A Comparative Analysis of Multi-Criteria Decision-Making Methods for Resource Selection in Mobile Crowd Computing
Abstract
:1. Introduction
1.1. Mobile Crowd Computing
1.2. Resource Selection in Mobile Crowd Computing
1.3. Resource Selection as an MCDM Problem
1.4. Paper Objective
1.5. Paper Contribution
- We use five distinct MCDM algorithms for the comparative analysis—EDAS, ARAS, MABAC, COPRAS, and MARCOS.
- The five algorithms that are used in this study are of distinctive nature in terms of their fundamental procedure. Moreover, the combination of the considered MCDM methods comprises some popularly used methods and some recently proposed methods. This diverse combination for a comparative study of MCDM methods is quite rare in the literature.
- To check the impact of the number of alternatives and criteria on the performance of the MCDM methods, we consider four data sets of different sizes. Each of the methods is implemented on all four datasets.
- We carry out an extensive comparative analysis of the results for all the considered scenarios under different variations of criteria and alternative sets. The comparative analysis is done on two aspects: (a) an exhaustive validation and robustness check and (b) the time complexity of each method.
- Along with the time complexity of each MCDM method, the actual runtime of each method on two different types of devices (laptop and smartphone) are compared and analyzed for each considered scenario.
- We found hardly any work in which computational and runtime-based comparison of different MCDM methods has been carried out apart from the validation and robustness check. To be specific, this paper is the first of its kind that compares the MCDM methods of different categories for resource selection in MCC or any other distributed mobile computing systems.
1.6. Paper Organization
2. Related Work
3. Research Background
3.1. MCDM Methods Considered for the Comparative Study
- (a)
- Separation from average solution (EDAS method).
- (b)
- The relative positioning of the alternatives with respect to the best one (ARAS method).
- (c)
- Utility-based classification and preferential ordering on the proportional scale (COPRAS method).
- (d)
- Approximation of the positions of the alternatives to the average solution area (MABAC method).
- (e)
- Compromise solution while trading of the effects of the criteria on the alternatives (MARKOS method).
3.1.1. EDAS Method
3.1.2. ARAS Method
3.1.3. MABAC Method
3.1.4. COPRAS Method
3.1.5. MARCOS Method
3.2. Entropy Method for Criteria Weight Calculation
4. Research Methodology
4.1. Resource Selection Criteria
4.2. Data Collection
4.3. Experiment Cases
4.3.1. Case 1: Full List of Alternatives and Full Criteria Set
4.3.2. Case 2: Lesser Number of Alternatives and Full Criteria Set
4.3.3. Case 3: Total Number of Alternatives and a Smaller Number of Criteria
4.3.4. Case 4: Minimized Number of Alternatives and Criteria
5. Experiment, Results, and Comparative Analysis
5.1. Experiment
5.2. Results
5.3. Sensitivity Analysis
5.4. Time Complexity Analysis
6. Discussion
6.1. Findings and Observations
- Condition 1: Full set (Case 1: complete set of 13 criteria and 50 alternatives)
- Condition 2: Reduction in the number of alternatives keeping the criteria set unaltered (Case 2: reduced set of 10 alternatives and complete set of 13 criteria)
- Condition 3: Variation in the criteria set (Case 3: reduced set of 6 criteria) keeping the alternative set the same (i.e., 50)
- Condition 4: Variations in both alternative and criteria sets (Case 4: reduced set of 10 alternatives and 6 criteria).
6.2. Rationality and Practicability
6.2.1. Assertion
6.2.2. Application
6.2.3. Implications
7. Conclusions, Limitations, and Further Research Scope
7.1. Summary
7.2. Observation
7.3. Conclusive Statement
7.4. Limitations and Improvement Scopes
7.5. Open Research Prospects
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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MCDM Approach | Representative Example | Reference |
---|---|---|
Distance-based method | TOPSIS | [30,31] |
EDAS | [32] | |
Area-based comparison and approximation method | MABAC | [33,34] |
Ratio-based additive method | ARAS | [35,36] |
SAW | [37] | |
COPRAS | [38,39] | |
Algorithms that work under compromising situations | VIKOR | [40,41] |
CoCoSo | [42] | |
MARCOS | [43] | |
RAFSI | [29] |
Acronym | Full Form |
---|---|
AHP | Analytic Hierarchy Process |
ANP | Analytic Network Process |
ARAS | Additive Ratio Assessment |
BWM | Best Worst Method |
CoCoSo | Combined Compromise Solution |
COMET | Characteristic Objects METhod |
COPRAS | Complex Proportional Assessment |
COPRAS | COmplex PRoportional ASsessment |
CPU | Central Processing Unit |
DEA | Data Envelopment Analysis |
DMU | Decision Making Unit |
EDAS | Evaluation based on Distance from Average Solution |
EDAS | Evaluation based on Distance from Average Solution |
ELECTRE | ELimination Et Choix Traduisant la REalité |
ESM | Even Swaps Method |
GDSS | Group Decision Support System |
GPU | Graphics Processing Unit |
GRA | Grey Relational Analysis |
HPC | High Performance Computing |
IoE | Internet of Everything |
IoT | Internet of Things |
MABAC | Multi-Attributive Border Approximation Area Comparison |
MACBETH | Measuring Attractiveness by a Categorical Based Evaluation Technique |
MARCOS | Measurement of Alternatives and Ranking according to COmpromise Solution |
MARE | Multi-Attribute Range Evaluations |
MAUT | Multi-Attribute Utility Theory |
MCC | Mobile Crowd Computing |
MCDM | Multi Criteria Decision Making |
MEW | Multiplicative Exponential Weighting |
MOORA | Multi-Objective Optimization on the basis of Ratio Analysis |
MULTIMOORA | Multiplicative MOORA |
PAPRIKA | Potentially All Pairwise RanKings of all possible Alternatives |
PIPRECIA | PIvot Pairwise RElative Criteria Importance Assessment |
PROMETHEE | Preference Ranking Organization METHod for Enrichment Evaluation |
RAFSI | Ranking of Alternatives through Functional mapping of criterion sub-intervals into a Single Interval |
RAM | Random Access Memory |
REMBRANDT | Ratio Estimations in Magnitudes or deci-Bells to Rate Alternatives which are Non-DominaTed |
SAW | Simple Additive Weighting |
SMART | Simple Multi-Attribute Rating Technique |
SMD | Smart Mobile Device |
SoC | System on Chip |
SWARA | Stepwise Weight Assessment Ratio Analysis |
TOPSIS | Technique for Order Preference by Similarity to Ideal Solution |
VIKOR | Više Kriterijumska optimizacija i Kompromisno Rešenje |
WASPAS | Weighted Aggregated Sum Product Assessment |
WPM | Weighted Product Method |
WSM | Weighted Sum Model |
Application Areas of MCDM Methods | Selected References |
---|---|
Finance and economics | [72,73,74] |
Waste management | [75,76,77,78] |
Engineering and production | [79,80,81,82] |
Organisations and corporates | [83,84,85,86] |
Business process and operations | [87,88,89,90] |
Supply chain management | [91,92,93,94] |
Energy sector | [95,96,97,98] |
Civil engineering | [99,100,101] |
Building construction and management | [102,103,104,105] |
City and society | [106,107,108] |
Education and e-learning | [109,110,111,112] |
Careers and job | [113,114,115,116] |
Transportation | [117,118,119,120] |
Healthcare | [121,122,123] |
Reference | MCDM Methods Compared | Application Focus | Analysis Performed | ||||
---|---|---|---|---|---|---|---|
Sensitivity Analysis | Result Comparison | Statistical Test/Analysis | Rank Reversal | Computation/Time Complexity | |||
[124] | ELECTRE, TOPSIS, MEW, SAW, and four versions of AHP | General MCDM problem of ranking | √ | √ | √ | √ | |
[125] | AHP and SAW | Ranking cloud render farm services | √ | √ | √ | ||
[126] | TOPSIS, AHP, and COMET | Assessing the severity of chronic liver disease | √ | √ | |||
[127] | CODAS, EDAS, WASPAS, and MOORA | Selecting material handling equipment | √ | √ | |||
[128] | TOPSIS, DEMATEL, and MACBETH | ERP package selection | √ | √ | √ | ||
[129] | AHP, ELECTRE, TOPSIS, and VIKOR | Enhancement of historical buildings | √ | √ | |||
[130] | MOORA, TOPSIS, and VIKOR | Material selection of brake booster valve body | √ | √ | |||
[131] | AHP, TOPSIS, and VIKOR | Manufacturing process selection | √ | √ | √ | ||
[132] | Multi-MOORA, TOPSIS, and three variants of VIKOR | Randomly generated MCDM problems (i.e., decision matrices) as per [124]. | √ | √ | √ | ||
[133] | WPM, WSM, revised AHP, TOPSIS, and COPRAS | Sustainable housing affordability | √ | √ | √ | ||
[134] | SAW, TOPSIS, PROMETHEE, and COPRAS | Stock selection using modern portfolio theory | √ | √ | |||
[135] | COMET, TOPSIS, and AHP | Assessment of mortality in patients with acute coronary syndrome | √ | √ | |||
[136] | SWARA, COPRAS, fuzzy ANP, fuzzy AHP, fuzzy TOPSIS, SAW, and EDAS | Risk assessment in public-private partnership projects | √ | √ | √ | ||
[137] | WSM, VIKOR, TOPSIS, and ELECTRE | Ranking renewable energy sources | √ | √ | √ | ||
[138] | WSM, WPM, WASPAS, MOORA, and MULTIMOORA | Industrial robot selection | √ | √ | √ | ||
[139] | WSM, WPM, AHP, and TOPSIS | Seismic vulnerability assessment of RC structures | √ | √ | √ | ||
[140] | AHP, TOPSIS, and PROMETHEE | Determining trustworthiness of cloud service providers | √ | √ | √ | ||
[141] | TOPSIS and VIKOR | Finding most important product aspects in customer reviews | √ | √ | |||
[142] | MABAC and WASPAS | Evaluating the effect of COVID-19 on countries’ sustainable development | √ | √ | √ | ||
[143] | WSM, TOPSIS, PROMETHEE, ELECTRE, and VIKOR | Utilization of renewable energy industry | √ | √ | √ | ||
[144] | WSM, TOPSIS, and ELECTRE | Flood disaster risk analysis | √ | √ | √ | ||
[145] | MAUT, TOPSIS, PROMETHEE, and PROMETHEE GDSS | Choosing contract type for highway construction in Greece | √ | √ | |||
[146] | TOPSIS, VIKOR, EDAS, and PROMETHEE-II | Suitable biomass material selection for maximum bio-oil yield | √ | √ | |||
[147] | TOPSIS, VIKOR, and COPRAS | COVID-19 regional safety assessment | √ | √ | √ | ||
[148] | EDAS and TOPSIS | General MCDM problem | √ | √ | √ | √ | |
[149] | AHP, TOPSIS, ELECTRE III, and PROMETHEE II | Building performance simulation | √ | √ | √ | ||
[150] | AHP, fuzzy AHP, and ESM | Aircraft type selection | √ | √ | |||
[151] | AHP, TOPSIS, and SAW | Intercrop selection in rubber plantations | √ | √ | |||
[152] | AHP, TOPSIS, SAW, and PROMETHEE | Employee placement | √ | √ | |||
[153] | TOPSIS, VIKOR, improved ELECTRE, PROMETHEE II, and WPM | Mining method selection | √ | √ | |||
[154] | AHP, SMART, and MACBETH | Incentive-based experiment (ranking coffee shops within university campus) | √ | √ | |||
[155] | AHP, fuzzy AHP, and fuzzy TOPSIS | Supplier selection | √ | √ | |||
[156] | TOPSIS, SAW, VIKOR, and ELECTRE | Evaluating the quality of urban life | √ | √ | √ | √ | |
[157] | AHP, MARE, ELECTRE III | Equipment selection | √ | √ | |||
[158] | VIKOR and TOPSIS | Forest fire susceptibility mapping | √ | √ | |||
[159] | PIPRECIA, MABAC, CoCoSo, and MARCOS | Measuring the performance of healthcare supply chains | √ | √ | √ | √ | |
[160] | MOORA, MULTIMOORA, and TOPSIS | Optimize the process parameters in the electro-discharge machine | √ | √ | √ | ||
[161] | AHP, AHP TOPSIS, and fuzzy AHP | Mobile-based culinary recommendation system | √ | √ | √ | ||
[162] | TOPSIS, COPRAS, and GRA | Evaluation of teachers | √ | √ | √ | ||
[163] | AHP, TOPSIS, ELECTRE III, and PROMETHEE II | Urban sewer network plan selection | √ | √ | |||
[164] | TOPSIS and AHP | Dam site selection using GIS | √ | √ | |||
This paper | EDAS, ARAS, MABAC, COPRAS, and MARCOS | Resource selection in mobile crowd computing | √ | √ | √ | √ |
MCDM Method | Merits | Demerits |
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EDAS |
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ARAS |
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MABAC |
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COPRAS |
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MARCOS |
|
|
Nature | Profit Type | Cost Type | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Criteria | CPU frequency (GHz) | CPU cores (in numbers) | GPU frequency (GHz) | Total RAM (GB) | Available memory (MB) | Battery capacity (mAh) | Battery available (%) | Wi-Fi strength (1–5) | CPU load (%) | GPU load (%) | CPU temp (Co) | Battery temp (Co) | GPU Architecture (nm) |
Code | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 |
Effect direction | (+) | (+) | (+) | (+) | (+) | (+) | (+) | (+) | (−) | (−) | (−) | (−) | (−) |
SMD | Profit Criteria | Cost Criteria | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | |
M1 | 2.2 | 2 | 650 | 8 | 895 | 2700 | 15 | 4 | 92 | 27 | 43 | 45 | 14 |
M2 | 1.5 | 4 | 450 | 4 | 3831 | 4000 | 39 | 4 | 16 | 76 | 39 | 40 | 10 |
M3 | 1.5 | 2 | 650 | 6 | 2694 | 2700 | 12 | 3 | 44 | 67 | 38 | 40 | 28 |
M4 | 1.3 | 8 | 650 | 8 | 518 | 4000 | 11 | 5 | 89 | 78 | 42 | 42 | 10 |
M5 | 1.3 | 8 | 650 | 8 | 1807 | 3000 | 10 | 4 | 13 | 8 | 31 | 38 | 10 |
M6 | 1.7 | 8 | 450 | 8 | 1982 | 3000 | 68 | 5 | 64 | 32 | 32 | 35 | 14 |
M7 | 2.5 | 2 | 400 | 6 | 3857 | 3500 | 18 | 1 | 60 | 16 | 38 | 36 | 10 |
M8 | 2.5 | 4 | 624 | 8 | 558 | 4000 | 56 | 5 | 99 | 87 | 50 | 48 | 10 |
M9 | 1.7 | 2 | 450 | 8 | 1908 | 2700 | 57 | 4 | 26 | 4 | 30 | 34 | 28 |
M10 | 2.5 | 2 | 450 | 6 | 1767 | 4000 | 24 | 2 | 53 | 93 | 45 | 44 | 10 |
M11 | 2.5 | 2 | 400 | 4 | 2853 | 4000 | 94 | 3 | 53 | 47 | 40 | 40 | 10 |
M12 | 2.2 | 2 | 624 | 6 | 3535 | 2700 | 24 | 3 | 26 | 67 | 37 | 39 | 28 |
M13 | 2.2 | 8 | 710 | 4 | 1734 | 3500 | 50 | 1 | 19 | 63 | 34 | 38 | 28 |
M14 | 1.5 | 8 | 650 | 4 | 2954 | 3000 | 59 | 5 | 15 | 3 | 34 | 33 | 10 |
M15 | 2.2 | 8 | 650 | 6 | 1916 | 3000 | 11 | 1 | 19 | 77 | 32 | 39 | 14 |
M16 | 1.3 | 2 | 400 | 6 | 870 | 2700 | 90 | 5 | 44 | 89 | 35 | 43 | 10 |
M17 | 1.5 | 4 | 400 | 4 | 2911 | 3500 | 17 | 2 | 18 | 96 | 36 | 47 | 10 |
M18 | 1.7 | 8 | 450 | 6 | 3876 | 4000 | 63 | 4 | 4 | 0 | 45 | 42 | 10 |
M19 | 1.3 | 4 | 650 | 6 | 944 | 2700 | 75 | 1 | 2 | 72 | 30 | 43 | 14 |
M20 | 1.7 | 2 | 450 | 6 | 2855 | 4000 | 22 | 5 | 62 | 9 | 32 | 40 | 10 |
M21 | 1.3 | 4 | 450 | 6 | 2973 | 3500 | 18 | 1 | 78 | 92 | 40 | 45 | 14 |
M22 | 1.5 | 8 | 624 | 8 | 3521 | 4000 | 22 | 1 | 42 | 44 | 38 | 37 | 10 |
M23 | 1.3 | 4 | 400 | 6 | 1734 | 3500 | 84 | 4 | 95 | 24 | 43 | 39 | 28 |
M24 | 2.5 | 2 | 710 | 4 | 3986 | 3000 | 16 | 1 | 8 | 57 | 36 | 40 | 28 |
M25 | 1.5 | 4 | 624 | 6 | 2851 | 3500 | 31 | 4 | 71 | 2 | 39 | 42 | 10 |
M26 | 1.7 | 4 | 710 | 6 | 2983 | 3000 | 50 | 1 | 61 | 58 | 38 | 45 | 10 |
M27 | 2.2 | 2 | 710 | 8 | 1932 | 4000 | 87 | 3 | 57 | 21 | 39 | 43 | 14 |
M28 | 2.5 | 2 | 624 | 6 | 972 | 4000 | 87 | 5 | 77 | 80 | 43 | 46 | 28 |
M29 | 1.3 | 2 | 710 | 6 | 2579 | 4000 | 16 | 2 | 69 | 0 | 41 | 40 | 14 |
M30 | 1.3 | 4 | 710 | 6 | 3537 | 3500 | 37 | 2 | 4 | 16 | 37 | 37 | 28 |
M31 | 2.5 | 2 | 650 | 4 | 809 | 2700 | 89 | 5 | 70 | 3 | 41 | 39 | 14 |
M32 | 1.3 | 4 | 450 | 4 | 3769 | 3500 | 56 | 2 | 5 | 35 | 33 | 40 | 28 |
M33 | 1.3 | 8 | 400 | 4 | 799 | 3000 | 39 | 1 | 65 | 47 | 35 | 44 | 10 |
M34 | 2.2 | 4 | 710 | 4 | 1938 | 4000 | 17 | 5 | 48 | 11 | 36 | 40 | 28 |
M35 | 1.3 | 8 | 710 | 6 | 2755 | 3000 | 92 | 4 | 1 | 48 | 34 | 39 | 14 |
M36 | 1.3 | 2 | 450 | 4 | 2663 | 2700 | 30 | 1 | 56 | 46 | 37 | 41 | 10 |
M37 | 2.5 | 8 | 450 | 4 | 1789 | 2700 | 12 | 2 | 4 | 15 | 32 | 36 | 14 |
M38 | 1.3 | 4 | 710 | 6 | 759 | 3500 | 44 | 2 | 66 | 0 | 34 | 35 | 28 |
M39 | 2.2 | 4 | 400 | 4 | 1748 | 3000 | 58 | 5 | 99 | 22 | 45 | 44 | 10 |
M40 | 1.3 | 8 | 450 | 8 | 2690 | 4000 | 56 | 4 | 22 | 13 | 33 | 34 | 28 |
M41 | 1.5 | 8 | 624 | 8 | 898 | 3500 | 82 | 4 | 47 | 22 | 34 | 36 | 10 |
M42 | 2.5 | 2 | 450 | 8 | 3681 | 3000 | 62 | 5 | 26 | 68 | 35 | 37 | 28 |
M43 | 1.3 | 8 | 624 | 8 | 2790 | 4000 | 16 | 3 | 84 | 15 | 37 | 39 | 14 |
M44 | 1.3 | 8 | 400 | 4 | 1582 | 3000 | 26 | 4 | 18 | 0 | 32 | 33 | 14 |
M45 | 2.5 | 8 | 650 | 4 | 2628 | 3500 | 69 | 4 | 94 | 11 | 42 | 40 | 28 |
M46 | 2.5 | 2 | 400 | 6 | 619 | 3000 | 52 | 2 | 40 | 52 | 41 | 39 | 14 |
M47 | 1.3 | 2 | 400 | 6 | 2760 | 2700 | 69 | 1 | 31 | 38 | 37 | 38 | 10 |
M48 | 2.5 | 8 | 624 | 8 | 1673 | 2700 | 29 | 5 | 26 | 7 | 35 | 36 | 28 |
M49 | 1.7 | 4 | 650 | 4 | 1647 | 3000 | 48 | 3 | 43 | 0 | 34 | 37 | 10 |
M50 | 1.3 | 8 | 450 | 6 | 1753 | 4000 | 29 | 3 | 91 | 64 | 39 | 45 | 28 |
SMD | Profit | Cost | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | |
M1 | 1.3 | 8 | 650 | 8 | 1807 | 3000 | 10 | 4 | 13 | 8 | 31 | 38 | 10 |
M10 | 2.5 | 2 | 450 | 6 | 1767 | 4000 | 24 | 2 | 53 | 93 | 45 | 44 | 10 |
M15 | 2.2 | 8 | 650 | 6 | 1916 | 3000 | 11 | 1 | 19 | 77 | 32 | 39 | 14 |
M20 | 1.7 | 2 | 450 | 6 | 2855 | 4000 | 22 | 5 | 62 | 9 | 32 | 40 | 10 |
M25 | 1.5 | 4 | 624 | 6 | 2851 | 3500 | 31 | 4 | 71 | 2 | 39 | 42 | 10 |
M30 | 1.3 | 4 | 710 | 6 | 3537 | 3500 | 37 | 2 | 4 | 16 | 37 | 37 | 28 |
M35 | 1.3 | 8 | 710 | 6 | 2755 | 3000 | 92 | 4 | 1 | 48 | 34 | 39 | 14 |
M40 | 1.3 | 8 | 450 | 8 | 2690 | 4000 | 56 | 4 | 22 | 13 | 33 | 34 | 28 |
M45 | 2.5 | 8 | 650 | 4 | 2628 | 3500 | 69 | 4 | 94 | 11 | 42 | 40 | 28 |
M50 | 1.3 | 8 | 450 | 6 | 1753 | 4000 | 29 | 3 | 91 | 64 | 39 | 45 | 28 |
Nature | Profit | Cost | ||||
---|---|---|---|---|---|---|
Criteria | CPU frequency (GHz) | CPU cores (in numbers) | Total RAM (GB) | Battery capacity (mAh) | Battery available (%) | CPU load (%) |
Code | C1 | C2 | C4 | C6 | C7 | C9 |
Effect direction | (+) | (+) | (+) | (+) | (+) | (−) |
SMD | Profit | Cost | SMD | Profit | Cost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C4 | C6 | C7 | C9 | C1 | C2 | C4 | C6 | C7 | C9 | ||
M1 | 2.2 | 2 | 895 | 2700 | 15 | 92 | M26 | 1.7 | 4 | 2983 | 3000 | 50 | 61 |
M2 | 1.5 | 4 | 3831 | 4000 | 39 | 16 | M27 | 2.2 | 2 | 1932 | 4000 | 87 | 57 |
M3 | 1.5 | 2 | 2694 | 2700 | 12 | 44 | M28 | 2.5 | 2 | 972 | 4000 | 87 | 77 |
M4 | 1.3 | 8 | 518 | 4000 | 11 | 89 | M29 | 1.3 | 2 | 2579 | 4000 | 16 | 69 |
M5 | 1.3 | 8 | 1807 | 3000 | 10 | 13 | M30 | 1.3 | 4 | 3537 | 3500 | 37 | 4 |
M6 | 1.7 | 8 | 1982 | 3000 | 68 | 64 | M31 | 2.5 | 2 | 809 | 2700 | 89 | 70 |
M7 | 2.5 | 2 | 3857 | 3500 | 18 | 60 | M32 | 1.3 | 4 | 3769 | 3500 | 56 | 5 |
M8 | 2.5 | 4 | 558 | 4000 | 56 | 99 | M33 | 1.3 | 8 | 799 | 3000 | 39 | 65 |
M9 | 1.7 | 2 | 1908 | 2700 | 57 | 26 | M34 | 2.2 | 4 | 1938 | 4000 | 17 | 48 |
M10 | 2.5 | 2 | 1767 | 4000 | 24 | 53 | M35 | 1.3 | 8 | 2755 | 3000 | 92 | 1 |
M11 | 2.5 | 2 | 2853 | 4000 | 94 | 53 | M36 | 1.3 | 2 | 2663 | 2700 | 30 | 56 |
M12 | 2.2 | 2 | 3535 | 2700 | 24 | 26 | M37 | 2.5 | 8 | 1789 | 2700 | 12 | 4 |
M13 | 2.2 | 8 | 1734 | 3500 | 50 | 19 | M38 | 1.3 | 4 | 759 | 3500 | 44 | 66 |
M14 | 1.5 | 8 | 2954 | 3000 | 59 | 15 | M39 | 2.2 | 4 | 1748 | 3000 | 58 | 99 |
M15 | 2.2 | 8 | 1916 | 3000 | 11 | 19 | M40 | 1.3 | 8 | 2690 | 4000 | 56 | 22 |
M16 | 1.3 | 2 | 870 | 2700 | 90 | 44 | M41 | 1.5 | 8 | 898 | 3500 | 82 | 47 |
M17 | 1.5 | 4 | 2911 | 3500 | 17 | 18 | M42 | 2.5 | 2 | 3681 | 3000 | 62 | 26 |
M18 | 1.7 | 8 | 3876 | 4000 | 63 | 4 | M43 | 1.3 | 8 | 2790 | 4000 | 16 | 84 |
M19 | 1.3 | 4 | 944 | 2700 | 75 | 2 | M44 | 1.3 | 8 | 1582 | 3000 | 26 | 18 |
M20 | 1.7 | 2 | 2855 | 4000 | 22 | 62 | M45 | 2.5 | 8 | 2628 | 3500 | 69 | 94 |
M21 | 1.3 | 4 | 2973 | 3500 | 18 | 78 | M46 | 2.5 | 2 | 619 | 3000 | 52 | 40 |
M22 | 1.5 | 8 | 3521 | 4000 | 22 | 42 | M47 | 1.3 | 2 | 2760 | 2700 | 69 | 31 |
M23 | 1.3 | 4 | 1734 | 3500 | 84 | 95 | M48 | 2.5 | 8 | 1673 | 2700 | 29 | 26 |
M24 | 2.5 | 2 | 3986 | 3000 | 16 | 8 | M49 | 1.7 | 4 | 1647 | 3000 | 48 | 43 |
M25 | 1.5 | 4 | 2851 | 3500 | 31 | 71 | M50 | 1.3 | 8 | 1753 | 4000 | 29 | 91 |
SMD | Profit | Cost | SMD | Profit | Cost | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C4 | C6 | C7 | C9 | C1 | C2 | C4 | C6 | C7 | C9 | ||
M1 | 1.3 | 8 | 1807 | 3000 | 10 | 13 | M30 | 1.3 | 4 | 3537 | 3500 | 37 | 4 |
M10 | 2.5 | 2 | 1767 | 4000 | 24 | 53 | M35 | 1.3 | 8 | 2755 | 3000 | 92 | 1 |
M15 | 2.2 | 8 | 1916 | 3000 | 11 | 19 | M40 | 1.3 | 8 | 2690 | 4000 | 56 | 22 |
M20 | 1.7 | 2 | 2855 | 4000 | 22 | 62 | M45 | 2.5 | 8 | 2628 | 3500 | 69 | 94 |
M25 | 1.5 | 4 | 2851 | 3500 | 31 | 71 | M50 | 1.3 | 8 | 1753 | 4000 | 29 | 91 |
Criteria | (+) | (+) | (+) | (+) | (+) | (+) | (+) | (+) | (−) | (−) | (−) | (−) | (−) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | |
Hj | 0.8436 | 0.8556 | 0.8985 | 0.8862 | 0.9456 | 0.8998 | 0.9178 | 0.9128 | 0.9498 | 0.9552 | 0.9816 | 0.9696 | 0.8996 |
wj | 0.1442 | 0.1332 | 0.0936 | 0.1050 | 0.0501 | 0.0924 | 0.0758 | 0.0804 | 0.0463 | 0.0414 | 0.0170 | 0.0281 | 0.0926 |
SMD | SP | SN | NSP | NSN | AS | Rank |
---|---|---|---|---|---|---|
M1 | 0.137 | 0.227 | 0.423 | 0.256 | 0.340 | 35 |
M2 | 0.145 | 0.146 | 0.446 | 0.521 | 0.484 | 25 |
M3 | 0.031 | 0.269 | 0.096 | 0.117 | 0.106 | 50 |
M4 | 0.251 | 0.224 | 0.771 | 0.266 | 0.518 | 21 |
M5 | 0.277 | 0.117 | 0.852 | 0.616 | 0.734 | 30 |
M6 | 0.246 | 0.057 | 0.758 | 0.811 | 0.785 | 7 |
M7 | 0.165 | 0.217 | 0.508 | 0.289 | 0.398 | 5 |
M8 | 0.230 | 0.174 | 0.708 | 0.429 | 0.568 | 32 |
M9 | 0.146 | 0.188 | 0.450 | 0.383 | 0.416 | 15 |
M10 | 0.115 | 0.241 | 0.354 | 0.211 | 0.283 | 44 |
M11 | 0.210 | 0.157 | 0.648 | 0.486 | 0.567 | 16 |
M12 | 0.098 | 0.225 | 0.300 | 0.261 | 0.281 | 45 |
M13 | 0.195 | 0.187 | 0.601 | 0.386 | 0.493 | 23 |
M14 | 0.311 | 0.066 | 0.957 | 0.782 | 0.870 | 2 |
M15 | 0.190 | 0.170 | 0.583 | 0.444 | 0.514 | 33 |
M16 | 0.168 | 0.247 | 0.517 | 0.189 | 0.353 | 22 |
M17 | 0.086 | 0.246 | 0.265 | 0.193 | 0.229 | 34 |
M18 | 0.325 | 0.030 | 1.000 | 0.902 | 0.951 | 47 |
M19 | 0.132 | 0.199 | 0.408 | 0.346 | 0.377 | 1 |
M20 | 0.155 | 0.156 | 0.476 | 0.489 | 0.482 | 26 |
M21 | 0.039 | 0.272 | 0.120 | 0.110 | 0.115 | 48 |
M22 | 0.233 | 0.123 | 0.718 | 0.597 | 0.658 | 11 |
M23 | 0.112 | 0.210 | 0.344 | 0.312 | 0.328 | 37 |
M24 | 0.162 | 0.305 | 0.499 | 0.000 | 0.250 | 46 |
M25 | 0.132 | 0.094 | 0.406 | 0.692 | 0.549 | 41 |
M26 | 0.092 | 0.131 | 0.283 | 0.569 | 0.426 | 18 |
M27 | 0.221 | 0.100 | 0.680 | 0.672 | 0.676 | 29 |
M28 | 0.209 | 0.249 | 0.644 | 0.184 | 0.414 | 10 |
M29 | 0.111 | 0.218 | 0.343 | 0.284 | 0.314 | 31 |
M30 | 0.131 | 0.164 | 0.403 | 0.464 | 0.433 | 28 |
M31 | 0.251 | 0.185 | 0.772 | 0.392 | 0.582 | 14 |
M32 | 0.105 | 0.202 | 0.324 | 0.339 | 0.331 | 36 |
M33 | 0.131 | 0.236 | 0.403 | 0.226 | 0.315 | 40 |
M34 | 0.156 | 0.171 | 0.480 | 0.440 | 0.460 | 27 |
M35 | 0.298 | 0.059 | 0.919 | 0.806 | 0.862 | 24 |
M36 | 0.048 | 0.283 | 0.146 | 0.070 | 0.108 | 3 |
M37 | 0.238 | 0.163 | 0.732 | 0.465 | 0.599 | 49 |
M38 | 0.079 | 0.204 | 0.243 | 0.330 | 0.287 | 13 |
M39 | 0.159 | 0.159 | 0.490 | 0.478 | 0.484 | 43 |
M40 | 0.259 | 0.119 | 0.796 | 0.610 | 0.703 | 8 |
M41 | 0.292 | 0.054 | 0.897 | 0.823 | 0.860 | 4 |
M42 | 0.229 | 0.197 | 0.705 | 0.353 | 0.529 | 19 |
M43 | 0.214 | 0.129 | 0.660 | 0.577 | 0.619 | 12 |
M44 | 0.208 | 0.155 | 0.639 | 0.492 | 0.566 | 17 |
M45 | 0.273 | 0.145 | 0.839 | 0.524 | 0.682 | 20 |
M46 | 0.094 | 0.194 | 0.289 | 0.365 | 0.327 | 9 |
M47 | 0.110 | 0.215 | 0.339 | 0.296 | 0.317 | 38 |
M48 | 0.306 | 0.119 | 0.941 | 0.611 | 0.776 | 39 |
M49 | 0.107 | 0.087 | 0.330 | 0.716 | 0.523 | 6 |
M50 | 0.113 | 0.236 | 0.347 | 0.227 | 0.287 | 42 |
SMD | Ø | ∂ | Rank |
---|---|---|---|
M1 | 0.0170 | 0.4682 | 38 |
M2 | 0.0187 | 0.5148 | 29 |
M3 | 0.0144 | 0.3967 | 49 |
M4 | 0.0202 | 0.5564 | 18 |
M5 | 0.0220 | 0.6075 | 19 |
M6 | 0.0219 | 0.6032 | 9 |
M7 | 0.0175 | 0.4836 | 10 |
M8 | 0.0211 | 0.5827 | 33 |
M9 | 0.0199 | 0.5505 | 12 |
M10 | 0.0169 | 0.4660 | 39 |
M11 | 0.0195 | 0.5382 | 20 |
M12 | 0.0163 | 0.4504 | 42 |
M13 | 0.0189 | 0.5208 | 26 |
M14 | 0.0264 | 0.7279 | 2 |
M15 | 0.0188 | 0.5181 | 13 |
M16 | 0.0175 | 0.4836 | 27 |
M17 | 0.0159 | 0.4400 | 34 |
M18 | 0.0242 | 0.6688 | 45 |
M19 | 0.0211 | 0.5810 | 4 |
M20 | 0.0191 | 0.5262 | 24 |
M21 | 0.0149 | 0.4114 | 48 |
M22 | 0.0204 | 0.5635 | 16 |
M23 | 0.0174 | 0.4805 | 36 |
M24 | 0.0164 | 0.4515 | 41 |
M25 | 0.0252 | 0.6964 | 47 |
M26 | 0.0180 | 0.4973 | 3 |
M27 | 0.0204 | 0.5636 | 30 |
M28 | 0.0190 | 0.5245 | 15 |
M29 | 0.0151 | 0.4173 | 25 |
M30 | 0.0194 | 0.5356 | 22 |
M31 | 0.0232 | 0.6390 | 5 |
M32 | 0.0176 | 0.4860 | 32 |
M33 | 0.0166 | 0.4591 | 40 |
M34 | 0.0187 | 0.5148 | 28 |
M35 | 0.0314 | 0.8678 | 23 |
M36 | 0.0139 | 0.3845 | 1 |
M37 | 0.0209 | 0.5777 | 50 |
M38 | 0.0153 | 0.4226 | 14 |
M39 | 0.0191 | 0.5271 | 46 |
M40 | 0.0212 | 0.5859 | 11 |
M41 | 0.0228 | 0.6292 | 7 |
M42 | 0.0194 | 0.5359 | 21 |
M43 | 0.0203 | 0.5616 | 17 |
M44 | 0.0176 | 0.4866 | 31 |
M45 | 0.0222 | 0.6122 | 35 |
M46 | 0.0161 | 0.4455 | 8 |
M47 | 0.0160 | 0.4421 | 43 |
M48 | 0.0230 | 0.6335 | 44 |
M49 | 0.0174 | 0.4815 | 6 |
M50 | 0.0173 | 0.4788 | 37 |
SMD | Sum (Si) | Rank |
---|---|---|
M1 | 0.03195 | 27 |
M2 | 0.03147 | 28 |
M3 | −0.15444 | 49 |
M4 | 0.16694 | 13 |
M5 | 0.17633 | 36 |
M6 | 0.18871 | 10 |
M7 | 0.04362 | 8 |
M8 | 0.22907 | 25 |
M9 | −0.03533 | 3 |
M10 | 0.03880 | 26 |
M11 | 0.10172 | 16 |
M12 | −0.04397 | 39 |
M13 | 0.08626 | 20 |
M14 | 0.18429 | 9 |
M15 | 0.11832 | 41 |
M16 | −0.08972 | 15 |
M17 | −0.11263 | 43 |
M18 | 0.24866 | 45 |
M19 | −0.05184 | 2 |
M20 | 0.06734 | 24 |
M21 | −0.13421 | 48 |
M22 | 0.20566 | 6 |
M23 | −0.08945 | 42 |
M24 | −0.04221 | 37 |
M25 | 0.08176 | 33 |
M26 | 0.03081 | 22 |
M27 | 0.22863 | 30 |
M28 | 0.09664 | 5 |
M29 | 0.00047 | 17 |
M30 | 0.00290 | 32 |
M31 | 0.08230 | 21 |
M32 | −0.11850 | 46 |
M33 | −0.10883 | 44 |
M34 | 0.08986 | 19 |
M35 | 0.19310 | 31 |
M36 | −0.22082 | 7 |
M37 | 0.07870 | 50 |
M38 | −0.04703 | 23 |
M39 | 0.00801 | 40 |
M40 | 0.14808 | 14 |
M41 | 0.25900 | 1 |
M42 | 0.09494 | 18 |
M43 | 0.17503 | 11 |
M44 | −0.00397 | 34 |
M45 | 0.17100 | 29 |
M46 | −0.02276 | 12 |
M47 | −0.12598 | 35 |
M48 | 0.22869 | 47 |
M49 | 0.03112 | 4 |
M50 | −0.04263 | 38 |
SMD | Q | U | Rank |
---|---|---|---|
M1 | 0.0179 | 64.9117 | 37 |
M2 | 0.0197 | 71.0934 | 27 |
M3 | 0.0155 | 56.0973 | 48 |
M4 | 0.0204 | 73.9355 | 21 |
M5 | 0.0245 | 88.6082 | 31 |
M6 | 0.0234 | 84.7260 | 5 |
M7 | 0.0188 | 68.0132 | 6 |
M8 | 0.0213 | 76.9171 | 32 |
M9 | 0.0188 | 68.0153 | 15 |
M10 | 0.0173 | 62.4978 | 45 |
M11 | 0.0207 | 74.9901 | 18 |
M12 | 0.0175 | 63.3945 | 43 |
M13 | 0.0201 | 72.7658 | 22 |
M14 | 0.0265 | 95.7698 | 2 |
M15 | 0.0200 | 72.5035 | 35 |
M16 | 0.0181 | 65.5115 | 24 |
M17 | 0.0165 | 59.5152 | 36 |
M18 | 0.0276 | 100.0000 | 47 |
M19 | 0.0183 | 66.3093 | 1 |
M20 | 0.0199 | 71.8945 | 25 |
M21 | 0.0155 | 56.0524 | 49 |
M22 | 0.0219 | 79.3701 | 12 |
M23 | 0.0184 | 66.4712 | 34 |
M24 | 0.0170 | 61.4502 | 46 |
M25 | 0.0206 | 74.4798 | 41 |
M26 | 0.0189 | 68.2442 | 20 |
M27 | 0.0221 | 79.8561 | 30 |
M28 | 0.0201 | 72.7628 | 10 |
M29 | 0.0176 | 63.5321 | 23 |
M30 | 0.0190 | 68.7025 | 29 |
M31 | 0.0210 | 75.9422 | 16 |
M32 | 0.0178 | 64.2474 | 39 |
M33 | 0.0175 | 63.4732 | 42 |
M34 | 0.0195 | 70.4855 | 28 |
M35 | 0.0246 | 89.1578 | 26 |
M36 | 0.0149 | 54.0259 | 4 |
M37 | 0.0220 | 79.7600 | 50 |
M38 | 0.0173 | 62.5282 | 11 |
M39 | 0.0197 | 71.0975 | 44 |
M40 | 0.0225 | 81.2178 | 9 |
M41 | 0.0247 | 89.3269 | 3 |
M42 | 0.0207 | 74.8716 | 19 |
M43 | 0.0214 | 77.2569 | 14 |
M44 | 0.0217 | 78.6526 | 13 |
M45 | 0.0227 | 82.2271 | 17 |
M46 | 0.0176 | 63.8470 | 8 |
M47 | 0.0178 | 64.3700 | 40 |
M48 | 0.0234 | 84.6420 | 38 |
M49 | 0.0209 | 75.5957 | 7 |
M50 | 0.0184 | 66.4773 | 33 |
SMD | f(Ki−) | f(Ki+) | f(Ki) | Rank |
---|---|---|---|---|
M1 | 0.22525 | 0.77475 | 0.56639 | 21 |
M2 | 0.22525 | 0.77475 | 0.44928 | 36 |
M3 | 0.22525 | 0.77475 | 0.46898 | 34 |
M4 | 0.22525 | 0.77475 | 0.71421 | 8 |
M5 | 0.22525 | 0.77475 | 0.52483 | 33 |
M6 | 0.22525 | 0.77475 | 0.66153 | 27 |
M7 | 0.22525 | 0.77475 | 0.43151 | 14 |
M8 | 0.22525 | 0.77475 | 0.85395 | 40 |
M9 | 0.22525 | 0.77475 | 0.48326 | 3 |
M10 | 0.22525 | 0.77475 | 0.54869 | 23 |
M11 | 0.22525 | 0.77475 | 0.54848 | 24 |
M12 | 0.22525 | 0.77475 | 0.57561 | 19 |
M13 | 0.22525 | 0.77475 | 0.71049 | 9 |
M14 | 0.22525 | 0.77475 | 0.51506 | 29 |
M15 | 0.22525 | 0.77475 | 0.58988 | 44 |
M16 | 0.22525 | 0.77475 | 0.35342 | 18 |
M17 | 0.22525 | 0.77475 | 0.32342 | 45 |
M18 | 0.22525 | 0.77475 | 0.64073 | 47 |
M19 | 0.22525 | 0.77475 | 0.37309 | 16 |
M20 | 0.22525 | 0.77475 | 0.46101 | 35 |
M21 | 0.22525 | 0.77475 | 0.41076 | 42 |
M22 | 0.22525 | 0.77475 | 0.64097 | 15 |
M23 | 0.22525 | 0.77475 | 0.56692 | 20 |
M24 | 0.22525 | 0.77475 | 0.54920 | 22 |
M25 | 0.22525 | 0.77475 | 0.50493 | 37 |
M26 | 0.22525 | 0.77475 | 0.50176 | 30 |
M27 | 0.22525 | 0.77475 | 0.74105 | 31 |
M28 | 0.22525 | 0.77475 | 0.86193 | 5 |
M29 | 0.22525 | 0.77475 | 0.44699 | 2 |
M30 | 0.22525 | 0.77475 | 0.54493 | 26 |
M31 | 0.22525 | 0.77475 | 0.54586 | 25 |
M32 | 0.22525 | 0.77475 | 0.42421 | 41 |
M33 | 0.22525 | 0.77475 | 0.31499 | 48 |
M34 | 0.22525 | 0.77475 | 0.70693 | 10 |
M35 | 0.22525 | 0.77475 | 0.63373 | 32 |
M36 | 0.22525 | 0.77475 | 0.15851 | 17 |
M37 | 0.22525 | 0.77475 | 0.44642 | 50 |
M38 | 0.22525 | 0.77475 | 0.52343 | 38 |
M39 | 0.22525 | 0.77475 | 0.48990 | 28 |
M40 | 0.22525 | 0.77475 | 0.71645 | 7 |
M41 | 0.22525 | 0.77475 | 0.67559 | 13 |
M42 | 0.22525 | 0.77475 | 0.73176 | 6 |
M43 | 0.22525 | 0.77475 | 0.67850 | 12 |
M44 | 0.22525 | 0.77475 | 0.33304 | 46 |
M45 | 0.22525 | 0.77475 | 0.87019 | 43 |
M46 | 0.22525 | 0.77475 | 0.43541 | 1 |
M47 | 0.22525 | 0.77475 | 0.22286 | 39 |
M48 | 0.22525 | 0.77475 | 0.82558 | 49 |
M49 | 0.22525 | 0.77475 | 0.37653 | 4 |
M50 | 0.22525 | 0.77475 | 0.67977 | 11 |
SMD | Ranking Results | Final Rank (SAW) | ||||
---|---|---|---|---|---|---|
EDAS | ARAS | MABAC | COPRAS | MARCOS | ||
M1 | 35 | 38 | 27 | 37 | 21 | 33 |
M2 | 25 | 29 | 28 | 27 | 36 | 27 |
M3 | 50 | 49 | 49 | 48 | 34 | 48 |
M4 | 21 | 18 | 13 | 21 | 8 | 14 |
M5 | 30 | 19 | 36 | 31 | 33 | 31 |
M6 | 7 | 9 | 10 | 5 | 27 | 10 |
M7 | 5 | 10 | 8 | 6 | 14 | 7 |
M8 | 32 | 33 | 25 | 32 | 40 | 32 |
M9 | 15 | 12 | 3 | 15 | 3 | 8 |
M10 | 44 | 39 | 26 | 45 | 23 | 35 |
M11 | 16 | 20 | 16 | 18 | 24 | 21 |
M12 | 45 | 42 | 39 | 43 | 19 | 38 |
M13 | 23 | 26 | 20 | 22 | 9 | 20 |
M14 | 2 | 2 | 9 | 2 | 29 | 4 |
M15 | 33 | 13 | 41 | 35 | 44 | 36 |
M16 | 22 | 27 | 15 | 24 | 18 | 22 |
M17 | 34 | 34 | 43 | 36 | 45 | 43 |
M18 | 47 | 45 | 45 | 47 | 47 | 47 |
M19 | 1 | 4 | 2 | 1 | 16 | 1 |
M20 | 26 | 24 | 24 | 25 | 35 | 24 |
M21 | 48 | 48 | 48 | 49 | 42 | 49 |
M22 | 11 | 16 | 6 | 12 | 15 | 12 |
M23 | 37 | 36 | 42 | 34 | 20 | 37 |
M24 | 46 | 41 | 37 | 46 | 22 | 40 |
M25 | 41 | 47 | 33 | 41 | 37 | 41 |
M26 | 18 | 3 | 22 | 20 | 30 | 16 |
M27 | 29 | 30 | 30 | 30 | 31 | 30 |
M28 | 10 | 15 | 5 | 10 | 5 | 9 |
M29 | 31 | 25 | 17 | 23 | 2 | 18 |
M30 | 28 | 22 | 32 | 29 | 26 | 26 |
M31 | 14 | 5 | 21 | 16 | 25 | 15 |
M32 | 36 | 32 | 46 | 39 | 41 | 44 |
M33 | 40 | 40 | 44 | 42 | 48 | 45 |
M34 | 27 | 28 | 19 | 28 | 10 | 23 |
M35 | 24 | 23 | 31 | 26 | 32 | 25 |
M36 | 3 | 1 | 7 | 4 | 17 | 2 |
M37 | 49 | 50 | 50 | 50 | 50 | 50 |
M38 | 13 | 14 | 23 | 11 | 38 | 19 |
M39 | 43 | 46 | 40 | 44 | 28 | 42 |
M40 | 8 | 11 | 14 | 9 | 7 | 11 |
M41 | 4 | 7 | 1 | 3 | 13 | 3 |
M42 | 19 | 21 | 18 | 19 | 6 | 17 |
M43 | 12 | 17 | 11 | 14 | 12 | 13 |
M44 | 17 | 31 | 34 | 13 | 46 | 29 |
M45 | 20 | 35 | 29 | 17 | 43 | 28 |
M46 | 9 | 8 | 12 | 8 | 1 | 6 |
M47 | 38 | 43 | 35 | 40 | 39 | 39 |
M48 | 39 | 44 | 47 | 38 | 49 | 46 |
M49 | 6 | 6 | 4 | 7 | 4 | 5 |
M50 | 42 | 37 | 38 | 33 | 11 | 34 |
Coefficient | Final Rank | EDAS Rank | ARAS Rank | MABAC Rank | COPRAS Rank | MARCOS Rank |
---|---|---|---|---|---|---|
Kendall’s tau | SAW_Rank | 0.817 ** | 0.778 ** | 0.829 ** | 0.830 ** | 0.510 ** |
Spearman’s rho | SAW_Rank | 0.947 ** | 0.917 ** | 0.960 ** | 0.951 ** | 0.704 ** |
Criteria | (+) | (+) | (+) | (+) | (+) | (+) | (+) | (+) | (−) | (−) | (−) | (−) | (−) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | C11 | C12 | C13 | |
Hj | 0.6296 | 0.8716 | 0.7732 | 0.9319 | 0.8127 | 0.8225 | 0.8202 | 0.9197 | 0.8744 | 0.9120 | 0.9181 | 0.9015 | 0.7753 |
wj | 0.1818 | 0.0630 | 0.1113 | 0.0334 | 0.0919 | 0.0871 | 0.0882 | 0.0394 | 0.0617 | 0.0432 | 0.0402 | 0.0484 | 0.1103 |
Criteria | (+) | (+) | (+) | (+) | (+) | (−) |
---|---|---|---|---|---|---|
C1 | C2 | C4 | C6 | C7 | C9 | |
Hj | 0.8436 | 0.8556 | 0.9456 | 0.8998 | 0.9178 | 0.9498 |
wj | 0.2660 | 0.2457 | 0.0925 | 0.1705 | 0.1398 | 0.0854 |
Criteria | (+) | (+) | (+) | (+) | (+) | (−) |
---|---|---|---|---|---|---|
C1 | C2 | C4 | C6 | C7 | C9 | |
Hj | 0.6296 | 0.8716 | 0.8127 | 0.8225 | 0.8202 | 0.8744 |
wj | 0.3169 | 0.1098 | 0.1602 | 0.1519 | 0.1538 | 0.1075 |
SMD | Comparative Ranking | Final Rank (SAW) | ||||
---|---|---|---|---|---|---|
EDAS | ARAS | MABAC | COPRAS | MARCOS | ||
M1 | 3 | 5 | 6 | 2 | 6 | 4 |
M10 | 9 | 8 | 9 | 9 | 5 | 9 |
M15 | 8 | 9 | 3 | 8 | 7 | 7 |
M20 | 7 | 4 | 4 | 6 | 4 | 5 |
M25 | 5 | 2 | 5 | 5 | 10 | 6 |
M30 | 6 | 7 | 8 | 7 | 8 | 8 |
M35 | 1 | 1 | 1 | 1 | 3 | 1 |
M40 | 4 | 6 | 7 | 4 | 1 | 2 |
M45 | 2 | 3 | 2 | 3 | 9 | 3 |
M50 | 10 | 10 | 10 | 10 | 2 | 10 |
SMD | Ranking Results | Final Rank (SAW) | ||||
---|---|---|---|---|---|---|
EDAS | ARAS | MABAC | COPRAS | MARCOS | ||
M1 | 50 | 48 | 46 | 48 | 42 | 50 |
M2 | 16 | 23 | 21 | 23 | 4 | 13 |
M3 | 48 | 50 | 49 | 50 | 22 | 46 |
M4 | 41 | 34 | 29 | 34 | 50 | 44 |
M5 | 40 | 42 | 44 | 42 | 32 | 43 |
M6 | 20 | 27 | 32 | 26 | 34 | 29 |
M7 | 10 | 9 | 18 | 11 | 25 | 15 |
M8 | 32 | 33 | 20 | 33 | 3 | 18 |
M9 | 26 | 20 | 9 | 20 | 48 | 31 |
M10 | 38 | 36 | 19 | 36 | 35 | 33 |
M11 | 11 | 12 | 4 | 14 | 13 | 7 |
M12 | 36 | 40 | 37 | 40 | 8 | 23 |
M13 | 4 | 6 | 3 | 6 | 30 | 4 |
M14 | 5 | 7 | 15 | 7 | 10 | 6 |
M15 | 24 | 4 | 41 | 3 | 44 | 30 |
M16 | 13 | 16 | 11 | 16 | 26 | 16 |
M17 | 43 | 44 | 48 | 43 | 46 | 49 |
M18 | 34 | 39 | 33 | 37 | 14 | 28 |
M19 | 1 | 2 | 2 | 2 | 2 | 2 |
M20 | 44 | 45 | 35 | 45 | 18 | 35 |
M21 | 46 | 43 | 42 | 44 | 12 | 39 |
M22 | 12 | 14 | 8 | 15 | 7 | 5 |
M23 | 37 | 30 | 40 | 30 | 37 | 36 |
M24 | 22 | 24 | 24 | 24 | 1 | 14 |
M25 | 49 | 47 | 45 | 47 | 24 | 45 |
M26 | 42 | 38 | 38 | 39 | 17 | 34 |
M27 | 30 | 31 | 34 | 31 | 11 | 22 |
M28 | 17 | 19 | 12 | 18 | 29 | 21 |
M29 | 19 | 18 | 10 | 19 | 40 | 24 |
M30 | 21 | 15 | 31 | 12 | 9 | 17 |
M31 | 28 | 28 | 27 | 28 | 43 | 37 |
M32 | 15 | 13 | 26 | 9 | 6 | 11 |
M33 | 27 | 29 | 36 | 29 | 45 | 40 |
M34 | 29 | 32 | 16 | 32 | 27 | 26 |
M35 | 31 | 26 | 25 | 27 | 33 | 32 |
M36 | 2 | 1 | 14 | 1 | 19 | 1 |
M37 | 47 | 49 | 50 | 49 | 23 | 47 |
M38 | 8 | 5 | 6 | 4 | 28 | 9 |
M39 | 45 | 46 | 43 | 46 | 47 | 48 |
M40 | 6 | 8 | 7 | 8 | 20 | 8 |
M41 | 9 | 10 | 13 | 10 | 41 | 19 |
M42 | 14 | 17 | 17 | 17 | 5 | 10 |
M43 | 23 | 21 | 22 | 21 | 16 | 20 |
M44 | 18 | 25 | 30 | 25 | 39 | 27 |
M45 | 33 | 35 | 39 | 35 | 38 | 38 |
M46 | 3 | 3 | 1 | 5 | 15 | 3 |
M47 | 35 | 37 | 28 | 38 | 49 | 42 |
M48 | 39 | 41 | 47 | 41 | 21 | 41 |
M49 | 7 | 11 | 5 | 13 | 31 | 12 |
M50 | 25 | 22 | 23 | 22 | 36 | 25 |
SMD | Comparative Ranking | Final Rank (SAW) | ||||
---|---|---|---|---|---|---|
EDAS | ARAS | MABAC | COPRAS | MARCOS | ||
M1 | 9 | 10 | 10 | 10 | 8 | 10 |
M10 | 6 | 5 | 2 | 5 | 2 | 3 |
M15 | 5 | 6 | 5 | 6 | 3 | 6 |
M20 | 7 | 8 | 7 | 8 | 10 | 8 |
M25 | 8 | 7 | 8 | 7 | 7 | 7 |
M30 | 4 | 4 | 6 | 3 | 4 | 4 |
M35 | 1 | 1 | 4 | 1 | 1 | 1 |
M40 | 3 | 3 | 3 | 4 | 9 | 5 |
M45 | 2 | 2 | 1 | 2 | 5 | 2 |
M50 | 10 | 9 | 9 | 9 | 6 | 9 |
Coefficient | Final Rank | EDAS Rank | ARAS Rank | MABAC Rank | COPRAS Rank | MARCOS Rank |
---|---|---|---|---|---|---|
Kendall’s tau | SAW_Rank | 0.778 ** | 0.556 * | 0.556 * | 0.778 ** | 0.067 |
Spearman’s rho | SAW_Rank | 0.903 ** | 0.758 * | 0.709 * | 0.927 ** | 0.139 |
Coefficient | Final Rank | EDAS Rank | ARAS Rank | MABAC Rank | COPRAS Rank | MARCOS Rank |
---|---|---|---|---|---|---|
Kendall’s tau | SAW_Rank | 0.763 ** | 0.701 ** | 0.659 ** | 0.700 ** | 0.407 ** |
Spearman’s rho | SAW_Rank | 0.917 ** | 0.870 ** | 0.840 ** | 0.866 ** | 0.585 ** |
Coefficient | Final Rank | EDAS Rank | ARAS Rank | MABAC Rank | COPRAS Rank | MARCOS Rank |
---|---|---|---|---|---|---|
Kendall’s tau | SAW_Rank | 0.733 ** | 0.867 ** | 0.733 ** | 0.911 ** | 0.511 * |
Spearman’s rho | SAW_Rank | 0.891 ** | 0.952 ** | 0.867 ** | 0.964 ** | 0.685 * |
Criteria | Criteria Weights under Different Experimental Cases | ||||
---|---|---|---|---|---|
Original | Exp1 | Exp2 | Exp3 | Exp4 | |
C1 | 0.1441964 | 0.0169798 | 0.0501301 | 0.1441964 | 0.1441964 |
C2 | 0.1331763 | 0.1331763 | 0.1331763 | 0.1331763 | 0.1331763 |
C3 | 0.0936409 | 0.0936409 | 0.0936409 | 0.0936409 | 0.0936409 |
C4 | 0.1049768 | 0.1049768 | 0.1049768 | 0.1049768 | 0.1049768 |
C5 | 0.0501301 | 0.0501301 | 0.1441964 | 0.0501301 | 0.0925919 |
C6 | 0.0924398 | 0.0924398 | 0.0924398 | 0.0924398 | 0.0924398 |
C7 | 0.0757997 | 0.0757997 | 0.0757997 | 0.0757997 | 0.0757997 |
C8 | 0.0803856 | 0.0803856 | 0.0803856 | 0.0803856 | 0.0803856 |
C9 | 0.0462696 | 0.0462696 | 0.0462696 | 0.0462696 | 0.0462696 |
C10 | 0.0413577 | 0.0413577 | 0.0413577 | 0.0413577 | 0.0413577 |
C11 | 0.0169798 | 0.1441964 | 0.0169798 | 0.0925919 | 0.0169798 |
C12 | 0.0280555 | 0.0280555 | 0.0280555 | 0.0280555 | 0.0280555 |
C13 | 0.0925919 | 0.0925919 | 0.0925919 | 0.0169798 | 0.0501301 |
Criteria | Criteria Weights under Different Experimental Cases | ||||
---|---|---|---|---|---|
Original | Exp1 | Exp2 | Exp3 | Exp4 | |
C1 | 0.1818299 | 0.1112996 | 0.0334131 | 0.1102984 | 0.1818299 |
C2 | 0.063014 | 0.063014 | 0.063014 | 0.063014 | 0.063014 |
C3 | 0.1112996 | 0.1818299 | 0.1112996 | 0.1112996 | 0.1112996 |
C4 | 0.0334131 | 0.0334131 | 0.1818299 | 0.0334131 | 0.0334131 |
C5 | 0.0919374 | 0.0919374 | 0.0919374 | 0.0919374 | 0.0919374 |
C6 | 0.0871434 | 0.0871434 | 0.0871434 | 0.0871434 | 0.0871434 |
C7 | 0.0882454 | 0.0882454 | 0.0882454 | 0.0882454 | 0.0882454 |
C8 | 0.0394249 | 0.0394249 | 0.0394249 | 0.0394249 | 0.0394249 |
C9 | 0.061668 | 0.061668 | 0.061668 | 0.061668 | 0.061668 |
C10 | 0.0431881 | 0.0431881 | 0.0431881 | 0.0431881 | 0.0431881 |
C11 | 0.0401855 | 0.0401855 | 0.0401855 | 0.0401855 | 0.1102984 |
C12 | 0.0483521 | 0.0483521 | 0.0483521 | 0.0483521 | 0.0483521 |
C13 | 0.1102984 | 0.1102984 | 0.1102984 | 0.1818299 | 0.0401855 |
Criteria | Criteria Weights under Different Experimental Cases | ||||
---|---|---|---|---|---|
Original | Exp1 | Exp2 | Exp3 | Exp4 | |
C1 | 0.2660 | 0.0854 | 0.0925 | 0.2660 | 0.2660 |
C2 | 0.2457 | 0.2457 | 0.2457 | 0.2457 | 0.1705 |
C4 | 0.0925 | 0.0925 | 0.2660 | 0.0854 | 0.0925 |
C6 | 0.1705 | 0.1705 | 0.1705 | 0.1705 | 0.2457 |
C7 | 0.1398 | 0.1398 | 0.1398 | 0.1398 | 0.1398 |
C9 | 0.0854 | 0.2660 | 0.0854 | 0.0925 | 0.0854 |
Criteria | Criteria Weights under Different Experimental Cases | ||||
---|---|---|---|---|---|
Original | Exp1 | Exp2 | Exp3 | Exp4 | |
C1 | 0.3168661 | 0.1074659 | 0.1098115 | 0.3168661 | 0.3168661 |
C2 | 0.1098115 | 0.1098115 | 0.3168661 | 0.1074659 | 0.1098115 |
C4 | 0.1602149 | 0.1602149 | 0.1602149 | 0.1602149 | 0.1518606 |
C6 | 0.1518606 | 0.1518606 | 0.1518606 | 0.1518606 | 0.1602149 |
C7 | 0.153781 | 0.153781 | 0.153781 | 0.153781 | 0.153781 |
C9 | 0.1074659 | 0.3168661 | 0.1074659 | 0.1098115 | 0.1074659 |
Coefficient | Method | Scenario | Exp1 | Exp2 | Exp3 | Exp4 |
---|---|---|---|---|---|---|
Kendall’s tau | EDAS | Original | 0.789 ** | 0.729 ** | 0.799 ** | 0.824 ** |
ARAS | 0.812 ** | 0.781 ** | 0.868 ** | 0.896 ** | ||
MABAC | 0.616 ** | 0.749 ** | 0.780 ** | 0.882 ** | ||
COPRAS | 0.799 ** | 0.755 ** | 0.827 ** | 0.874 ** | ||
MARCOS | 0.734 ** | 0.752 ** | 0.796 ** | 0.881 ** | ||
Spearman’s rho | EDAS | Original | 0.932 ** | 0.892 ** | 0.938 ** | 0.952 ** |
ARAS | 0.948 ** | 0.936 ** | 0.971 ** | 0.981 ** | ||
MABAC | 0.816 ** | 0.914 ** | 0.935 ** | 0.979 ** | ||
COPRAS | 0.939 ** | 0.910 ** | 0.950 ** | 0.973 ** | ||
MARCOS | 0.905 ** | 0.914 ** | 0.945 ** | 0.974 ** |
Coefficient | Method | Scenario | Exp1 | Exp2 | Exp3 | Exp4 |
---|---|---|---|---|---|---|
Kendall’s tau | EDAS | Original | 0.911 ** | 0.733 ** | 0.689 ** | 0.867 ** |
ARAS | 0.778 ** | 0.689 ** | 0.956 ** | 0.733 ** | ||
MABAC | 0.556 * | 0.200 | 0.556 * | 0.600 * | ||
COPRAS | 0.911 ** | 0.689 ** | 0.867 ** | 0.778 ** | ||
MARCOS | 0.511 * | 0.111 | 0.556 * | 0.867 ** | ||
Spearman’s rho | EDAS | Original | 0.976 ** | 0.806 ** | 0.806 ** | 0.939 ** |
ARAS | 0.903 ** | 0.806 ** | 0.988 ** | 0.879 ** | ||
MABAC | 0.709 * | 0.370 | 0.758 * | 0.745 * | ||
COPRAS | 0.964 ** | 0.830 ** | 0.939 ** | 0.915 ** | ||
MARCOS | 0.673 * | 0.212 | 0.661 * | 0.964 ** |
Coefficient | Method | Scenario | Exp1 | Exp2 | Exp3 | Exp4 |
---|---|---|---|---|---|---|
Kendall’s tau | EDAS | Original | 0.665 ** | 0.685 ** | 0.980 ** | 0.863 ** |
ARAS | 0.767 ** | 0.706 ** | 0.985 ** | 0.878 ** | ||
MABAC | 0.615 ** | 0.628 ** | 0.976 ** | 0.830 ** | ||
COPRAS | 0.778 ** | 0.719 ** | 0.982 ** | 0.879 ** | ||
MARCOS | 0.946 ** | 0.956 ** | 1.000 ** | 0.979 ** | ||
Spearman’s rho | EDAS | Original | 0.844 ** | 0.863 ** | 0.998 ** | 0.964 ** |
ARAS | 0.923 ** | 0.870 ** | 0.999 ** | 0.974 ** | ||
MABAC | 0.799 ** | 0.811 ** | 0.998 ** | 0.956 ** | ||
COPRAS | 0.926 ** | 0.880 ** | 0.998 ** | 0.974 ** | ||
MARCOS | 0.992 ** | 0.994 ** | 1.000 ** | 0.998 ** |
Coefficient | Method | Scenario | Exp1 | Exp2 | Exp3 | Exp4 |
---|---|---|---|---|---|---|
Kendall’s tau | EDAS | Original | 0.600 * | 0.600 * | 1.000 ** | 1.000 ** |
ARAS | 0.600 * | 0.556 * | 1.000 ** | 1.000 ** | ||
MABAC | 0.556 * | 0.289 | 1.000 ** | 1.000 ** | ||
COPRAS | 0.556 * | 0.511 * | 1.000 ** | 1.000 ** | ||
MARCOS | 1.000 ** | 0.867 ** | 1.000 ** | 1.000 ** | ||
Spearman’s rho | EDAS | Original | 0.709 * | 0.770 ** | 1.000 ** | 1.000 ** |
ARAS | 0.745 * | 0.685 * | 1.000 ** | 1.000 ** | ||
MABAC | 0.709 * | 0.345 | 1.000 ** | 1.000 ** | ||
COPRAS | 0.721 * | 0.673 * | 1.000 ** | 1.000 ** | ||
MARCOS | 1.000 ** | 0.952 ** | 1.000 ** | 1.000 ** |
Method | Time Complexity | Case | Average Runtime on Laptop (Milliseconds) | Average Runtime on Smartphone (Milliseconds) | ||||
---|---|---|---|---|---|---|---|---|
Best Case | Average Case | Worst Case | Data in Memory | Data in Secondary Storage | Data in Memory | Data in Phone Storage | ||
Entropy (criteria weight calculation) | Ω(m + n) | θ(mn) | O(mn) | Case 1 | 0.28391 | 135.1061 | 0.69546 | 1.16032 |
Case 2 | 0.08841 | 125.0397 | 0.17581 | 0.36809 | ||||
Case 3 | 0.12917 | 124.2696 | 0.34542 | 0.73407 | ||||
Case 4 | 0.06234 | 83.45512 | 0.09523 | 0.28998 | ||||
EDAS | Ω(m + n) | θ(mn) | O(mn) | Case 1 | 0.36754 | 124.50158 | 2.02136 | 2.46483 |
Case 2 | 0.08993 | 65.93222 | 0.42106 | 0.63313 | ||||
Case 3 | 0.16748 | 67.90012 | 0.97938 | 1.36073 | ||||
Case 4 | 0.06874 | 54.86296 | 0.22848 | 0.39752 | ||||
ARAS | Ω(mn) | θ(mn) | O(mn) | Case 1 | 0.30266 | 139.12975 | 0.87001 | 1.32013 |
Case 2 | 0.06918 | 65.64650 | 0.22711 | 0.41631 | ||||
Case 3 | 0.08789 | 62.64661 | 0.44734 | 0.80465 | ||||
Case 4 | 0.04303 | 49.42035 | 0.12672 | 0.30301 | ||||
MABAC | Ω(m + n) | θ(mn) | O(mn) | Case 1 | 0.27496 | 118.52908 | 1.03990 | 1.50524 |
Case 2 | 0.0904 | 64.17373 | 0.26752 | 0.45166 | ||||
Case 3 | 0.11870 | 66.00892 | 0.53094 | 0.90594 | ||||
Case 4 | 0.07156 | 52.62466 | 0.14914 | 0.34052 | ||||
COPRAS | Ω(m + n) | θ(mn) | O(mn) | Case 1 | 0.12264 | 122.95953 | 0.61347 | 1.05754 |
Case 2 | 0.04076 | 64.35327 | 0.13521 | 0.34481 | ||||
Case 3 | 0.05597 | 64.29061 | 0.32844 | 0.69645 | ||||
Case 4 | 0.03058 | 50.04589 | 0.08334 | 0.25656 | ||||
MARCOS | Ω(mn) | θ(mn) | O(mn) | Case 1 | 0.30410 | 127.74245 | 0.85634 | 1.29126 |
Case 2 | 0.06955 | 64.84879 | 0.21106 | 0.40832 | ||||
Case 3 | 0.09898 | 64.22248 | 0.44186 | 0.81885 | ||||
Case 4 | 0.04487 | 53.29281 | 0.12259 | 0.29045 |
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Pramanik, P.K.D.; Biswas, S.; Pal, S.; Marinković, D.; Choudhury, P. A Comparative Analysis of Multi-Criteria Decision-Making Methods for Resource Selection in Mobile Crowd Computing. Symmetry 2021, 13, 1713. https://doi.org/10.3390/sym13091713
Pramanik PKD, Biswas S, Pal S, Marinković D, Choudhury P. A Comparative Analysis of Multi-Criteria Decision-Making Methods for Resource Selection in Mobile Crowd Computing. Symmetry. 2021; 13(9):1713. https://doi.org/10.3390/sym13091713
Chicago/Turabian StylePramanik, Pijush Kanti Dutta, Sanjib Biswas, Saurabh Pal, Dragan Marinković, and Prasenjit Choudhury. 2021. "A Comparative Analysis of Multi-Criteria Decision-Making Methods for Resource Selection in Mobile Crowd Computing" Symmetry 13, no. 9: 1713. https://doi.org/10.3390/sym13091713
APA StylePramanik, P. K. D., Biswas, S., Pal, S., Marinković, D., & Choudhury, P. (2021). A Comparative Analysis of Multi-Criteria Decision-Making Methods for Resource Selection in Mobile Crowd Computing. Symmetry, 13(9), 1713. https://doi.org/10.3390/sym13091713