A Hybrid MultiCriteria DecisionMaking Framework for ShipEquipment Suitability Evaluation Using Improved ISM, AHP, and Fuzzy TOPSIS Methods
Abstract
:1. Introduction
 A hybrid MCDM framework is developed for the scientific evaluation of shipequipment suitability.
 A structural modeling method is introduced to construct the shipequipment suitability evaluation index system.
 The applicability of AHP and Fuzzy TOPSIS methods in shipequipment suitability evaluation is analyzed systematically.
 Individual consistency and group consensus are thoroughly investigated to improve rationality and operability in shipequipment suitability evaluation.
2. Methodology
2.1. Improved ISM Technique to Construct Evaluation Index Systems
2.1.1. ISM Technique
 (1)
 If ${o}_{ij}=>$, then ${a}_{ij}=1$ and ${a}_{ji}=0$;
 (2)
 If ${o}_{ij}=<$, then ${a}_{ij}=0$ and ${a}_{ji}=1$;
 (3)
 If ${o}_{ij}=\sim $, then ${a}_{ij}={a}_{ji}=1$;
 (4)
 If ${o}_{ij}=\times $, then ${a}_{ij}={a}_{ji}=0$.
2.1.2. Expert Judgment Aggregation
2.1.3. Group Consensus Verification
 The comparability coefficient for the expert group (CCG) is given as
 The direction violation number for the expert group (DVN) is given as
2.1.4. Expert Judgment Modification
Algorithm 1. Group consensus improvement algorithm. 
Input: SSIM ${O}_{k}$ Output: The modified SSM ${S}_{k}^{\prime}$, the modified SSIM ${O}_{k}^{\prime}$, the associated value $CCG\left({S}_{k}^{\prime}\right)$ and $DVN\left({S}_{k}^{\prime}\right)$ Step 0. Suppose ${r}_{i}$ (${c}_{i}$) denotes the subscript of the row (column) vector corresponding to ${x}_{i}\in X$ in the skeleton matrices, ${S}^{{r}_{i}}$ (${S}^{{c}_{i}}$) denotes the row (column) vector corresponding to ${x}_{i}\in X$ in the skeleton matrices. Let ${t}_{i}=\left\{{r}_{i},{c}_{i}\right\}$. Step 1. Compute $J\left({S}_{k}^{{r}_{i}}/{S}_{B}^{{r}_{i}}\right)$, $J\left({S}_{k}^{{c}_{i}}/{S}_{B}^{{c}_{i}}\right)$ and ${J}_{k}^{{x}_{i}}$ for all ${x}_{i}\in X$. Step 2. Choose the factor ${x}_{i}^{\prime}$ for which ${J}_{k}^{{x}_{i}}$ has the largest value, let ${x}_{i}={x}_{i}^{\prime}$. Step 3. Choose the subscript ${t}_{i}^{\prime}$ for which $J\left({S}_{k}^{{t}_{i}}/{S}_{B}^{{t}_{i}}\right)$ has the largest value, if $J\left({S}_{k}^{{r}_{i}}/{S}_{B}^{{r}_{i}}\right)=J\left({S}_{k}^{{c}_{i}}/{S}_{B}^{{c}_{i}}\right)$, use ${t}_{i}^{\prime}={r}_{i}$ and let ${t}_{i}={t}_{i}^{\prime}$. Step 4. Suppose $K=\left\{\left(r,s\right)\right\}$ denotes the index set of the elements of the vector corresponding to ${t}_{i}$ in the skeleton matrices. Let $\left(i,j\right)=\left(r,s\right)$, compute ${I}_{ij}\left({S}_{k}/{S}_{B}\right)$ for all $\left(i,j\right)\in K$. Let $L=\left\{\left(i,j\right):{I}_{ij}\left({S}_{k}/{S}_{B}\right)=0\right\}$. Step 5. Choose the subscript $\left({i}^{\prime},{j}^{\prime}\right)$, i.e., the first $\left(i,j\right)\in L$, let $\left(i,j\right)=\left({i}^{\prime},{j}^{\prime}\right)$. Step 6. If expert ${P}_{k}$ agrees to revise the interrelation ${s}_{ij}^{k}$, update the individual skeleton matrix ${S}_{k}$ with new values ${s}_{ij}^{k}={s}_{ij}^{B}$, update $L=L\backslash \left({i}^{\prime},{j}^{\prime}\right)$ and proceed to Step 7. Otherwise, update $L=L\backslash \left({i}^{\prime},{j}^{\prime}\right)$ and proceed to Step 5. Step 7. Calculate $CCG\left({S}_{k}^{\prime}\right)$ and $DVN\left({S}_{k}^{\prime}\right)$. (a) If $CCG\left({S}_{k}^{\prime}\right)\ge \overline{CCG}$ and $DVN\left({S}_{k}^{\prime}\right)\ge \overline{DVN}$, update SSIM ${O}_{k}$ with the modified interrelations, and provide ${O}_{k}^{\prime}$, ${S}_{k}^{\prime}$, $CCG\left({S}_{k}^{\prime}\right)$ and $DVN\left({S}_{k}^{\prime}\right)$. (b) Otherwise, if $K\ne \varnothing $, repeat Steps 5 through 7. (c) Otherwise, update ${t}_{i}={t}_{i}\backslash {t}_{i}^{\prime}$, if ${t}_{i}\ne \varnothing $, repeat Steps 3 through 7. (d) Otherwise, update $X=X\backslash {x}_{i}^{\prime}$, if $X\ne \varnothing $, repeat Steps 2 through 7 
2.2. Applicability Analysis of AHP and Fuzzy TOPSIS
2.3. Improved AHP Technique to Distribute Index Weights
2.3.1. AHP Technique
2.3.2. Individual Consistency Improvement
Algorithm 2. GCIbased individual consistency improvement algorithm. 
Input: The initial pairwise comparison matrix $A$, the permissibility coefficient $\rho $ Output: The modified pairwise comparison matrix ${A}^{\prime}$, the improved $GCI\left({A}^{\prime}\right)$ Step 0. Let $J=\left\{\left(r,s\right)r<s\right\}$ be the index set corresponding to the expert judgments. Step 1. Compute $\frac{\left\mathrm{log}{e}_{rs}\right}{{a}_{rs}}$ for all $\left(r,s\right)\in J$, where ${e}_{rs}={a}_{rs}\frac{{w}_{s}}{{w}_{r}}$. Step 2. Choose the pair $\left({r}^{\prime},{s}^{\prime}\right)\in J$ which $\frac{\left\mathrm{log}{e}_{{r}^{\prime}{s}^{\prime}}\right}{{a}_{{r}^{\prime}{s}^{\prime}}}$ has the largest value. Step 3. If ${a}_{{r}^{\prime}{s}^{\prime}}>1$, then let $\left(r,s\right)=\left({r}^{\prime},{s}^{\prime}\right)$. Otherwise, let $\left(r,s\right)=\left({s}^{\prime},{r}^{\prime}\right)$. Step 4. Compute ${t}_{rs}^{*}={e}_{rs}^{n/\left(n2\right)}$. Modify ${a}_{rs}$ with ${t}_{rs}$, which depends on the sign of $\mathrm{log}{e}_{rs}$. a. If $\mathrm{log}{e}_{rs}<0$, let ${t}_{rs}=min\left\{1+\rho ,{t}_{rs}^{*}\right\}$. b. If $\mathrm{log}{e}_{rs}>0$, let ${t}_{rs}=max\left\{\frac{1}{1+\rho},{t}_{rs}^{*}\right\}$. Update matrix $A$ with revised values ${a}_{rs}^{\prime}={a}_{rs}{t}_{rs}$ and ${a}_{sr}^{\prime}=1/{a}_{rs}^{\prime}$. Update index set $J=J\backslash \left({r}^{\prime},{s}^{\prime}\right)$. Step 5. Compute $GCI\left({A}^{\prime}\right)$. a. If $GCI\left({A}^{\prime}\right)<\overline{GCI}$, provide ${A}^{\prime}$ and $GCI\left({A}^{\prime}\right)$. b. Otherwise, if $J\ne \varnothing $, repeat steps 1 through 4. c. Otherwise, the algorithm has no solution, so enlarge the permissibility coefficient $\rho $ or organize experts to modify the judgments. 
2.3.3. Expert Preference Aggregation
2.3.4. Group Consensus Verification
 Geometric Compatibility Index (GCOMPI): the cardinal compatibility between the group priority vector and the individual expert judgments.$$GCOMPI\left(B\right)={{\displaystyle \sum}}_{k=1}^{l}{\lambda}_{k}^{p}\xb7GCOMPI\left({A}_{k}\right),$$$$GCOMPI\left({A}_{k}\right)=\frac{2}{\left(n1\right)\left(n2\right)}{{\displaystyle \sum}}_{i<j}lo{g}^{2}\left({a}_{ij}^{k}{w}_{j}/{w}_{i}\right),$$
 Priority violation number for the expert group (PVN): the ordinal compatibility between the group priority vector and the individual expert judgments.$$PVN\left(B\right)={{\displaystyle \sum}}_{k=1}^{l}{\lambda}_{k}^{p}\xb7PVN\left({A}_{k}\right),$$$$PVN\left({A}_{k}\right)=\frac{2}{\left(n1\right)\left(n2\right)}{{\displaystyle \sum}}_{i<j}{I}_{ij}\left({A}_{k}/B\right),$$$${I}_{ij}\left({A}_{k}/B\right)=\{\begin{array}{cc}1& if{a}_{ij}^{k}1and{w}_{i}{w}_{j}\\ 1& if{a}_{ij}^{k}1and{w}_{i}{w}_{j}\\ 0.5& if{a}_{ij}^{k}=1and{w}_{i}\ne {w}_{j}\\ 0.5& if{a}_{ij}^{k}\ne 1and{w}_{i}={w}_{j}\\ 0& otherwise\end{array},$$
 Average variance (AV): the average change between the group priority vector and the individual priority vector.$$d\left(w,{w}^{k}\right)=\frac{1}{n}{{\displaystyle \sum}}_{i=1}^{n}\left{w}_{i}{w}_{i}^{k}\right,$$
 Kendall’s tau distance ($\tau $): the ranking changes between two rankings derived from the group judgment matrix $B$ and the individual judgment matrix ${A}_{k}$.$$\tau \left({\gamma}_{B},{\gamma}_{{A}_{k}}\right)=\frac{2}{n\left(n1\right)}\left({N}_{concordantpairs}{N}_{disconcordantpairs}\right),$$
2.4. Fuzzy TOPSIS Technique to Evaluate, Rank and Select Ship Designs
2.4.1. Linguistic Scales
2.4.2. Fuzzy TOPSIS Technique
3. Case Study: ShipEquipment Environmental Suitability Evaluation
3.1. Problem Statement
3.2. Establishment of the Expert Group
3.3. Identification and Selection of Assessment Indicators
3.4. Construction of Appropriate Hierarchical Structures
${O}_{1}$  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22 
1  ~  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  × 
2  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  <  <  ×  ×  ×  <  <  <  <  <  
3  ~  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
4  ~  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
5  ~  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
6  ~  ×  ×  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
7  ~  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
8  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
9  ~  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
10  ~  ×  ×  ×  ×  ×  <  ×  ×  ×  ×  ×  ×  
11  ~  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
12  ~  ×  ×  >  ×  ×  ×  ×  <  ×  ×  
13  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  
14  ~  ×  ×  ×  ×  ×  ×  ×  ×  
15  ~  ×  <  ×  ×  ×  ×  ×  
16  ~  ×  ×  ×  ×  ×  ×  
17  ~  ×  ×  ×  ×  ×  
18  ~  ×  ×  ×  ×  
19  ~  ×  ×  ×  
20  ~  ×  ×  
21  ~  ×  
22  ~ 
${O}_{2}$  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22 
1  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  × 
2  ~  ×  ×  <  <  <  ×  <  ×  ×  ×  ×  <  ×  <  <  <  <  <  <  <  
3  ~  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
4  ~  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
5  ~  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
6  ~  ×  ×  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
7  ~  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
8  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
9  ~  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
10  ~  ×  ×  ×  ×  ×  <  ×  ×  ×  ×  ×  ×  
11  ~  ×  ×  ×  >  ×  <  ×  ×  ×  ×  ×  
12  ~  ×  ×  >  ×  <  ×  ×  ×  ×  ×  
13  ~  >  ×  ×  ×  ×  ×  ×  ×  ×  
14  ~  ×  <  ×  >  ×  ×  ×  ×  
15  ~  ×  <  ×  ×  ×  ×  ×  
16  ~  ×  >  ×  ×  ×  ×  
17  ~  ×  ×  ×  ×  ×  
18  ~  ×  ×  ×  ×  
19  ~  ×  ×  ×  
20  ~  ×  ×  
21  ~  ×  
22  ~ 
${O}_{3}$  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22 
1  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  × 
2  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  <  <  ×  ×  ×  <  <  <  <  <  
3  ~  >  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
4  ~  ×  ×  <  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
5  ~  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
6  ~  ×  ×  ×  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
7  ~  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
8  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  ×  
9  ~  ×  ×  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
10  ~  <  <  ×  ×  ×  <  <  ×  ×  ×  <  ×  
11  ~  ×  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
12  ~  ×  ×  >  ×  ×  ×  ×  ×  ×  ×  
13  ~  ×  ×  ×  ×  ×  ×  ×  ×  ×  
14  ~  ×  ×  ×  ×  ×  ×  ×  ×  
15  ~  ×  <  ×  ×  ×  ×  ×  
16  ~  ×  ×  ×  ×  ×  ×  
17  ~  ×  ×  ×  ×  ×  
18  ~  ×  ×  ×  ×  
19  ~  ×  ×  ×  
20  ~  ×  ×  
21  ~  ×  
22  ~ 
3.5. Weight Distribution for the Assessment Indicators
3.6. Evaluation, Ranking, and Selection of Alternative Designs
3.7. Analysis of Individual Consistency and Group Consensus
3.7.1. Expert Judgment Aggregation in Evaluation Index System Construction
3.7.2. Group Consensus Improvement in Evaluation Index System Construction
3.7.3. Individual Consistency Improvement in Index Weight Distribution
3.7.4. Expert Preference Aggregation Using Integrated Expert Weights
3.7.5. Cardinal and Ordinal Consensus of Index Weight Distribution
3.8. Sensitivity Analysis Regarding the Predetermined Expert Weights
3.9. Comparative Analysis of Index Weights and Criteria Performances
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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${\mathit{m}}_{1}$  ${\mathit{m}}_{1.1}$  ${\mathit{m}}_{2}$  ${\mathit{m}}_{3}$  ${\mathit{m}}_{3.1}$  ${\mathit{m}}_{4}$  ${\mathit{m}}_{4.1}$  ${\mathit{m}}_{\mathrm{4.1.1}}$  ${\mathit{m}}_{\mathrm{4.1.2}}$  

Characteristics of shipequipment suitability evaluation  3  2  2  2  3  2  1,2  2  2 
Properties of AHP and Fuzzy TOPSIS methods  3  2  2  2  3  2  1,2  2  2 
Intensity of Importance  Definition 

1  ${X}_{i}$ and ${X}_{j}$ contribute equally to the objective. 
3  Experience and knowledge slightly favor ${X}_{i}$ over ${X}_{j}$. 
5  Experience and knowledge strongly favor ${X}_{i}$ over ${X}_{j}$. 
7  ${X}_{i}$ is strongly favored, and its dominance is demonstrated in practice. 
9  The evidence favoring ${X}_{i}$ over ${X}_{j}$ is of the highest possible order of affirmation. 
2,4,6,8  Intermediate values between the two adjacent judgments 
Reciprocals of the above nonzero  If ${X}_{i}$ has one of the aforementioned nonzero values, ${a}_{ij}$ is assigned to it when compared to ${X}_{j}$. Thus, ${X}_{j}$ has a reciprocal value, ${a}_{ji}=1/{a}_{ij}$, when compared to ${X}_{i}$. 
$\mathit{n}$  $\overline{\mathit{G}\mathit{C}\mathit{I}}$ 

3  0.31 
4  0.35 
>4  0.37 
Linguistic Terms (Evaluation Set)  TFNs 

Very low (VL)  (0.0, 0.0, 2.5) 
Low (L)  (0.0, 2.5, 5.0) 
Average (A)  (2.5, 5.0, 7.5) 
High (H)  (5.0, 7.5, 10.0) 
Very high (VH)  (7.5, 10.0, 10.0) 
Expert  Institute  Job Title  Educational Level  Years Experienced  Age 

${P}_{1}$  MARIC ^{a}  Chief Engineer, Prof.  Ph.D.  18  46 
${P}_{2}$  HEU ^{b}  Prof.  Ph.D.  12  41 
${P}_{3}$  SMERI ^{c}  Chief Engineer, Prof.  Ph.D.  15  43 
No.  Indicators  Description  Unit  Benefit/Cost 

${X}_{1}$  Explosive gases  The explosionproof electrical equipment and prevention measures in explosive dangerous places where explosive gases accumulate or spread must satisfy the safety requirements.  Linguistic  Benefit 
${X}_{2}$  Operational environment  The actual environmental conditions under the coupling of various factors should satisfy the environmental requirements for the normal operation of the mothership, shipborne equipment, and ship crew.  Linguistic  Benefit 
${X}_{3}$  Impact  The antiimpact design of ship hull and shipborne equipment should be carried out to enable them to operate safely in cases of severe impacts such as underwater explosions.  Linguistic  Benefit 
${X}_{4}$  Bending deflection of the ship hull  The maximum bending deflection of the ship hull with the wave and still bending moment coupling should be less than a critical value.  m  Cost 
${X}_{5}$  Ship vibration  The ship hull’s natural frequency must avoid the propellers’ and generators’ operating frequency. The vibration amplitude of the ship hull must also be controlled.  %  Benefit 
${X}_{6}$  Atmospheric temperature  The normal working and nondamage temperatures of shipborne equipment should be adapted to the ambient atmospheric temperature.  °C  Benefit 
${X}_{7}$  Bumping  Shipborne equipment should withstand repetitive lowintensity bumping caused by wave shocks (including bow shocks, stern shocks, etc.) and operate continuously and effectively.  Linguistic  Benefit 
${X}_{8}$  Electromagnetic environment  The spectrum allocation of electronic equipment should be compatible with the management and control measures in time, space, frequency domain, and power supply.  Linguistic  Benefit 
${X}_{9}$  Oceanic temperature  The normal working and nondamage temperatures of shipborne equipment exposed to seawater should be adapted to the ocean temperature.  °C  Benefit 
${X}_{10}$  Mechanical environment  A general term for environmental factors, such as tilting, swaying, vibration, and impact caused by the navigation attitude of the mothership, the running state of shipborne equipment, and other influencing factors.  Linguistic  Benefit 
${X}_{11}$  Impregnation  The effects of impregnation on shipborne equipment should be considered, and waterproof or watertight design should be carried out for specific shipborne equipment.  Linguistic  Benefit 
${X}_{12}$  Mold, oil mist, and salt spray  The effects of mold, oil mist, and salt spray on shipborne equipment should be considered. The climate protection design should be carried out so that the shipborne equipment can operate normally under specific molds, oil mist, and salt spray concentrations.  Linguistic  Benefit 
${X}_{13}$  Draft  The mothership should be able to sink to appropriate draught at a certain speed so that the shipborne equipment can smoothly get in and out of the cabin.  Linguistic  Benefit 
${X}_{14}$  Course and attitude  The mothership should control its course and attitude so the shipborne equipment can smoothly get in and out of the cabin.  Linguistic  Benefit 
${X}_{15}$  Climatic environment  The climatic factors that have an impact on the mothership and shipborne equipment.  Linguistic  Benefit 
${X}_{16}$  Tilting and swaying  The mothership should adequately control the amplitude and period of its tilting and swaying so that the coverage area of the envelope diagram describing the normal operation of shipborne equipment is at least a specific value.  %  Benefit 
${X}_{17}$  Relative humidity  Shipborne equipment should operate normally in a specific range of relative humidity.  %  Benefit 
${X}_{18}$  Waves in the cabin  The mother ship should control its course and attitude and install wave suppression devices so the shipborne equipment can smoothly get in and out of the cabin.  Linguistic  Benefit 
${X}_{19}$  High temperature and highspeed airflow emitted by shipborne equipment  To deal with the hightemperature and highspeed airflow emitted by shipborne equipment, protective designs, and prevention measures should be carried out to enable the mothership, shipborne equipment, and ship crew to operate safely.  Linguistic  Benefit 
${X}_{20}$  Air pollutants emitted by shipborne equipment  To deal with the air pollutants emitted by shipborne equipment, protective designs, and prevention measures should be carried out to enable the shipborne equipment and ship crew to operate safely.  Linguistic  Benefit 
${X}_{21}$  Intense heat emitted by shipborne equipment  Protective designs and prevention measures should be carried out to deal with the intense heat emitted by shipborne equipment to enable the mothership, shipborne equipment, and ship crew to operate safely.  Linguistic  Benefit 
${X}_{22}$  Intense noise emitted by shipborne equipment  Protective designs and prevention measures should be carried out to deal with the intense noise emitted by shipborne equipment to enable the mothership, shipborne equipment, and ship crew to operate safely.  Linguistic  Benefit 
Expert  $\mathit{C}\mathit{C}{\mathit{G}}_{0.9}$  $\mathit{D}\mathit{V}{\mathit{N}}_{0.9}$ 

${P}_{1}$  0.9710  0.9957 
${P}_{2}$  0.8489 0.9037  0.9719 0.9805 
${P}_{3}$  0.9106  0.9827 
Group  0.9162 0.9327  0.9846 0.9872 
Subsets  Indicators 

1  2, 13, 14, 18, 19, 20, 21, 22 
2  8 
3  3, 4, 5, 7, 10, 16 
4  1, 6, 9, 11, 12, 15, 17 
Hierarchical Levels  Indicators 

1  2, 8, 10, 15 
2  1, 3, 4, 5, 6, 7, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22 
Expert  ${\mathit{X}}_{13}$  ${\mathit{X}}_{14}$  ${\mathit{X}}_{18}$  ${\mathit{X}}_{19}$  ${\mathit{X}}_{20}$  ${\mathit{X}}_{21}$  ${\mathit{X}}_{22}$  $\mathit{G}\mathit{C}{\mathit{I}}_{0.37}$ 

${P}_{1}$  0.4180  0.2709  0.1280  0.0891  0.0259  0.0406  0.0275  0.3399 
${P}_{2}$  0.4132  0.2494  0.1232  0.0900  0.0386  0.0470  0.0386  0.2189 
${P}_{3}$  0.4092  0.3094  0.1168  0.0802  0.0251  0.0357  0.0236  0.3709 0.3593 
Expert  $\mathit{G}\mathit{C}{\mathit{I}}_{0.37}$  ${\mathit{\nu}}_{\mathit{k}}^{\mathit{p}}$  ${\mathit{w}}_{\mathit{k}}^{\mathit{p}}$  ${\mathit{\lambda}}_{\mathit{k}}^{\mathit{p}}$  $\mathit{G}\mathit{C}\mathit{C}{\mathit{I}}_{0.9}$  GCOMPI  PVN  AV  $\mathit{\tau}$ 

${P}_{1}$  0.3399  0.2858  0.4  0.3429  0.9684  0.3513  0.0333  0.0028  1.0000 
${P}_{2}$  0.2189  0.4438  0.3  0.3719  0.9376  0.2695  0.0667  0.0074  0.9048 
${P}_{3}$  0.3593  0.2704  0.3  0.2852  0.9457  0.3988  0.0333  0.0102  0.9048 
Group          0.9505  0.3344  0.0457  0.0066  0.9374 
${\mathit{X}}_{13}$  ${\mathit{X}}_{14}$  ${\mathit{X}}_{18}$  ${\mathit{X}}_{19}$  ${\mathit{X}}_{20}$  ${\mathit{X}}_{21}$  ${\mathit{X}}_{22}$  ${\mathit{X}}_{8}$  ${\mathit{X}}_{3}$  ${\mathit{X}}_{4}$  
${F}_{1}$  H,H,H  H,H,VH  VH,H,A  VH,H,VH  H,H,H  H,VH,VH  H,H,H  VH,H,H  H,H,A  0.4846 
${F}_{2}$  L,H,H  H,A,H  H,A,A  VH,H,H  A,L,A  A,VH,H  L,H,H  H,H,H  A,L,A  0.5064 
${F}_{3}$  H,A,H  H,A,H  A,A,A  A,A,A  A,H,A  L,A,A  H,A,A  VH,H,H  H,A,A  0.4986 
Weight  0.1988  0.1311  0.0591  0.0417  0.0143  0.0199  0.0144  0.2440  0.0262  0.0107 
${\mathit{X}}_{5}$  ${\mathit{X}}_{7}$  ${\mathit{X}}_{16}$  ${\mathit{X}}_{1}$  ${\mathit{X}}_{6}$  ${\mathit{X}}_{9}$  ${\mathit{X}}_{11}$  ${\mathit{X}}_{12}$  ${\mathit{X}}_{17}$  
${F}_{1}$  10.6  H,H,H  68.3  H,H,H  60  36  H,H,H  H,H,A  90  
${F}_{2}$  10.0  A,A,L  62.6  VH,VH,VH  60  36  A,L,A  A,A,H  90  
${F}_{3}$  10.8  VH,VH,H  71.2  H,H,VH  60  32  A,H,A  H,VH,A  100  
Weight  0.0165  0.0193  0.0386  0.0613  0.0288  0.0316  0.0108  0.0121  0.0209 
${\mathit{F}}^{+}$  
${\mathit{X}}_{13}$  ${\mathit{X}}_{14}$  ${\mathit{X}}_{18}$  ${\mathit{X}}_{19}$  ${\mathit{X}}_{20}$  ${\mathit{X}}_{21}$  ${\mathit{X}}_{22}$  ${\mathit{X}}_{8}$  ${\mathit{X}}_{3}$  ${\mathit{X}}_{4}$  ${\mathit{X}}_{5}$  ${\mathit{X}}_{7}$  ${\mathit{X}}_{16}$  ${\mathit{X}}_{1}$  ${\mathit{X}}_{6}$  ${\mathit{X}}_{9}$  ${\mathit{X}}_{11}$  ${\mathit{X}}_{12}$  ${\mathit{X}}_{17}$  
${F}_{1}$  0.0642  0.0348  0.0158  0.008  0.0046  0.0042  0.0046  0.0602  0.0091  0  0.0003  0.0062  0.0016  0.0198  0  0  0.0035  0.0042  0.0021 
${F}_{2}$  0.0982  0.0503  0.0245  0.0103  0.0087  0.0069  0.0071  0.0788  0.0153  0.0005  0.0012  0.0118  0.0047  0.0088  0  0  0.0066  0.0053  0.0021 
${F}_{3}$  0.0763  0.0503  0.0301  0.0225  0.0068  0.0126  0.0065  0.0602  0.0109  0.0003  0  0.0037  0  0.0163  0  0.0035  0.0051  0.0035  0 
${\mathit{F}}^{}$  
${\mathit{X}}_{13}$  ${\mathit{X}}_{14}$  ${\mathit{X}}_{18}$  ${\mathit{X}}_{19}$  ${\mathit{X}}_{20}$  ${\mathit{X}}_{21}$  ${\mathit{X}}_{22}$  ${\mathit{X}}_{8}$  ${\mathit{X}}_{3}$  ${\mathit{X}}_{4}$  ${\mathit{X}}_{5}$  ${\mathit{X}}_{7}$  ${\mathit{X}}_{16}$  ${\mathit{X}}_{1}$  ${\mathit{X}}_{6}$  ${\mathit{X}}_{9}$  ${\mathit{X}}_{11}$  ${\mathit{X}}_{12}$  ${\mathit{X}}_{17}$  
${F}_{1}$  0.1545  0.1074  0.0485  0.0366  0.0111  0.0172  0.0112  0.2033  0.02  0.0107  0.0162  0.015  0.037  0.0476  0.0288  0.0316  0.0084  0.0093  0.0188 
${F}_{2}$  0.1166  0.0925  0.0405  0.0347  0.0068  0.0143  0.0084  0.1897  0.0133  0.0102  0.0153  0.0091  0.034  0.0566  0.0288  0.0316  0.0051  0.008  0.0188 
${F}_{3}$  0.1402  0.0925  0.0345  0.0225  0.0087  0.0089  0.0091  0.2033  0.0179  0.0104  0.0165  0.0169  0.0386  0.0502  0.0288  0.0281  0.0066  0.0098  0.0209 
Alternatives  ${\mathit{d}}_{\mathit{i}}^{+}$  ${\mathit{d}}_{\mathit{i}}^{}$  $\mathit{C}{\mathit{C}}_{\mathit{i}}$  Rankings 

${F}_{1}$  0.2432  0.8331  0.7741  1 
${F}_{2}$  0.3411  0.7343  0.6828  3 
${F}_{3}$  0.3085  0.7644  0.7125  2 
NO.  ${\mathit{X}}_{1}$  ${\mathit{X}}_{2}$  ${\mathit{X}}_{3}$  ${\mathit{X}}_{4}$  ${\mathit{X}}_{5}$  ${\mathit{X}}_{6}$  ${\mathit{X}}_{7}$  ${\mathit{X}}_{8}$  ${\mathit{X}}_{9}$  ${\mathit{X}}_{10}$  ${\mathit{X}}_{11}$ 
${J}_{2}^{{x}_{i}}$  1  0.73  1  1  0.83  0.83  0.83  1  0.83  1  0.75 
Rank  14  4  14  14  8  8  8  14  8  14  5 
$J\left({S}_{2}^{{r}_{i}}/{S}_{B}^{{r}_{i}}\right)$  1  1  1  1  0.67  0.67  0.67  1  0.67  1  1 
$J\left({S}_{2}^{{c}_{i}}/{S}_{B}^{{c}_{i}}\right)$  1  0.46  1  1  1  1  1  1  1  1  0.5 
NO.  ${\mathit{X}}_{12}$  ${\mathit{X}}_{13}$  ${\mathit{X}}_{14}$  ${\mathit{X}}_{15}$  ${\mathit{X}}_{16}$  ${\mathit{X}}_{17}$  ${\mathit{X}}_{18}$  ${\mathit{X}}_{19}$  ${\mathit{X}}_{20}$  ${\mathit{X}}_{21}$  ${\mathit{X}}_{22}$ 
${J}_{2}^{{x}_{i}}$  0.75  0.67  0.33  0.93  0.83  0.6  0.75  1  1  1  1 
Rank  5  3  1  13  8  2  5  14  14  14  14 
$J\left({S}_{2}^{{r}_{i}}/{S}_{B}^{{r}_{i}}\right)$  1  0.33  0.33  1  0.67  0.2  1  1  1  1  1 
$J\left({S}_{2}^{{c}_{i}}/{S}_{B}^{{c}_{i}}\right)$  0.5  1  0.33  0.86  1  1  0.5  1  1  1  1 
Iter# 
$$\mathit{C}\mathit{C}\mathit{G}$$

$$\mathit{D}\mathit{V}\mathit{N}$$

$$\left(\mathit{i},\mathit{j}\right)$$

$${\mathit{s}}_{\mathit{i}\mathit{j}}^{2}$$

$${{\mathit{s}}_{\mathit{i}\mathit{j}}^{2}}^{\prime}$$

$${\mathit{C}\mathit{C}\mathit{G}}^{\prime}$$

$$\nabla \mathit{C}\mathit{C}\mathit{G}\left(\mathit{\%}\right)$$

$${\mathit{D}\mathit{V}\mathit{N}}^{\prime}$$

$$\nabla \mathit{D}\mathit{V}\mathit{N}\left(\mathit{\%}\right)$$


1  0.8489  0.9719  (14,2)  0  1  0.8582  1.1  0.974  0.22 
2  0.8582  0.974  (14,18)  1  0  0.8772  2.21  0.9762  0.23 
3  0.8772  0.9762  (13,14)  1  0  0.8847  0.85  0.9784  0.23 
4  0.8847  0.9784  (16,14)  1  0  0.9037  2.15  0.9805  0.21 
Expert  ${\mathit{w}}_{\mathit{k}}^{\mathit{p}}$  $\mathit{G}\mathit{C}\mathit{I}$  ${\mathit{\nu}}_{\mathit{k}}^{\mathit{p}}$  ${\mathit{\lambda}}_{\mathit{k}}^{\mathit{p}}\left(\mathit{\alpha},\mathit{\beta}=0.5\right)$  Node 

${P}_{1}$  0.4  0.1075  0.3665  0.3833  1 
0.3399  0.2858  0.3429  2  
0.2278  0.2408  0.3204  3  
0.1427  0.2984  0.3492  4  
${P}_{2}$  0.3  0.1154  0.3414  0.3207  1 
0.2189  0.4438  0.3719  2  
0.1934  0.2836  0.2918  3  
0.1231  0.3459  0.3229  4  
${P}_{3}$  0.3  0.1349  0.2921  0.296  1 
0.3593  0.2704  0.2852  2  
0.1153  0.4757  0.3878  3  
0.1197  0.3557  0.3279  4 
Expert  $\mathit{p}$  $\mathit{A}\mathit{V}$  $\nabla \mathit{A}\mathit{V}\left(\mathit{\%}\right)$ 

${P}_{1}$  0.9614  0.0037  7.11 
${P}_{2}$  0.9614  0.0042  7.90 
${P}_{3}$  0.9623  0.0038  7.20 
Cases  ${\mathit{w}}_{1}^{\mathit{p}}$  ${\mathit{w}}_{2}^{\mathit{p}}$  ${\mathit{w}}_{3}^{\mathit{p}}$  

Case 1  Current  0.4  0.3  0.3 
Case 2  Average  1/3  1/3  1/3 
Case 3  ${P}_{1}$ High, The Rest Low  2/3  1/6  1/6 
Case 4  ${P}_{2}$ High, The Rest Low  1/6  2/3  1/6 
Case 5  ${P}_{3}$ High, The Rest Low  1/6  1/6  2/3 
Case 6  ${P}_{1}$ Low, The Rest High  1/6  5/12  5/12 
Case 7  ${P}_{2}$ Low, The Rest High  5/12  1/6  5/12 
Case 8  ${P}_{3}$ Low, The Rest High  5/12  5/12  1/6 
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Chen, C.; Zhang, X.; Wang, G.; Feng, F.; Sun, C.; He, Q. A Hybrid MultiCriteria DecisionMaking Framework for ShipEquipment Suitability Evaluation Using Improved ISM, AHP, and Fuzzy TOPSIS Methods. J. Mar. Sci. Eng. 2023, 11, 607. https://doi.org/10.3390/jmse11030607
Chen C, Zhang X, Wang G, Feng F, Sun C, He Q. A Hybrid MultiCriteria DecisionMaking Framework for ShipEquipment Suitability Evaluation Using Improved ISM, AHP, and Fuzzy TOPSIS Methods. Journal of Marine Science and Engineering. 2023; 11(3):607. https://doi.org/10.3390/jmse11030607
Chicago/Turabian StyleChen, Cheng, Xiangrui Zhang, Guo Wang, Feng Feng, Cong Sun, and Qin He. 2023. "A Hybrid MultiCriteria DecisionMaking Framework for ShipEquipment Suitability Evaluation Using Improved ISM, AHP, and Fuzzy TOPSIS Methods" Journal of Marine Science and Engineering 11, no. 3: 607. https://doi.org/10.3390/jmse11030607