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Multi-criteria evaluation

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

### Wind Farm Siting

Roadmap

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

Introduction

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

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

- Ian McHarg (1969) Design with Nature

GIS approaches

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

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).

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

Question…

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

Roadmap

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

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 ]

- Decision frame: the set of all possible alternatives

Roadmap

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

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

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

Roadmap

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

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)

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

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.

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.

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.

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)

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!

MCE – pros and cons- 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

Roadmap

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

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

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

255

Output

Output

Poor: 0

0

low

high

low

high

Input

Input

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)

- Range (convert all

- Need to compare apples to apples, not apples to oranges to walnuts. For example:

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)

Factor normalization: example

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.

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.

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.

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: 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.

Analytical hierarchy process

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

Refer to description of ArcGIS extension ext_ahp.

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 > 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.

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

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.

Map 2

Map 3

Map 4

Standardise

Evaluation matrix

User weights

MCE routine

Output

Example: weighted linear summationExample

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

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)

Roadmap

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

Gavin Fleming, Marna van der Merwe, Graeme McFerren, Kerry Murphy

CSIR, South Africa

Vibrio cholerae Murphy

- 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

Geosphere Murphy

Biosphere (plants&animals)

Atmosphere

(air)

V. cholerae

Lithosphere

(soil)

Hydrosphere

(water)

The complex nature of choleraTransmitted to humans: Murphy

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

Transmission to humans

Zooplankton:

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

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

Algae:

- Promote survival of V. cholerae
- Provide indirectly favourable conditions for growth and maybe expression of virulence
- Provide food for zooplankton

Phytoplankton & Aquatic plants

Temperature, pH Fe+, salinity sunlight

Abiotic conditions:

- Favour growth of V. cholerae and/or
- expression of virulence

Inputs Murphy

Literature survey and expert workshops to:

- Determine possible contributing factors to a cholera outbreak

Simulation model to:

- Provide some of the input into the expert system
- Simulate the relative importance of different variables

Expert system to:

- Capture the knowledge and data
- Establish the high-level structure and flow of the integrated model

GIS and fuzzy logic to implement model thus defined

Outputs

- Possible cholera outbreak location and date

GIS and Fuzzy Logic MurphyArcInfo: raster, AML

Variable Murphy

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<0.1

Moderate=0.1 to 0.5

High>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

Model variablesMCE @ Shepshed Murphy

100m < 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

Comparison of results Murphy

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

Conclusions Murphy

- 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

Dennis Scanlin Murphy

(Department of Technology)

Xingong Li

Chris Larson

(Department of Geography & Planning)

Appalachian State University

Spatial Analytical Hierarchy Process Murphy

- Wind farm siting
- Find the best wind farm sites based on siting factors

- Alternatives
- Location—infinite
- Divide the space into squares/cells (200m * 200m)

- Evaluate each cell based on the siting factors

Preliminary Siting Factors Murphy

- 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

Siting Steps (MCE) Murphy

- 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

AHP Murphy

Factor Layers Murphy

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

Wind Turbine visibility--ViewshedWind Turbine Viewshed Size Murphy

- Red—505km2
- Greed--805km2
- Blue--365km2
- Software tool developed to calculate viewshed size for each cell

Visibility Factor—Viewshed Size Murphy

- 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

2000 census block data Murphy

Visibility Factor--# of People in ViewshedFinal Score Layer Murphy

Candidate Sites Murphy

Constraints (binary) Murphy

Sites Murphy

Roadmap Murphy

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

Multi-objective land allocation Murphy

- 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

- procedure for solving multi-objective land allocation problems for cases with conflicting objectives

Principles of MOLA Murphy

- 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

MOLA decision space Murphy

255

Non-conflicting choices

Conflicting choices

Objective 2

Non-conflicting choices

Unsuitable choices

0

0

255

Objective 1

Roadmap Murphy

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

Carpet and agriculture in Kathmandu Murphy

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

Carpet and agriculture in Kathmandu Murphy

- 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.

Overview Murphy

- 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.

Conclusions Murphy

- 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

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