0
Multi Criteria DSS on
Mobile Phone Selection
With AHP & TOPSIS
Electronic & Computer Department
Isfahan University Of Tech...
Outline
 Multi-Criteria Decision Making (MCDM)
 Analytic Hierarchy Process (AHP)
 Technique for Order Preference by
Sim...
Mobile Phones
 By the late 1980s, launch of the first GSM
phone.
 Swift evolution as the generations develop.
 Addition...
Mobile producer
 By Mobile Development:
The producers had started to develop their sale
strategies based on consumer pref...
Is Mobile Phone Selection
Important?
 The number of published papers on mobile
phones.
 The rapid evolution of the mobil...
Lecture aim
 Propose a multi-criteria decision making
(MCDM) approach.
 Show the most important mobile phone
features.
...
MCDM
 MCDM is a powerful tool used widely for
evaluating and ranking problems containing
multiple, usually conflicting cr...
MCDM Methods
 Some MCDM methods: Priority
based, outranking, distance-based and mixed
methods.
 One of the most outstand...
The Evaluation
Procedure Step 1. Identifying the mobile phone
selection (evaluation) criteria that are
considered the mos...
The Evaluation
Procedure
10
Evaluation Criteria
 Main objective: Select the best alternative
among a number of mobile phone options in
respect to the...
Evaluation Criteria
Some Examples from two groups:
1) The Product-related criteria.
2) The User-friendly criteria.
 Basic...
13
14
By collected data, the essential criteria are decided to
be into two Class: product-related and user-related.
15
By interview, the essential criteria are decided to be
into two Class: product-related and user-related.
16
Analytical Hierarchy
Process (AHP) Formulated way to structure decision problem.
 The best-known and most widely used mo...
AHP Procedure – Build the
Hierarchy Very similar to hierarchical value structure
– Goal on top (Fundamental Objective)
– ...
Categories of
“Elements” Objective
 Criteria
 Alternatives
 Goals
19
20
AHP Procedure – Judgments and
Comparisons
21
AHP Steps (Step 1)
Step 1:
 AHP uses several small sub problems to
present a complex decision problem.
 Thus, the first ...
Building the Hierarchy
23
Our Study Hierarchically
24
Another Example
25
AHP Steps (Step 2)
Step 2:
 The Decision Matrix, Decision Vector
(Saaty's nine-point scale), must constructed.
 Use the ...
1 -9 Scale
Intensity of Importance Definition
1 Equal Importance
3 Moderate Importance
5 Strong Importance
7 Very Strong I...
Decision Matrix
28
Normalized Decision Matrix For
Mobile Phone
Motorola V80Sony Ericsson K700iNokia 7260Decision Matrix
0.3330.3330.333Basic ...
Decision Vector
30
AHP Steps (Step 3)
Step 3:
Pairwise Comparison Matrix
 Compare the pairs of the elements of the
constructed hierarchy.
 ...
Pairwise Comparison
Matrix
32
Pairwise Comparison
Matrix
 Ways to build pairwise comparison matrix:
1) Build From Decision Vector
2) Build Directly wit...
Decision Vector:
Will Become:
Surly this is consistence.
Pairwise Comparison
Matrix (Direct)
A
B
C
A B C
1
1
1
5/3 5
3/5
1...
Pairwise Comparison
Matrix (Solicit)
Purchase Cost Maintenance Cost Gas Mileage
• Want to find weights on these criteria
•...
(2) Compare Purchase Cost to
– Which is more important?
Say purchase cost
– By how much? Say more important 5
Gas Mileage
...
This set of comparisons gives the following
matrix:
P
M
G
P M G
1
1
1
3 5
1/3
1/5
3
1/3
• Ratings mean that P is 3 times m...
Pairwise Comparison
Matrix
38
AHP Steps (Step 4)
Step 4:
 Calculate
 Is Pairwise Comparison Matrix Consistent?
 Consistency Ratio
 Reflect the consi...
Consistency
 Ratings should be consistent in two ways:
(1) Ratings should be transitive
– That means that
If A is better ...
Consistency
Ways to understand whether a matrix is
consistent or not?
 Matrix Rank
 Eigenvalue
 Consistency Ratio
41
Consistent Matrix
(Rank)Consistent matrix for the car example would
look like:
P
M
G
P M G
1
1
1
3 5
1/3
1/5
5/3
3/5
– No...
43
Consistent Matrix
(Eigenvalue)
87654321n
1.41.351.251.110.890.5200R.I. 44
Consistent Matrix
(Consistency Ratio)
45
Consistent Matrix
(Consistency Ratio)
AHP Steps (Step 5)
Step 5:
Compute Criterias' Weight
 Compute Weights in 2 different situation:
 Consistent Pairwise Com...
Criterias' Weight
(Consistent) Each pairwise comparison matrix column
has to be divided by the sum of entries of the
corr...
P
M
G
P M G
1
1
1
3 5
1/3
1/5
5/3
3/5
P
M
G
P M G
15/23
5/23
3/23
15/23 15/23
5/23
3/23
5/23
3/23
=
Sum = 1 1 1Sum = 23/15...
Criterias' Weight
(Inconsistent) Eigenvalue/Eigenvector Method:
– Eigenvalues are important tools in several
math, scienc...
Compute the Eigenvalues for the inconsistent
matrix:
P
M
G
P M G
1
1
1
3 5
1/3
1/5
3
1/3
w = vector of weights
– Must solv...
51
Criterias' Weight
(Inconsistent)
Car example with geometric means
P
M
G
P M G
1
1
1
3 5
1/3
1/5
3
1/3
Normalized
P
M
G
P M G
.65
.23
.11
.69 .56
.22
.13
.3...
AHP Steps (Step 6)
Step 6:
 Calculate weight vector!
 Multiply weight vector by weight
coefficients of the elements at t...
Normalized Weights of the
Criterias
54
Normalized Weights of the
Criterias
55
TOPSIS
 Technique for Order Preference by Similarity
to Ideal Solution (TOPSIS)
 TOPSIS is based on positive and negativ...
Evaluating Alternatives by
TOPSIS TOPSIS method, which is based on choosing the
best alternative having the:
 Shortest d...
Topsis Steps (Step 1)
58
C1
C2
C3
A1 A2 A3
1
3
1
3 5
7
3
3
5
Normalized
C1
C2
C3
A1 A2 A3
0.16
0.36
0.16
0.50 0.84
0.85
0.50
0.36
0.84
59
Example
C...
Topsis Steps (Step 2)
60
WNDM – Mobile Phone
Motorola V80Sony Ericsson K700iNokia 7260WeightWeighted Decision Matrix
0.0210.0210.0210.064Basic Requ...
Topsis Steps (Step 3)
62
Ideal and Negative-ideal
Solutions
Motorola V80Sony Ericsson K700Nokia 7260Weighted Decision Matrix
0.0210.0210.0210.0210....
Topsis Steps (Step 4)
64
Alternatives’ Distances
65
The distance of each alternative to the ideal
solution and the non-ideal solution:
Motorola V80...
Topsis Steps (Step 5)
66
Relative Closeness To The
Ideal Solution
67
Motorola V80Sony Ericsson K700iNokia 7260
0.11350.70460.4868
Topsis Steps (Step 6)
68
The End
Thanks For Your
Regard
69
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Multi criteria decision support system on mobile phone selection with ahp and topsis

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Transcript of "Multi criteria decision support system on mobile phone selection with ahp and topsis"

  1. 1. Multi Criteria DSS on Mobile Phone Selection With AHP & TOPSIS Electronic & Computer Department Isfahan University Of Technology To: Dr M.A.Montazeri , By: Reza Ramezani 1 In The Name Of Allah
  2. 2. Outline  Multi-Criteria Decision Making (MCDM)  Analytic Hierarchy Process (AHP)  Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) 2
  3. 3. Mobile Phones  By the late 1980s, launch of the first GSM phone.  Swift evolution as the generations develop.  Additional value-added services and high computing capabilities on 3G. 3
  4. 4. Mobile producer  By Mobile Development: The producers had started to develop their sale strategies based on consumer preferences over time.  To achieve maximum number of consumer: They throw different types of handsets every so often on the market. 4
  5. 5. Is Mobile Phone Selection Important?  The number of published papers on mobile phones.  The rapid evolution of the mobile phone has produced a proliferation of models and features.  Selecting a mobile phone is now a complex multi-criteria problem (MCDM).  Customers may find online decision support useful. 5
  6. 6. Lecture aim  Propose a multi-criteria decision making (MCDM) approach.  Show the most important mobile phone features.  Evaluating the mobile phone options in respect to the users' preferences order.  Finally, ranking mobile phone alternatives by AHP and TOPSIS methods. 6
  7. 7. MCDM  MCDM is a powerful tool used widely for evaluating and ranking problems containing multiple, usually conflicting criteria.  MCDM refers to find the best opinion from all of the feasible alternatives in the presence of multiple decision criteria.  MCDM helps offer recommendations when decisions involve trade-offs among different decision criteria.  The MCDM generally enable to structure the problem clearly and systematically. 7
  8. 8. MCDM Methods  Some MCDM methods: Priority based, outranking, distance-based and mixed methods.  One of the most outstanding MCDM approaches is the Analytic Hierarchy Process (AHP) 8
  9. 9. The Evaluation Procedure Step 1. Identifying the mobile phone selection (evaluation) criteria that are considered the most important for the users.  Step 2. Calculating the criteria weights by applying AHP method.  Step 3. Conducting TOPSIS method to achieve the final ranking results. 9
  10. 10. The Evaluation Procedure 10
  11. 11. Evaluation Criteria  Main objective: Select the best alternative among a number of mobile phone options in respect to the users' preferences order.  Criteria list resources:  A literature research in depth  A survey conducted among the target group  The experiences of the telecommunication sector experts 11
  12. 12. Evaluation Criteria Some Examples from two groups: 1) The Product-related criteria. 2) The User-friendly criteria.  Basic Requirements - Marketability  Usability - Style  Customer Excitement - Luxuriousness  Simplicity - Attractiveness  Colorfulness - Texture  Design Standards - Acceptability  Reliability - Harmoniousness. 12
  13. 13. 13
  14. 14. 14
  15. 15. By collected data, the essential criteria are decided to be into two Class: product-related and user-related. 15
  16. 16. By interview, the essential criteria are decided to be into two Class: product-related and user-related. 16
  17. 17. Analytical Hierarchy Process (AHP) Formulated way to structure decision problem.  The best-known and most widely used model in decision making.  Powerful Methodology in order to determine the priorities among different criteria.  Attempts to mirror human decision process.  Easy to use.  Well accepted by decision makers.  Can be used for multiple decision makers. 17
  18. 18. AHP Procedure – Build the Hierarchy Very similar to hierarchical value structure – Goal on top (Fundamental Objective) – Decompose into sub-goals (Means objectives) – Further decomposition as necessary – Identify criteria (attributes) to measure achievement of goals (attributes and objectives) – Alternatives added to bottom – Different from decision tree – Alternatives show up in decision nodes – Alternatives affected by uncertain events – Alternatives connected to all criteria 18
  19. 19. Categories of “Elements” Objective  Criteria  Alternatives  Goals 19
  20. 20. 20
  21. 21. AHP Procedure – Judgments and Comparisons 21
  22. 22. AHP Steps (Step 1) Step 1:  AHP uses several small sub problems to present a complex decision problem.  Thus, the first act is to decompose the decision problem into a hierarchy with:  a goal at the top  criteria and sub-criteria at sub-levels  and alternatives at the bottom 22
  23. 23. Building the Hierarchy 23
  24. 24. Our Study Hierarchically 24
  25. 25. Another Example 25
  26. 26. AHP Steps (Step 2) Step 2:  The Decision Matrix, Decision Vector (Saaty's nine-point scale), must constructed.  Use the fundamental 1–9 scale defined by Saaty to assess the priority score.  The decision matrix involves the assessments of each alternative in respect to the decision criteria.  The decision vector involves the criteria's preferences. 26
  27. 27. 1 -9 Scale Intensity of Importance Definition 1 Equal Importance 3 Moderate Importance 5 Strong Importance 7 Very Strong Importance 9 Extreme Importance 2, 4, 6, 8 For compromises between the above Reciprocals of above In comparing elements i and j - if i is 3 compared to j - then j is 1/3 compared to i Rationals Force consistency Measured values available 27
  28. 28. Decision Matrix 28
  29. 29. Normalized Decision Matrix For Mobile Phone Motorola V80Sony Ericsson K700iNokia 7260Decision Matrix 0.3330.3330.333Basic Requirements 0.3820.3820.235Physical characteristics 0.2720.4560.272Technical features 0.2730.4540.273Functionality 0.1100.3350.555Brand choice 0.2300.3850.385Customer excitement 29
  30. 30. Decision Vector 30
  31. 31. AHP Steps (Step 3) Step 3: Pairwise Comparison Matrix  Compare the pairs of the elements of the constructed hierarchy.  The aim is to set their relative priorities with respect to each of the elements at the next higher level. 31
  32. 32. Pairwise Comparison Matrix 32
  33. 33. Pairwise Comparison Matrix  Ways to build pairwise comparison matrix: 1) Build From Decision Vector 2) Build Directly with solicit from user  Weight determination of criteria is more reliable when using pairwise comparisons than obtaining them directly. 33
  34. 34. Decision Vector: Will Become: Surly this is consistence. Pairwise Comparison Matrix (Direct) A B C A B C 1 1 1 5/3 5 3/5 1/5 3 1/3 A B C 5 3 1 34
  35. 35. Pairwise Comparison Matrix (Solicit) Purchase Cost Maintenance Cost Gas Mileage • Want to find weights on these criteria • AHP compares everything two at a time (1) Compare Purchase Cost to Maintenance Cost – Which is more important? Say purchase cost – By how much? Say moderately 3 35 P = 3M
  36. 36. (2) Compare Purchase Cost to – Which is more important? Say purchase cost – By how much? Say more important 5 Gas Mileage (3) Compare to – Which is more important? Say maintenance cost – By how much? Say more important 3 Gas MileageMaintenance Cost 36 Pairwise Comparison Matrix (Solicit) P = 5G M = 3G
  37. 37. This set of comparisons gives the following matrix: P M G P M G 1 1 1 3 5 1/3 1/5 3 1/3 • Ratings mean that P is 3 times more important than M and P is 5 times more important than G • What’s wrong with this matrix? The ratings are inconsistent (Step 4)! 37 Pairwise Comparison Matrix (Solicit) P = 3M, P=5M  3M = 5G  M = (5/3)G But here M = 3G
  38. 38. Pairwise Comparison Matrix 38
  39. 39. AHP Steps (Step 4) Step 4:  Calculate  Is Pairwise Comparison Matrix Consistent?  Consistency Ratio  Reflect the consistency of decision maker's judgments during the evaluation phase. 39
  40. 40. Consistency  Ratings should be consistent in two ways: (1) Ratings should be transitive – That means that If A is better than B and B is better than C then A must be better than C (2) Ratings should be numerically consistent – In car example we made 1 more comparison than we needed We know that P = 3M and P = 5G 3M = 5G M = (5/3)G 40
  41. 41. Consistency Ways to understand whether a matrix is consistent or not?  Matrix Rank  Eigenvalue  Consistency Ratio 41
  42. 42. Consistent Matrix (Rank)Consistent matrix for the car example would look like: P M G P M G 1 1 1 3 5 1/3 1/5 5/3 3/5 – Note that matrix has Rank = 1 – That means that all rows are multiples of each other and matrix can build from one row. 42
  43. 43. 43 Consistent Matrix (Eigenvalue)
  44. 44. 87654321n 1.41.351.251.110.890.5200R.I. 44 Consistent Matrix (Consistency Ratio)
  45. 45. 45 Consistent Matrix (Consistency Ratio)
  46. 46. AHP Steps (Step 5) Step 5: Compute Criterias' Weight  Compute Weights in 2 different situation:  Consistent Pairwise Comparison Matrix Normalization  Inconsistent Pairwise Comparison Matrix Eigenvector Geometric Mean 46
  47. 47. Criterias' Weight (Consistent) Each pairwise comparison matrix column has to be divided by the sum of entries of the corresponding column.  A normalized matrix is obtained in which the sum of the elements of each column vector is 1. 47
  48. 48. P M G P M G 1 1 1 3 5 1/3 1/5 5/3 3/5 P M G P M G 15/23 5/23 3/23 15/23 15/23 5/23 3/23 5/23 3/23 = Sum = 1 1 1Sum = 23/15 23/5 23/3 W(P) = 15/23, W(M)= 5/23, W(G) = 3/23 48 Criterias' Weight (Consistent) Normalization:
  49. 49. Criterias' Weight (Inconsistent) Eigenvalue/Eigenvector Method: – Eigenvalues are important tools in several math, science and engineering applications – Compute by solving the characteristic equation: det( I – A) = | A – I | = 0 – Use the largest , for the computation. – Defined as follows: for matrix A and vector x, Eigenvalue of A when Aw = w, w is nonzero w is then the eigenvector associated with 49
  50. 50. Compute the Eigenvalues for the inconsistent matrix: P M G P M G 1 1 1 3 5 1/3 1/5 3 1/3 w = vector of weights – Must solve: Aw = w by solving det( I – A) = 0 – We get: 10.0,26.0,64.0 GMP www Different than before! max = 3.039 Find the eigenvector for 3.039 and normalize 50 Criterias' Weight (Inconsistent)
  51. 51. 51 Criterias' Weight (Inconsistent)
  52. 52. Car example with geometric means P M G P M G 1 1 1 3 5 1/3 1/5 3 1/3 Normalized P M G P M G .65 .23 .11 .69 .56 .22 .13 .33 .08 w w w p M G = [(.65)(.69)(.56)] 1/3 = [(.22)(.23)(.33)] 1/3 = [(.13)(.08)(.11)] 1/3 = 0.63 = 0.26 = 0.05 Normalized = 0.67 = 0.28 = 0.05 w w w p M G 52 Criterias' Weight (Inconsistent) Compute
  53. 53. AHP Steps (Step 6) Step 6:  Calculate weight vector!  Multiply weight vector by weight coefficients of the elements at the higher levels, until the top of the hierarchy is reached. 53
  54. 54. Normalized Weights of the Criterias 54
  55. 55. Normalized Weights of the Criterias 55
  56. 56. TOPSIS  Technique for Order Preference by Similarity to Ideal Solution (TOPSIS)  TOPSIS is based on positive and negative ideal solutions.  Solutions are determined in respect to the distance of each alternative to the best and the worst performing alternative.  The alternative ratings and criterion weights, must pass from AHP phase to 56
  57. 57. Evaluating Alternatives by TOPSIS TOPSIS method, which is based on choosing the best alternative having the:  Shortest distance to the ideal solution  Farthest distance from the negative-ideal solution  The ideal solution is the solution that maximizes the benefit and also minimizes the total cost.  The negative-ideal solution is the solution that minimizes the benefit and also maximizes the total cost. 57
  58. 58. Topsis Steps (Step 1) 58
  59. 59. C1 C2 C3 A1 A2 A3 1 3 1 3 5 7 3 3 5 Normalized C1 C2 C3 A1 A2 A3 0.16 0.36 0.16 0.50 0.84 0.85 0.50 0.36 0.84 59 Example Calculate the normalized decision matrix.
  60. 60. Topsis Steps (Step 2) 60
  61. 61. WNDM – Mobile Phone Motorola V80Sony Ericsson K700iNokia 7260WeightWeighted Decision Matrix 0.0210.0210.0210.064Basic Requirements 0.0360.0360.0220.094Physical characteristics 0.0480.0800.0480.175Technical features 0.1120.1860.1120.409Functionality 0.0190.0580.0960.173Brand choice 0.0190.0320.0320.84Customer excitement 61
  62. 62. Topsis Steps (Step 3) 62
  63. 63. Ideal and Negative-ideal Solutions Motorola V80Sony Ericsson K700Nokia 7260Weighted Decision Matrix 0.0210.0210.0210.0210.021Basic Requirements 0.0360.0360.0220.0220.036Physical characteristics 0.0480.0800.0480.0480.080Technical features 0.1120.1860.1120.1860.112Functionality 0.0190.0580.0960.0190.96Brand choice 0.0190.0320.0320.0190.032Customer excitement 63
  64. 64. Topsis Steps (Step 4) 64
  65. 65. Alternatives’ Distances 65 The distance of each alternative to the ideal solution and the non-ideal solution: Motorola V80Sony Ericsson K700iNokia 7260 0.11240.03840.0822 0.01440.09160.0780
  66. 66. Topsis Steps (Step 5) 66
  67. 67. Relative Closeness To The Ideal Solution 67 Motorola V80Sony Ericsson K700iNokia 7260 0.11350.70460.4868
  68. 68. Topsis Steps (Step 6) 68
  69. 69. The End Thanks For Your Regard 69
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