Multi-criteria evaluation

1
Multi-criteria evaluation
Geography 570 B. Klinkenberg
2
Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MEC
• Multi-objective land allocation (MOLA)
• Example

3
Introduction

• Land is a scarce resource
• essential to make best possible use
• identifying suitability for
• agriculture
• forestry
• recreation
• housing
• etc.

4
Sieve mapping

• Early methods
• Ian McHarg (1969) Design with Nature
• tracing paper overlays
• landscape architecture and facilities location
• Bibby Mackney (1969) Land use capability
  classification
• tracing paper overlays
• optimal agricultural land use mapping

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GIS approaches

• Sieve mapping using
• polygon overlay (Boolean logic)
• cartographic modelling
• Example uses
• nuclear waste disposal site location
• highway routing
• land suitability mapping
• etc.

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Sieve mapping / boolean overlay

• The easiest way to do sieve mapping to use
  Boolean logic to find combinations of layers that
  are defined by using logical operators AND for
  intersection, OR for union, and NOT for exclusion
  of areas (Jones, 1997). In this approach, the
  criterion is either true or false. Areas are
  designated by a simple binary number, 1,
  including, or 0, excluding them from being
  suitable for consideration (Eastman, 1999).

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Boolean example

• Within 500m from Shepshed
• Within 450m from roads
• Slope between 0 and 2.5
• Land grade III
• Suitable land, min 2.5 ha

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Question

• What problems or limitations are there with the
  sieve mapping approach?

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Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MCE
• Multi-objective land allocation (MOLA)
• Example MOLA

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Definitions

• Decision a choice between alternatives
• Decision frame the set of all possible
  alternatives
• Parks Forestry
• Candidate set the set of all locations pixels
  that are being considered
• all Crown lands
• Decision set the areas assigned to a decision
  (one alternative)
• all pixels identified as Park

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Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MCE
• Multi-objective land allocation (MOLA)
• ExampleMOLA

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Definitions

• Criterion some basis for a decision. Two main
  classes
• Factors enhance or detract from the suitability
  of a land use alternative (OIR) e.g., distance
  from a road
• Constraints limit the alternatives (N) e.g.,
  crown/private lands boolean
• Can be a continuum from crisp decision rules
  (constraints) to fuzzy decision rules (factors)
• Goal or target some characteristic that the
  solution must possess (a positive constraint)
• E.g., 12 of the land base identified as park

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Definitions

• Decision rule the procedure by which criteria
  are combined to make a decision. Can be
• Functions numerical, exact decision rules
• Heuristics approximate procedures for finding
  solutions that are good enough
• Objective the measure by which the decision rule
  operates (e.g., identify potential parks)
• Evaluation the actual process of applying the
  decision rule

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Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MCE
• Multi-objective land allocation (MOLA)
• Example MOLA

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Kinds of evaluations

• Single-criterion evaluation (e.g., do I have
  enough money to see a movie?)
• Multi-criteria evaluation to meet one objective,
  several criteria must be considered (e.g., do I
  have enough to see a movie, do I want to see an
  action flick or a horror movie, which theatre is
  closest?)
• Multi-objective evaluations
• Complementary objectives non-conflicting
  objectives (e.g., extensive grazing and
  recreational hiking)
• Conflicting objectives both cannot exist at the
  same place, same time (e.g., ecological reserves
  and timber licenses)

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Multi-criteria evaluation

• Basic MCE theory
• Investigate a number of choice possibilities in
  the light of multiple criteria and conflicting
  objectives (Voogd, 1983)
• Generate rankings of choice alternatives
• Two basic methodologies
• Boolean overlays (polygon-based methods) A
• Weighted linear combinations (WLC) (raster-based
  methods) B

B
A
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Multi-criteria evaluation

• Multicriteria analysis appeared in the 1960s as a
  decision-making tool. It is used to make a
  comparative assessment of alternative projects or
  heterogeneous measures. With this technique,
  several criteria can be taken into account
  simultaneously in a complex situation. The method
  is designed to help decision-makers to integrate
  the different options, reflecting the opinions of
  the actors concerned, into a prospective or
  retrospective framework. Participation of the
  decision-makers in the process is a central part
  of the approach. The results are usually directed
  at providing operational advice or
  recommendations for future activities.

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Multi-criteria evaluation

• Multicriteria evaluation be organised with a view
  to producing a single synthetic conclusion at the
  end of the evaluation or, on the contrary, with a
  view to producing conclusions adapted to the
  preferences and priorities of several different
  partners.
• Multi-criteria analysis is a tool for comparison
  in which several points of view are taken into
  account, and therefore is particularly useful
  during the formulation of a judgement on complex
  problems. The analysis can be used with
  contradictory judgement criteria (for example,
  comparing jobs with the environment) or when a
  choice between the criteria is difficult.

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MCE

• Non-monetary decision making tool
• Developed for complex problems,where uncertainty
  can arise if a logical, well-structured
  decision-making process is not followed
• Reaching consensus in a (multidisciplinary) group
  is difficult to achieve.

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MCE techniques

• Many techniques (decision rules)
• Most developed for evaluating small problem sets
  (few criteria, limited candidate sets)
• Some are suitable for large (GIS) matrices
• layers criteria
• cells or polygons choice alternatives
• Incorporation of levels of importance (weights
  WLC methods)
• Incorporation of constraints (binary maps)

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MCE pros and cons

• Cons
• Dynamic problems strongly simplified into a
  linear model
• Static, lacks the time dimension
• Controversial method too subjective?

• Pros
• Gives a structured and traceable analysis
• Possibility to use different evaluation factors
  makes it a good tool for discussion
• Copes with large amounts of information
• It works!

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MCE pros and cons

• MCE is not perfectquick and dirty-option,
  unattractive for real analysts
• but what are the alternatives? - system
  dynamics modelling impossible for huge
  socio-technical problems - BOGSATT is not
  satisfactory (Bunch of Old Guys/Gals Sitting
  Around a Table Talking)
• MCE is good for complex spatial problems
• Emphasis on selecting good criteria, data
  collection and sensitivity analysis

23
Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example
• Multi-objective land allocation (MOLA)
• Example

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Principles of MCE

• Methodology
• Determine criteria (factors / constraints) to be
  included
• Standardization (normalization) of factors /
  criterion scores
• Determining the weights for each factor
• Evaluation using MCE algorithms
• Sensitivity analysis of results

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Determine the criteria to be included

• Oversimplification of the decision problem could
  lead to too few criteria being used
• Using a large number of criteria reduces the
  influence of any one criteria
• They should be comprehensive, measurable,
  operational, non-redundant, and minimal
• Often proxies must be used since the criteria of
  interest may not be determinable (e.g., slope
  is used to represent slope stability)
• A multistep, iterative process that considers the
  literature, analytical studies and, possibly,
  opinions

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Factor normalization

• Standardization of the criteria to a common scale
  (commensuration)
• Need to compare apples to apples, not apples to
  oranges to walnuts. For example
• Distance from a road (km)
• Slope ()
• Wind speed
• Consider
• Range (convert all
• to a common range)
• Meaning
• (which end of the
• scale good)

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Fuzzy membership functions
Used to standardize the criterion
scores Linguistic concepts are inherently
fuzzy (hot/cold short/tall)
Graphs of the Fuzzy Memberships within
IDRISI (Based on Eastman 1999)
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Factor normalization example
Cholera Health Risk Prediction in Southern
Africathe relation between temperature and risk
Below 28.5 there is no risk, above 37.5 it cant
rise.
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Determine the weights

• By normalizing the factors we make the choice of
  the weights an explicit process.
• A decision is the result of a comparison of one
  or more alternatives with respect to one or more
  criteria that we consider relevant for the task
  at hand. Among the relevant criteria we consider
  some as more important and some as less
  important this is equivalent to assigning
  weights to the criterion according to their
  relative importance.

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Determine the weights

• Multiple criteria typically have varying
  importance. To illustrate this, each criterion
  can be assigned a specific weight that reflects
  it importance relative to other criteria under
  consideration. The weight value is not only
  dependent the importance of any criterion, it is
  also dependent on the possible range of the
  criterion values. A criterion with variability
  will contribute more to the outcome of the
  alternative and should consequently be regarded
  as more important than criteria with no or little
  changes in their range.

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Determine the weights

• Weights are usually normalised to sum up to 1, so
  that in a set of weights (w1, w2, ., wn) 1.
• There are several methods for deriving weights,
  among them (Malczewski, 1999)
• Ranking
• Rating
• Pairwise Comparison (AHP)
• Trade-off
• The simplest way is straight ranking (in order of
  preference 1most important, 2second most
  important, etc.). Then the ranking is converted
  into numerical weights on a scale from 0 to 1, so
  that they sum up to 1.

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Analytical hierarchy process

• One of the more commonly-used methods to
  calculate the weights.

Refer to description of ArcGIS extension ext_ahp.
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Analytical hierarchy process

• IDRISI features a weight routine to calculate
  weights, based on the pairwise comparison method,
  developed by 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. Then, a
  weight estimate is calculated and used to derive
  a consistency ratio (CR) of the pairwise
  comparisons.
• If CR gt 0.10, then some pairwise values need to
  be reconsidered and the process is repeated till
  the desired value of CR lt 0.10 is reached.

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MCE Algorithms

• The most commonly used decision rule is the
  weighted linear combination
• where
• S is the composite suitability score
• x factor scores (cells)
• w weights assigned to each factor
• c constraints (or boolean factors)
• ? -- sum of weighted factors
• ? -- product of constraints (1-suitable,
  0-unsuitable)

S ?wixi x ?cj
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MCE

• A major difference between boolean (sieve
  methods) and MCE is that for boolean and
  methods every condition must be met before an
  area is included in the decision set. There is
  no distinction between those areas that fully
  meet the criteria and those that are at the
  edges of the criteria.
• There is also no room for weighting the factors
  differentially.

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Example weighted linear summation
Example
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Sensitivity analysis

• Choice for criteria (e.g., why included?)
• Reliability data
• Choice for weighing factors is subjective
• Will the overall solution change if you use other
  weighing factors?
• How stable is the final conclusion?
• sensitivity analysis vary the scores / weights
  of the factors to determine the sensitivity of
  the solution to minor changes

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Sensitivity analysis

• Only addresses one of the sources of uncertainty
  involved in making a decision (i.e., the validity
  of the information used)
• A second source of uncertainty concerns future
  events that might lead to differentially
  preferred outcomes for a particular decision
  alternative.
• Decision rule uncertainty should also be
  considered (? MCE itself)

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Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MCE
• Multi-objective land allocation (MOLA)
• Example MOLA

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Fuzzy Expert Systems and GIS for Cholera Health
Risk Prediction in Southern Africa

• Gavin Fleming, Marna van der Merwe, Graeme
  McFerren, Kerry Murphy
• CSIR, South Africa

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Vibrio cholerae

• Untreated death within 24h from loss of fluid
• Transmission ingest contaminated material
• Treatment fluid replacement and antibiotics
• Origins in the Orient
• Now endemic in many places

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The complex nature of cholera
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Hierarchical approach
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GIS and Fuzzy LogicArcInfo raster, AML
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Model variables
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MCE _at_ Shepshed

• 100m lt Shepshed lt1000m
• Between 50m and 600m to roads
• Slope between 1 and 5
• Land grade III and grade IV
• Varying suitability, min 2.5 ha

Bright areas have highest suitability
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Comparison of results

• The Boolean constrains leave no room for
  prioritisation, all suitable areas are of equal
  value, regardless of their position in reference
  to their factors.  
• Minimal fuzzy membership the minimum suitability
  value from each factor at that location is chosen
  from as the "worst case" suitability. This can
  result in larger areas, with highly suitable
  areas.  
• Probabilistic fuzzy intersection fewer suitable
  areas than the minimal fuzzy operation. This is
  due to the fact that this effectively is a
  multiplication. Multiplying suitability factors
  of 0.9 and 0.9 at one location yields an overall
  suitability of 0.81, whereas the fuzzy approach
  results in 0.9. Thus, it can be argued that the
  probabilistic operation is counterproductive when
  using fuzzy variables (Fisher, 1994). When using
  suitability values larger than 1 this does of
  course not occur.  
• Weighted Overlay produces many more areas. This
  shows all possible solutions, regardless whether
  all factors apply or not, as long as at least one
  factor is valid for that area. This is so,
  because even if one factor is null, the other
  factors still sum up to a value. This also shows
  areas that are outside of the initial
  constraints.

http//www.husdal.com/blog/2002/09/how-to-use-idri
.html
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Conclusions

• An integrative approach is effective for
  modelling complex problems
• Non-linear simulation modelling
• Expert systems
• AI integration (fuzzy logic)
• Established a framework and working model

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Wind Farm Siting

• Dennis Scanlin
• (Department of Technology)
• Xingong Li
• Chris Larson
• (Department of Geography Planning)
• Appalachian State University

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Spatial Analytical Hierarchy Process

• Wind farm siting
• Find the best wind farm sites based on siting
  factors
• Alternatives
• Locationinfinite
• Divide the space into squares/cells (200m 200m)
• Evaluate each cell based on the siting factors

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Preliminary Siting Factors

• Accessibility to roads
• Distance to primary roads
• Distance to secondary roads
• Distance to rural roads
• Accessibility to transmission lines
• Distance to 100K lines
• Distance to 250K lines
• Distance to above250K lines
• Wind power (or wind speed)
• Visibility
• Viewshed size
• of people in viewshed

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Siting Steps (MCE)

• Factor generation
• Distance calculation
• Visibility calculation
• Factor standardization (0 100)
• Each factor is a map layer
• Factor weights determination by AHP
• Final score
• Weighted combination of factors
• Exclusion areas

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AHP
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Factor Layers
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Wind Turbine visibility--Viewshed
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Wind Turbine Viewshed Size

• Red505km2
• Greed--805km2
• Blue--365km2
• Software tool developed to calculate viewshed
  size for each cell

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Visibility FactorViewshed Size

• Computational expensive
• About 700,000 cells
• Each cell requires 10 seconds
• About 76 days
• Parallel computing
• 12 computers
• Each computer runs two counties
• About 55000 cells
• 6 days
• Succeed with 3000 cells but failed with 55,000
  cells

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Visibility Factor-- of People in Viewshed
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Final Score Layer
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Candidate Sites
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Constraints (binary)
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Sites
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Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MCE
• Multi-objective land allocation (MOLA)
• Example

66
Multi-objective land allocation

• Basic MOLA theory
• procedure for solving multi-objective land
  allocation problems for cases with conflicting
  objectives
• based on information from set of suitability maps
• one map for each objective
• relative weights assigned to objectives
• amount of area to be assigned to each land use
• determines compromise solution that attempts to
  maximize suitability of lands for each objective
  given weights assigned

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Principles of MOLA

• Methodology
• construct ranked suitability maps for each
  objective using MCE
• decide on relative objective weights and area
  tolerances
• evaluate conflict demands on limited land via
  iterative process

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MOLA decision space
255
Non-conflicting choices
Conflicting choices
Objective 2
Non-conflicting choices
Unsuitable choices
0
0
255
Objective 1
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Roadmap

• Outline
• Introduction
• Definitions
• Multi-criteria evaluation (MCE)
• Principles of MCE
• Example MCE
• Multi-objective land allocation (MOLA)
• Example MOLA

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Carpet and agriculture in Kathmandu

• MOLA, Conflicting objectives Protecting 6000 ha
  of agricultural land while leaving 1500 ha for
  industrial development
• Step 1 Standardised factors
• Proximity to water
• Proximity to power
• Proximity to roads
• Proximity to market
• Slope

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Carpet and agriculture in Kathmandu

• Step 2 Suitability for each objective
• Agriculture 
• Carpet industry
• Best 6000 ha for agriculture
•  
• Best 1500 ha for carpet industry
• Conflict area

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Overview

• In the Boolean Intersection all criteria are
  assumed to be constraints. Suitability in one
  constraint will not compensate for
  non-suitability in any other constraint. This
  procedure also seems to carry the lowest possible
  uncertainty since only areas considered suitable
  in all criteria are entered into the result.
  However, this method requires crisp entities as
  criteria, a requirement that may be hard to meet.
  The advantage of the Boolean Intersection is that
  is straightforward and easy to apply. A
  disadvantage is that it might exclude or include
  areas that are not truly representative. Boolean
  Intersection is best applied either as a crude
  estimation or when all factors are of equal
  weight and when it can be assumed that the
  factors are of equal importance in any of the
  area they cover.
• Weighted Linear Combination allows each factor to
  display its potential because of the factor
  weights. Factor weights are very important in WLC
  because they determine how individual factors
  will aggregate. Thus, deciding on the correct
  weighting becomes essential. The advantage of
  this method is that all factors contribute to the
  solution based on their importance. The
  aggregation of individual weights is prone to be
  very subjective, even when pairwise comparison is
  used for ensuring consistent weights.
• Multi Objective Land Allocation blends
  priorities, whereas WLC favors one over the
  other, creating zones that do not overlap. MOLA
  is therefore preferable for solving conflicts
  that arise when multiple conflicting objectives
  exist and where an incorrect decision might be
  highly damaging.

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Conclusions

• Few GIS packages provide MCE functionality (e.g.
  Idrisi)
• Most GIS provide facilities for building MCE
  analyses (e.g. ArcGIS modelbuilder)
• Important method for
• Site and route selection
• land suitability modelling