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

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  • 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. Outline  Multi-Criteria Decision Making (MCDM)  Analytic Hierarchy Process (AHP)  Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) 2
  • 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. 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. 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. 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. 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. 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. 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. The Evaluation Procedure 10
  • 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. 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
  • 14. 14
  • 15. By collected data, the essential criteria are decided to be into two Class: product-related and user-related. 15
  • 16. By interview, the essential criteria are decided to be into two Class: product-related and user-related. 16
  • 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. 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. Categories of “Elements” Objective  Criteria  Alternatives  Goals 19
  • 20. 20
  • 21. AHP Procedure – Judgments and Comparisons 21
  • 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. Building the Hierarchy 23
  • 24. Our Study Hierarchically 24
  • 25. Another Example 25
  • 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. 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. Decision Matrix 28
  • 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. Decision Vector 30
  • 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. Pairwise Comparison Matrix 32
  • 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. 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. 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. (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. 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. Pairwise Comparison Matrix 38
  • 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. 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. Consistency Ways to understand whether a matrix is consistent or not?  Matrix Rank  Eigenvalue  Consistency Ratio 41
  • 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 Consistent Matrix (Eigenvalue)
  • 44. 87654321n 1.41.351.251.110.890.5200R.I. 44 Consistent Matrix (Consistency Ratio)
  • 45. 45 Consistent Matrix (Consistency Ratio)
  • 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. 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. 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. 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. 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 Criterias' Weight (Inconsistent)
  • 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. 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. Normalized Weights of the Criterias 54
  • 55. Normalized Weights of the Criterias 55
  • 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. 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. Topsis Steps (Step 1) 58
  • 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. Topsis Steps (Step 2) 60
  • 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. Topsis Steps (Step 3) 62
  • 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. Topsis Steps (Step 4) 64
  • 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. Topsis Steps (Step 5) 66
  • 67. Relative Closeness To The Ideal Solution 67 Motorola V80Sony Ericsson K700iNokia 7260 0.11350.70460.4868
  • 68. Topsis Steps (Step 6) 68
  • 69. The End Thanks For Your Regard 69

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