Applications of different MCDM tools in the selection of best laptop model. Mainly AHP-FUZZY

1. A COMPARATIVE STUDY OF DIFFERENT INTEGRATED MULTIPLE CRITERIA
DECISION MAKING METHODOLOGIES AND THEIR APPLICATIONS
SHANKHA SHUBHRA GOSWAMI
Mechanical Engineering
(Specialization In Production Technology and Management)
2nd Year M. Tech Student, 4th Semester
Jalpaiguri Government Engineering College
Registration Number - 171010410006 of 2017 - 2018
Roll Number - 17101203011
UNDER THE SUPERVISION OF
Dr. Soupayan Mitra
Associate Professor
Jalpaiguri Government Engineering College

2. Objectives of this research work
To select the best suitable product, process and strategies among various available options having different
criteria and sub-criteria by applying hybrid Multi Criteria Decision Making methodologies (like AHP-
TOPSIS, AHP-FUZZY etc.)
To validate the output by comparing the results from AHP, TOPSIS, SAW, AHP-FUZZY etc. that can be
applied to various fields of application like vendor selection, green supply chain management, waste
management, selection of different household appliances like television, air-conditioner, laptop, mobiles and
many more, selection of car etc.
To study in details the step by step process of different MCDM methodology like AHP, TOPSIS, SAW,
PROMETHEE, AHP-FUZZY etc.
To consider the selection of best laptop model based on actual physical market survey to illustrate different
MCDM methodology.
To compare the results obtained by different MCDM methodologies for best laptop selection and preference
order of ranking.
To discuss different applicable areas of different MCDM methodologies.

3. What is MCDM process?
Multiple-criteria decision-making (MCDM) or multiple-criteria decision analysis (MCDA) is a sub-
discipline of operations research that explicitly evaluates multiple conflicting criteria in decision making
(both in daily life and in settings such as business, government and medicine). Conflicting criteria are typical
in evaluating options: cost or price is usually one of the main criteria, and some measure of quality is
typically another criterion, easily in conflict with the cost.
In recent years various MCDM techniques have been suggested to do optimization. Among many multi-
criteria techniques AHP, TOPSIS, SAW, PROMETHEE, AHP-FUZZY are the most commonly used
methods.

4. Applicable Areas of MCDM Methods
 Manufacturing industry-Selection of Lathe, Best manufacturing process for a given product, best process planning,
Project Selection etc.
 Shipping Industry - Crane Selection, Best transportation selection etc.
 Electronics Industry- Selection of best refrigerator, Washing Machine, Mobile etc.
 Telecommunications Industry–Selection of best network, Selection of best location for mounting tower.
 Automobile industry- Four- wheeler and Two- Wheeler Selection, Selection for Two-Stroke Petrol Engines etc.
 Economic Sector – Rural development decision making selection, Resource Planning selection etc.
 Strategic decision making sector - Risk management decision making selection, Maintenance strategy selection etc.

5. What is AHP-FUZZY?
• Fuzzy set theory is an extension of classical set theory that “allows solving a lot of problems related to dealing
the imprecise and uncertain data”. Fuzzy set theory was first introduced by Zadeh in 1965.
• FAHP is an extension of conventional AHP process and is introduced when the decision maker has to take
decisions in uncertainty circumstances.
• FUZZY-AHP geometric mean method is proposed by Buckley in 1985 and extent analysis method is proposed
by Chang in 1996.
Difference Between Classical Approach and Fuzzy Logic
Classical or Crisp Logic
Considering the speed of a car: 10km/hr→Very Slow 20km/hr→Slow 40km/hr→Medium 60km/hr→High 80km/hr→Very High
Fuzzy Logic
≤ 10km/hr→Very Slow 11-20km/hr→Slow 21-40km/hr→Medium 41-60km/hr→High 61-80km/hr→Very High > 80km/hr →Extreme Speed
In crisp logic either a statement is true (1) or it is not (0), meanwhile fuzzy logic captures the degree to which something is true.
Consider the statement: “Ben agreed to met at 12 o’clock but ben was not puntual”
• Crisp logic: If Ben showed up precisely at 12, he is puntual, otherwise he is too early or too late.
• Fuzzy logic: The degree, to which ben was puntual, can be identified by on how much earlier or later he showed up (e.g. 0, if he showed up 11:45 or
12:15, 1 at 12:00)

6. Conversion of Crisp Numeric Values into Triangular Fuzzy Numbers
Graph showing the relative importance of the
linguistic variables Triangular Fuzzy Number of the Crisp Numeric
Values

7. Calculations Details of AHP-FUZZY
Criteria and Sub-criteria of the Laptop Model to be
Considered
 Processor (I3, I5, I7)
 Hard Disk Capacity (512GB, 1TB, 2TB)
 RAM (4GB, 8GB, 16GB)
 Operating System (DOS, Linux, Windows)
 Screen Size (14Inch, 15.6 Inch, 17.3 Inch)
Pair-Wise Comparison Matrix of the Main Criteria
of Laptop
 Brand (HP, Lenovo, Dell, Acer, Asus)
 Color (Silver, Gold, Black)
Fuzzified Pair-Wise Comparison Matrix of the Main
Criteria of Laptop

8. Determination of Fuzzy Geometric Mean Value 𝒓𝒊 (Main Criteria)
For Processor, The Fuzzy Geometric Mean Value 𝑟𝑖 is as follows:
𝑟1 = {(𝑙1×𝑙2×𝑙3×𝑙4×𝑙5×𝑙6×𝑙7)1/𝑛, (𝑚1×𝑚2×𝑚3×𝑚4×𝑚5×𝑚6×𝑚7)1/𝑛, (𝑢1×𝑢2×𝑢3×𝑢4×𝑢5×𝑢6×𝑢7)1/𝑛}
where n is the order of the matrix, here n = 7
𝑟1 = {(1×3×5×1×1×5×9)1/7, (1×5×7×3×2×7×9)1/7, (1×7×9×5×3×9×9)1/7}
𝑟1 = (2.536, 3.880, 4.985)

9. Determination of Fuzzy Weights 𝒘𝒊 (Main Criteria)
𝑖=1
7
𝑟𝑖 = (6.203, 10.180, 15.209)
Inverse of the total sum, ( 𝑟1 + 𝑟2 + 𝑟3 + 𝑟4 +
𝑟5 + 𝑟6 + 𝑟7)-1
(6.203, 10.180, 15.209)-1 = (1/15.209,
1/10.180, 1/6.203)
For Processor, the Fuzzy Weights ( 𝑤1) is as
follows:
𝑤1 = 𝑟1 × ( 𝑟1 + 𝑟2 + 𝑟3 + 𝑟4 + 𝑟5 + 𝑟6 + 𝑟7)-1
𝑤1 = 𝑟1 × (6.203, 10.180, 15.209)-1
𝑤1 = (2.536, 3.880, 4.985) × (1/15.209,
1/10.180, 1/6.203)
𝑤1 = (2.536/15.209, 3.880/10.180,
4.985/6.203)
𝑤1 = (0.167, 0.381, 0.804)

10. Defuzzification (Main Criteria)
For Processor, defuzzified value M1 is as follows:
(𝑙 𝑤1
, 𝑚 𝑤2
, 𝑢 𝑤3
) = (0.167, 0.381, 0.804)
Defuzzified weights (M1) =
𝑙 𝑤1+ 𝑚 𝑤2+ 𝑢 𝑤3
3
=
0.167+ 0.381+0.804
3
= 0.451
Summary of the Weightages of the Main Criteria and Sub-Criteria
Weights % Weights % Weights % Weights % Weights % Weights % Weights %
Main Criteria Processor 35.04 Hard Disk
Capacity
10.33 Operating
System
5.13 RAM 21.83 Screen
Size
17.33 Brand 8.16 Color 2.18
Sub-Criteria I3 27.14 512GB 7.23 DOS 7.79 4GB 30.04 14 Inch 26.62 HP 47.69 Silver 77.47
I5 63.09 1TB 61.85 Linux 18.44 8GB 63.73 15.6 Inch 55.31 Lenovo 27.94 Gold 14.23
I7 9.77 2TB 30.92 Windows 73.76 16GB 6.22 17.3 Inch 18.07 Dell 14.45 Black 8.30
Acer 6.44
Asus 3.48

11. Outcome Results from FUZZY-AHP (FAHP)
Overall Weightage and Ranking of the Laptop
Models by FAHP
For Model 1
(0.35042735 × 0.27140549) + (0.10334110 × 0.07226891) +
(0.05128205 × 0.07794677) + (0.21833722 × 0.30044444) +
(0.17327117 × 0.26622419) + (0.08158508 × 0.47693647) +
(0.02175602 × 0.08300395) = 0.25901744 or 25.90%
Ranking
Model 5 > Model 3 > Model 2 > Model 6 > Model 1 > Model 4

12. Outcome Results from SAW Outcome Results from PROMETHEE
Additive Weighted Sum of the Laptop Models and
their Ranking
Ranking of the Laptop Models Based on Net
Outflow of the Models

13. Outcome Results from AHP Outcome Results from TOPSIS
Overall Weightage Summation Percentage and
Ranking of the Laptop Models
Ranking of the Laptop Models based on Relative
Closeness Co-Efficient values

14. Results Comparison of the Ranking of Laptop Models by Applied
MCDM Process (AHP, TOPSIS, SAW, FAHP)

15. Conclusions
• The present analysis to find out the acceptable ranking of available laptop computers by using different
hybrid methodology based on market survey that helps the prospective customers to take proper decision in
selecting laptop model and also survey as a guide to the laptop manufacturing companies to frame their
future market strategy.
• From this present analysis it can be concluded that Model 5 is the best laptop model among these 6 available
models in the market based on the opinion of the common laptop users and the ranking of the laptop models
from best to worst is proposed.
• The outcome results and ranking are perfectly same for all the process.
• From this present research work it can also be concluded that the above mentioned diversified MCDM
methodologies is giving the same output results and ranking, moreover the validation is also same for all the
MCDM techniques adopted for this analysis.
Scope for Future Work : Here in this work few important criteria and sub-criteria have considered which
influence the selection of the laptop model. Other criteria and sub-criteria of laptop model can also be
considered in addition to it for this analysis. The scope of work can be extended by applying different MCDM
methods on some more problems and applications of other MCDM tool like MAXMIN, MAXMAX,
ELECTRA, VIKOR, SMART etc. can also be applied to get the possible ranking order and it can be applied
after AHP for getting more probabilistic results considering real-life industrial and domestic problems. The
same decision-making tools can also be applied to other field of applications based on strategic selection e.g.
supplier selection, personnel selection, vendor selection, selection of cranes etc.

16. Paper Publications and Conference Attended
1. Mitra, S., & Goswami, S. S. (2019) “Selection of the Desktop Computer Model by AHP-TOPSIS Hybrid MCDM Methodology,”
International Journal of Research and Analytical Reviews (IJRAR), Vol. 6 No. 1, pp. 784-790. Doi:
http://doi.one/10.1729/Journal.19551 (published)
2. Mitra, S., & Goswami, S. S. (2019) “Application of Integrated MCDM Technique (AHP-SAW) for the Selection of Best Laptop
Computer Model,” International Journal for Research in Engineering Application & Management (IJREAM), Vol. 4 No. 12, pp. 1-6.
Doi: 10.18231/2454-9150.2019.0091 (published)
3. Mitra, S., & Goswami, S. S. (2018) “Selection of Best Laptop by Applying Analytic Hierarchy Process (AHP),” 3rd Regional Science
and Technology Congress 2018, West Bengal (Northern Region), Abstract Volume, As a Presenting Author. (attended)
4. Mitra, S., & Goswami, S. S. (2018) “Application of TOPSIS Multi-Criteria Decision Making Tool for Best Desktop Computer
Selection,” 3rd Regional Science and Technology Congress 2018, West Bengal (Northern Region), Abstract Volume, As a Co-Author.
(attended)
5. Mitra, S., & Goswami, S. S. (2019) “Selection of The Best Laptop Model by the Application of FUZZY-AHP Methodology,” Journal
of Management, i-manager Publications (in progress)
6. Mitra, S., & Goswami, S. S. (2019) “A Comprehensive Study of Weighted Product Model for Selecting the Best Product in Our Daily
Life,” European Journal of Operations Research (EJOR), Elsevier (in progress)
7. Mitra, S., & Goswami, S. S. (2019) “Application of Simple Average Weighting Optimization Method in the Selection of Best
Desktop Computer Model,” Advanced Journal of Graduate Research (AJGR), Advanced International Journals of Research (AIJR)
(in progress)
8. Goswami, S. S., & Mitra, S. (2019) “Application of Analytic Hierarchy Process for the Selection of Best Tablet Model,”
International Conference on Emerging Trends in Electro-Mechanical Technologies and Management (TEMT 2019) (accepted)

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