Transcript of "Multi criteria decision support system on mobile phone selection with ahp and topsis"
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
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Outline
Multi-Criteria Decision Making (MCDM)
Analytic Hierarchy Process (AHP)
Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS)
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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.
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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.
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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
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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.
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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
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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)
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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
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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
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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.
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By collected data, the essential criteria are decided to
be into two Class: product-related and user-related.
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By interview, the essential criteria are decided to be
into two Class: product-related and user-related.
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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.
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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
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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
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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
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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
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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.
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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.
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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
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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
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P = 3M
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(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
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Pairwise Comparison
Matrix (Solicit)
P = 5G
M = 3G
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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)!
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Pairwise Comparison
Matrix (Solicit)
P = 3M, P=5M 3M = 5G M = (5/3)G But here M = 3G
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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.
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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
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Consistency
Ways to understand whether a matrix is
consistent or not?
Matrix Rank
Eigenvalue
Consistency Ratio
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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.
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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.
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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
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Criterias' Weight
(Consistent)
Normalization:
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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
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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
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Criterias' Weight
(Inconsistent)
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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
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Criterias' Weight
(Inconsistent)
Compute
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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.
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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
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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.
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Alternatives’ Distances
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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
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