Multi-Criteria Decision
Analysis
Spatial analysis in decision making
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Outline
• Introduction
• Basic principles of GIS-based MCDA
• Methods multi-criteria evaluation
• Multi-objective evaluation
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Definition
• Multiple-criteria decision analysis (MCDA) can
be defined as ‘a collection of formal approaches
which seek to take explicit account of [key factors]
in helping individuals or groups explore decisions
that matter’ (Belton and Stewart 2002).
• GIS-MCDA can be thought of as a process that
transforms & combines geographical data & value
judgments (the decision-maker’s preferences) to
obtain information for decision making
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Suitability analysis & Hazard Map
• The concept of Suitability analysis describes the search
for locations or areas that are characterized by a
combination of certain properties. Often, the result of a
suitability analysis is a suitability map. It shows which
locations or areas are suitable for a specific use in form
of a thematic map (e.g. agricultural suitability map).
• The negative variation of the suitability map is
the hazard or risk map. It segregates areas that are
exposed to a specific hazard based on the criteria given
(e.g. avalanche hazard maps).
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Basic principles of GIS-based
MCDA
• Multi-criteria evaluation (MCE) or Multi-attribute
decision making (MADM)-With a single objective
• recommending the site for a new fire station,
• site suitability analysis for housing development
• Multi-criteria evaluation (MCE) techniques are required
to evaluate the suitability of sites falling within the
feasible areas identified using standard GIS overlay
procedures. [Carver, 1991]
• Multi-objective evaluation (MOE)- more objective
• Allocating urban land either to housing or green space
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Boolean overlay
• Conjunctive: Accept alternatives if they meet a cut-off value
on every criterion
• In each layer there is only binary true/false information
(forest / non forest). By logically intersecting this
information, the desired locations and areas wanted are
determined.
• Example: Criteria (looking for a plot of land)- satisfies all of
the criteria.
• Road -within 1km
• Drainage -within 200m
• Slope - less than 15 degree
• Intersect
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ANDAND
ROAD_1KM
INTERSECT
SLOPE<15 degreeWater_200m
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Boolean overlay
• Disjunctive: Accept alternatives that meet a cut-off
value on at least one criterion
• It can also be implemented for spatial problems using
binary overlay, where the map criteria layers are
combined using a union (logical OR) operation. It is a
risk-taking method, because only one criterion must be
met.
• Example: Criteria (looking for a plot of land)- satisfies
one of the criteria.
• Road -within 1km
• Drainage -within 200m
• Slope - less than 15 degree
• Union
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OROR
ROAD_1KM
UNION
SLOPE<15 degreeWater_200m
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Methods of Multi-Criteria
Evaluation (MCE)
Steps:
1. Define the problem
2. Determine the criteria (factors/constraints)
3. Standardize the factors
4. Determine the weight of each factor
5. Aggregate the criteria
6. Validate/verify the result
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Set the goal/define the problem
• the first step of an MCE is the definition of the
problem.
• “Which parts of area is suitable for building?”
• “the best site for a new school”
• “the suitable areas for beekeeping”
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Determine the criteria (factors/
constraints)
• Criteria are set of guidelines or requirements used as basis
for a decision
• Two types: factors & constraints
• A factor is a criterion that enhances or detracts from the
suitability of a specific alternative for the activity under
consideration
• i.e. distance to road (near = most suitable; far = least suitable)
• A constraint serves to limit the alternatives under
consideration; element or feature that represents limitations
or restrictions; area that is not preferred in any way or
considered unsuitable.
• i.e. protected area, water body, etc. (usually represented by a
Boolean mask) 12
Determine the criteria (factors/
constraints)
• The chosen criteria should reflect the characteristics of the
desired location or area as closely as possible.
• how much details are needed in the analysis affects the set of
criteria to be used
• i.e. main roads only vs. including minor roads; no. of
houses vs. no. of residents; etc.
• Criteria should be measurable
• If not determinable, use proxies
• i.e. slope stability can be represented by slope gradient
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Standardize the factors/criterion
scores
• Set the suitability values of the factors to a common
scale to make comparisons possible
• All factor should be of same scale either 1-10 or 0-
255 or 0-99 by Rescale by function
• Fuzzy Membership Functions are used to
standardize the criterion scores (0-1)
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Determine the weight of each
factor
There are several methods
• Ranking
• i.e. 3 factors: rank the factors with 1, 2, & 3, where 1 is the
least important while 3 is the most important
• Rating
• i.e. 3 factors: rate the factors using percentile – Factor 1
with the lowest percentage as the least important & Factor
3 with the highest percentage as the most important
• Rankings & ratings are usually converted to
numerical weights on a scale 0 to 1 with overall
summation of 1 (normalization).
• i.e. Factor 1 = 0.17; Factor 2 = 0.33; & Factor 3 = 0.50;
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Determine the weight of each
factor (AHP)
• Pairwise comparison- Analytical Hierarchy Process (AHP)
(Saaty, 1980)
• A matrix is constructed, where each criterion is compared with the
other criteria, relative to its importance, on a scale from 1 to 9.
• where 1 = equal preference between two factors; 9 = a particular
factor is extremely favored over the other
• a weight estimate is calculated & used to derive a consistency ratio
(CR) of the pairwise comparisons
• If CR > 0.10, then some pairwise values need to be reconsidered &
the process is repeated until the desired value of CR < 0.10 is
reached.
• Like in ranking & rating, AHP weights are also expressed in
numerical weights that sum up to 1. 16
Drainage Road Slope
Drainage 1 1/3 1/7
Road 3 1 1/5
Slope 7 5 1
sum 11.00 6.33 1.34
Drainage Road Slope
Drainage 0.091 0.053 0.106
Road 0.273 0.158 0.149
Slope 0.636 0.789 0.745
weight
0.083
0.193
0.724
1/11 =0.091
0.333/6.33 =0.053
Analytic hierarchy process
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Analytic hierarchy process
Calculate the Consistency Ratio (CR)
• CR = Consistency index (CI)/Random Consistency Index (RI)
CI = (λmax – n)/n – 1
• λmax is the Principal Eigen Value; ‘n’ is the number of factors
• λmax = Sum of the products between each element of the priority
vector and column totals.
λmax = (11*0.083) + (6.33*0.193) + (1.34*0.724) = 3.105
CI = (3.105 – 3)/3-1
CI = 0.0525
CR = 0.0525/0.58 CR = 0.09 < 0.10 (Acceptable)
n 1 2 3 4 5 6 7 8 9 10
RI 0 0 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 (Saaty, 1980)
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Aggregate the criteria
Weighted Linear Combination is the most commonly used
decision rule
• Formula:
S = Σwixi x Πcj
Where:
• S – is the composite suitability score
• xi – factor scores (cells)
• wi – weights assigned to each factor
• cj – constraints (or Boolean factors)
• Σ -- sum of weighted factors
• Π -- product of constraints (1-suitable, 0-unsuitable)
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Aggregate the criteria (Weighted
overlay)
• A numerical weighting factor is assigned to each
thematic layer according to its relative importance
compared to all other layers.
• weighted overlay is possible with rasters and
vectors just like Boolean overlay
• Example: Applying weight on Binary overlay
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Raster model
Vector model
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Aggregate the criteria (Weighted
linear combination)
Standardise the range of all the variables (note
Layers have values between 0 and 1, 1 is most
suitable, 0 least)
• Weight them according to perceived importance
(score 1 to 10, 10 as most important) or by AHP
• Add the layers and derive a map of nominal
suitability
• The location with the highest score is the most
suitable
• GIS raster calculator or weighted sum
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Standardised (0-1) Weighted (0-5)
Vegetation
Slope
Landuse
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Validate/verify the result
To assess the reliability of the output
• Ground truth verification
• i.e. conduct a field survey to verify sample areas
• Sensitivity analysis
• How do the following affect the result?
• altering the set of criteria (plus or minus)
• altering the respective weights of the factors
• Is the result reasonable?
• Does the result reflect reality?
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Multi-objective evaluation (MOE)
• When there is more than one goal, MCE is no
longer sufficient for use, instead a decision support
with multiple objectives (Multi Objective
Evaluation, MOE) should be implemented.
• Allocating urban land either to housing (objective
A) or green space (objective B)
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• The spatial allocation of the urban
land on the two uses. White is
suitable for neither (A) nor (B).
Blue was assigned to (A) and
green to (B)and Where blue and
green overlay, there is a land use
conflict (pink).
• The conflict area has to be
individually decided as to which
land use they are assigned. In the
simplest case, an area in dispute is
assigned to the land use it is better
suited (divide the area for both
landuse (B) and (A).
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Next: Demonstration on MCDA using AHP for Landslide
susceptibility mapping.
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Demonstration on MCDA using AHP
for Landslide susceptibility mapping.
• Weights by AHP
• Standardized by:
• Slope- Fuzzy membership
• Road and Drainage- Rescale by function
• Overlay by Weighted linear combination
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Drainage Road Slope
Drainage 1 0.333 0.143
Road 3 1 0.2
Slope 7 5 1
sum 11.00 6.33 1.34
Drainage Road Slope
Drainage 0.091 0.053 0.106
Road 0.273 0.158 0.149
Slope 0.636 0.789 0.745
weight
0.083
0.193
0.724
1/11 =0.091
0.333/6.33 =0.053
Analytic hierarchy process
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30
Model
weight
0.724
0.083
0.193
Drainage (rescaled)
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Landslide_Clip
ROAD_Scale
Value
High : 1
Low : -1.19209e-007
DRAINAGE_Scale
Value
High : 1
Low : -1.19209e-007
SLOPE_Fuzzy
Value
High : 1
Low : 0
Lighter the colour- closer to the drainage
Distance to Road (rescaled)
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Landslide_Clip
ROAD_Scale
Value
High : 1
Low : -1.19209e-007
DRAINAGE_Scale
Value
High : 1
Low : -1.19209e-007
SLOPE_Fuzzy
Value
High : 1
Low : 0
Lighter the colour- closer to the road
Slope degree (rescaled)
Landslide_Clip
ROAD_Scale
Value
High : 1
Low : -1.19209e-007
DRAINAGE_Scale
Value
High : 1
Low : -1.19209e-007
SLOPE_Fuzzy
Value
High : 1
Low : 0
Lighter the colour- steeper the slope
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Landslide susceptibility mapping (LSM)
with existing landslide
Legend
combination_S_R_D_1
<VALUE>
Very Low Susceptibility
Low Susceptibility
Moderate Susceptibility
High Susceptibility
Very High Susceptibility
Validation
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Frequency of
Landslide
pixels
Percent Cumulative Percent
Very Low 44 6.3 6.3
Low 71 10.2 16.6
Moderate 134 19.3 35.9
High 221 31.9 67.8
Very High 223 32.2 100
Total 693 100
-by overlaying the existing landslide on the LSM
Validation
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Thank you
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