multi-criteria evaluation

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Multi-criteria evaluation

Geography 570B. Klinkenberg

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Roadmap

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

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Introduction

Land is a scarce resourceessential to make best possible useidentifying suitability for:• agriculture• forestry• recreation• housing• etc.

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Sieve mappingEarly 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 approachesSieve 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 overlayThe 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 alternativesDecision 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) Example:MOLA

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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

Definitions

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Definitions

Decision rule: the procedure by which criteria are combined to make a decision. Can be:

Functions: numerical, exact decision rulesHeuristics: 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


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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 evaluationBasic MCE theory:

“Investigate a number of choice possibilities in the light of multiple criteria and conflicting objectives” (Voogd, 1983)Generate rankings of choice alternativesTwo basic methodologies:

• Boolean overlays (polygon-based methods) [A]• Weighted linear combinations (WLC) (raster-based

methods) [B]

A

B

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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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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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MCENon-monetary decision making toolDeveloped for complex problems,where uncertainty can arise if a logical, well-structured decision-making process is not followedReaching consensus in a (multidisciplinary) group is difficult to achieve.

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MCE techniquesMany 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 consCons:

Dynamic problems strongly simplified into a linear modelStatic, lacks the time dimensionControversial method – too subjective?

Pros:Gives a structured and traceable analysisPossibility to use different evaluation factors makes it a good tool for discussionCopes with large amounts of informationIt works!

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MCE is not perfect…“quick 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

MCE – pros and cons

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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

Methodology1. Determine criteria (factors /

constraints) to be included2. Standardization (normalization) of

factors / criterion scores3. Determining the weights for each

factor4. Evaluation using MCE algorithms5. 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 usedUsing a large number of criteria reduces the influence of any one criteriaThey should be comprehensive, measurable, operational, non-redundant, and minimalOften 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 normalizationStandardization 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)

Input

Output

low high

Poor: 0

Good: 255

Output

low high

0

255

Input

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Fuzzy membership functions

Graphs of the Fuzzy Memberships within IDRISI(Based on Eastman 1999)

Used to standardize the criterion scores

Linguistic conceptsare inherently fuzzy(hot/cold; short/tall)

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Factor normalization: examplefuzzy membership

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fuzzy membership

Cholera Health Risk Prediction in Southern Africa—the relation between temperature and risk

Below 28.5 there is no risk, above 37.5 it can’t rise.

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Determine the weightsBy 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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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.

Determine the weights

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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: 1=most important, 2=second 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.

Determine the weights

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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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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 > 0.10, then some pairwise values need to be reconsidered and the process is repeated till the desired value of CR < 0.10 is reached.

Analytical hierarchy process

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MCE Algorithms

The most commonly used decision rule is the weighted linear combination

where:S is the composite suitability scorex – factor scores (cells)w – weights assigned to each factorc – 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

User weights

Map 1 Map 2 Map 3 Map 4

Evaluation matrix

MCE routine

Output

Standardise

Example

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Sensitivity analysisChoice for criteria (e.g., why included?)Reliability dataChoice 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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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)

Sensitivity analysis

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Roadmap


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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 MurphyCSIR, South Africa

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Vibrio cholerae

Untreated: death within 24h from loss of fluidTransmission: ingest contaminated materialTreatment: fluid replacement and antibioticsOrigins in the OrientNow endemic in many places

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Lithosphere (soil)

Hydrosphere(water)

Atmosphere(air)

Biosphere (plants&animals)

V. cholerae

Geosphere

The complex nature of cholera

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Phytoplankton & Aquatic plants

Zooplankton: copepods & other crustaceans (fresh & saltwater systems)

Temperature, pH Fe+, salinity

sunlight

Transmission to humans

Abiotic conditions:Favour growth of V. cholerae and/orexpression of virulence

Zooplankton:V. cholerae associates with zooplankton for survival, multiplication & transmission purposes

Algae:Promote survival of V. cholerae Provide indirectly favourable conditions for growth and maybe expression of virulenceProvide food for zooplankton

Transmitted to humans:Ingestion of an infectious dose of V. cholerae (critical threshold value of 106 cells)Socio-cultural-economic vulnerability factors

Hierarchical approach

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InputsLiterature survey and expert workshops to:Determine possible contributing factors to a cholera outbreak

Simulation model to: Provide some of the input into the expert systemSimulate the relative importance of different variables

Expert system to: Capture the knowledge and dataEstablish the high-level structure and flow of the integrated model

GIS and fuzzy logic to implement model thus defined

OutputsPossible cholera outbreak location and date

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GIS and Fuzzy LogicArcInfo: raster, AML

fuzzy membership

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Model variables

Variable Range Optimal value

Occurrence of cholera in the past Poor indication of epidemic reservoir

Average rainfall (mm/month) > 600mm

Mean maximum daily surface temperature (C/day) 30-38C 37 (<15C reduces growth and survival rates significantly)

Number of consecutive ‘hot’ months overlapping with the rainy season

1-4 >1 month

Salinity for growth purposes (total salts, %). 0-45 Values between 5-25% considered to be optimal

Salinity for expression of toxigenity (total salts, %) (Häse and Barquera, 2001).

0.05-2.5 Values between 2-2.5% considered to be optimal

pH 8-8.6 8.2 (< 4.6 with low temperatures reduce growth and survival rates significantly)

Fe+ (soluble and/or insoluble form) Must be present (moderate amounts)

Low<0.1Moderate=0.1 to 0.5High>0.5

Presence of phytoplankton and algae Similar growth & survival factors. Photosynthesis also increases pH.

Presence of zooplankton The simple presence of crustacean copepods enhances the survival of V. cholerae

Dissolved Oxygen daily cycles for every month of the year (mg/l)

Daily fluctuations provide a preliminary indication of algal blooms

Oxidation-Reduction Potential daily cycles for every month of the year

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MCE @ Shepshed100m < Shepshed <1000m

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 resultsThe 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 modellingExpert systemsAI integration (fuzzy logic)

Established a framework and working model

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Wind Farm Siting

Dennis Scanlin (Department of Technology)

Xingong LiChris Larson

(Department of Geography & Planning)Appalachian State University

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Spatial Analytical Hierarchy Process

Wind farm sitingFind the best wind farm sites based on siting factors

AlternativesLocation—infinite 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 roadsDistance to primary roadsDistance to secondary roadsDistance to rural roads

Accessibility to transmission lines

Distance to 100K linesDistance to 250K linesDistance to above250K lines

Wind power (or wind speed)Visibility

Viewshed size# of people in viewshed

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Siting Steps (MCE)

Factor generationDistance calculationVisibility calculation

Factor standardization (0 – 100)Each factor is a map layer

Factor weights determination by AHPFinal score

Weighted combination of factors

Exclusion areas

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AHP

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Factor Layers

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(Turbine: 50m; Observer: 1.5m; Visual distance: 20mi)

Wind Turbine visibility--Viewshed

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Wind Turbine Viewshed Size

Red—505km2

Greed--805km2

Blue--365km2

Software tool developed to calculate viewshed size for each cell

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Visibility Factor—Viewshed Size

Computational expensiveAbout 700,000 cellsEach cell requires 10 secondsAbout 76 days

Parallel computing12 computersEach computer runs two counties

• About 55000 cells

6 days

Succeed with 3000 cells but failed with 55,000 cells

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2000 census block data

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

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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

Methodologyconstruct ranked suitability maps for each objective using MCE decide on relative objective weights and area tolerancesevaluate conflict demands on limited land via iterative process

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MOLA decision space

Non-conflicting choices

Non-co

nflictin

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choice

s

Unsuitable choices

Conflicting choices

Objective 1

Objective 2

0

0 255

255

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Roadmap


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Carpet and agriculture in KathmanduMOLA, 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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Step 2 Suitability for each objective:

Agriculture

Carpet industry

Best 6000 ha for agriculture

Best 1500 ha for carpet industry

Conflict area

Step 3 MOLA

Compromise solution

It can be noted that industry is located particularly close to where roads and rivers coincide. This is consistent with the fact that proximity to water and power respectively had the highest weighting for agricultural development and industrial location, respectively, since power lines were assumed to be along major roads.

Carpet and agriculture in Kathmandu

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OverviewIn 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 selectionland suitability modelling

multi-criteria evaluation

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