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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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