electronic Components Procurement: An Integration of Evidence Theory and RuleBased Transformation into TOPSIS to Tackle Uncertain and Incomplete Information. Symmetry. 2020; 12(7):1109. https://doi.org/10.3390/sym12071109
Chicago/Turabian StyleSureeyatanapas, Panitas, Nantana Waleekhajornlert, Sirawadee Arunyanart, and Thanawath Niyamosoth. 2020. "Resilient Supplier Selection in Electronic Components Procurement: An Integration of Evidence Theory and RuleBased Transformation into TOPSIS to Tackle Uncertain and Incomplete Information" Symmetry 12, no. 7: 1109. https://doi.org/10.3390/sym12071109