Agricultural Feasibility Analysis in China: A GIS-based
Spatial Fuzzy Multi-Criteria Decision Making Approach
Presenter: Fei Carnes
Date: July 17, 2013
Email: fmeng@cga.harvard.edu
Glossary
1. Raster
A raster consists of a matrix of cells (or pixels) organized into rows and columns (or a grid)
where each cell contains a value representing information, such as temperature. Rasters are
digital aerial photographs, imagery from satellites, digital pictures, or even scanned maps.
cell
• The entire area is divided into a uniform matrix
of cells which are organized into a regular grid.
• All space is represented by cells, even where
there is nothing of interest
• Rows and columns are used to designate their
location.
• All cells must have a value. The number inside a
cell represents some value for that cell location.
The cell value may be an ID for a feature or it
may be an attribute value.
• There is only one value for each cell.
• Cells are independent data units. The computer
does not know if they are connected or not, but
knows their relative position.
• Each cell has its size and area.
2. Raster vs. Vector
• Raster allows to illustrate gradual changes
and variation in attributes from one place to
another.
• Raster has a simple data structure—A
matrix of cells with values representing a
coordinate and sometimes linked to an
attribute table.
• Raster is better in advanced spatial and
statistical analysis.
• Raster allows to perform fast overlays with
complex datasets
3. Spatial Modeling (Raster modeling)
• Suitablity Analysis
• Hydrologic Modeling
• Distance Modeling
... ...
3. Spatial Modeling
• Suitablity Analysis ( feasiblity \ vulnerability \ sensitivity analysis)
Calculate optimal site locations by identifying possible influential factors. The optimal
suitability map may provide new insight into the ideal areas where a new site should be
located.
To solve ...
Where are the optimum locations for a new school, landfill?
• Hydrologic Modeling
• Distance Modeling
... ...
3. Spatial Modeling
• Suitablity Analysis
• Hydrologic Modeling
Provide methods for describing the hydrologic characteristics of a surface. Using an
elevation raster data set as input, it is possible to model where water will flow, create
watersheds and stream networks, and derive other hydrologic characteristics.
To solve ...
Where will the water flow to?
• Distance Modeling
... ...
3. Spatial Modeling
• Suitablity Analysis
• Hydrologic Modeling
• Distance Modeling
Determine the least expensive method for a new road, flight pattern, shipping route, or
any factor that is affected by time and cost.
To solve ...
... ...
Where will be the areas which has the nearest distance from
a emergency helicopter?
4. Fuzzy
A method to standardized factors based on a series of specific mathematical functions. It
reclassifies or transforms the input data to standardized scale ([0,1], [0,10] ,[0, 255],
etc.).
How to standarize?
• Different approaches are used with continuous (quantitative) and categorical
(qualitative) data
• Different functions available (linear, sigmoidal, J-shaped, user-defined)
5. Multi-Criteria Decision Making (MCDM)
• It considers multiple criteria in decision making environment.
• It provides a framework to represent the decision groups into a single model.
GIS-based MCDM integrates the MCDM approach and GIS techniques to
solve spatial issues. It has been received considerable attentions among
planners since 1990s.
This method has been shown in studies related to site determination for a
nuclear waste facility, forest conservation.
Objective
1. The main aim of this project is to solve data confidentiality issue.
2. Develop multi-criteria decision making technique using fuzzy
approach for agricultural feasibility analysis.
3. Help people understand raster GIS analysis (spatial modeling).
Data & Software
Data：
Weather
Annual Precipitation
Accumulated Temperature >10 °C
Source:
Yu Deng, China Academy of Science
Sunshine Hours
Hydrology
Water Resources
Topography Elevation
Soil
Soil PH
Soil Depth
Soil Drainage
Software:
Source: CGA
IDRISI is a GIS and image processing software,
developed by Clark Labs, Clark University.
In 1993, IDRISI introduced the first instance of MultiCriteria and Multi-Objective decision making tools in GIS.
Eighteen years later, IDRISI is still the industry leader,
responsible for:
• The first implementation of the Ordered-Weighted
Average for multi-criteria evaluation that allows one to
balance the relative amount of tradeoff between criteria with
decision risk in balancing discordant information.
• The first implementation of the MOLA heuristic for multiobjective land allocation.
• The first GIS software implementation of Saatys Analytical
Hierarchy Process (AHP).
ArcGIS is a platform for designing
and managing solutions through
the application of geographic
knowledge.
Methodology
1. Data Determination and Processing
2. Criteria Standardization (Fuzzy)
3. Weight Determination
4. Weighted Linear Combination (weighted overlay)
Methodology
1. Data Processing
1) Denoise and reclassify imageries
2) Data transformation. e.g. river (shapefile)  distance to river (raster); elevation  slope(degree)
3) Make sure all the data have the similar extents , and the same coordinate system.
……
Annual
Precipitation
Accumulated
Temperature >10 °C
Elevation
Sunshine Hour
Slope
Soil PH
Distance to River
Soil Depth
Soil Drainage
Methodology
2. Fuzzy
Fuzzy evaluates the possibility that each pixel belongs to a fuzzy set by evaluating any of a series of
fuzzy set membership functions. --- Idrisi Selva Help Document
“0” is assigned to those locations that are definitely not a member of the specified set, “1” is
assigned to those values that are definitely a member of the specified set. All the in-between values
receive some membership values based on the function.
Fuzzy membership
function
Annual Precipitation （ml）
Fuzzy Annual Precipitation [0,1]
Methodology
2.1 Fuzzy (for continues\ quantitative data)
In Idrisi: “ FUZZY” module provides 4 fuzzy membership function types
* Sigmoidal
* J-Shaped
* Linear
* User-defined
(“ S-Shape”)
Monotonically
increasing
Monotonically
decreasing
Symmetric
.
Control points
Control Points:
a = membership rises above 0; b = membership becomes 1; c = membership falls below 1; d = membership becomes 0
Methodology
2.1 Fuzzy (continues data)
Annual
Precipitation
0
1500ml
Sigmoidal
increasing
Fuzzy
Precipitation
Accumulated
Temperature>10°C
-117
3200
4800
9600
Sigmoidal
Symmetric
Fuzzy
Temperature
Elevation
0
2700 m
Linear
Fuzzy
Elevation
Slope
0
7
Distance
to River
0
max
Sigmoidal
decreasing
Linear
Fuzzy
Slope
Fuzzy
Distance to River
Sunshine Hour
0
max
Linear
Fuzzy
Sunshine hour
Methodology
2.2 Fuzzy (for categorical \ qualitiative data)
Reclassify and assign new values to each category.
For example, land use types.
1
0.8
0.6
0.2
0
Deciduous forest
Coniferous forest
Cropland
Methodology
2. 2 Fuzzy (categorical data)
New Values
Old Values
[5.8, 6.9)
Soil Drainage
Soil Depth
Soil PH
1
New Values
Old Values
Very deep (150-300cm)
1
Deep (100-150cm)
0.8
[4.5, 5.5) or [7.2,8.5)
0.6
Moderately deep (50-100cm)
0.6
<4.5 or >8.5
0.2
Shallow (10-50cm)
0.4
Very shallow (<10cm)
0.1
Other
0
Fuzzy
Soil PH
Fuzzy
Soil Depth
Well
1
0.9
0.8
0.6
…
0.8
New Values
…
[5.5, 5.8) or [6.9,7.2)
Old Values
Low
0
Fuzzy
Soil Drainage
Methodology
2. Fuzzy
Fuzzy
Precipitation
Fuzzy
Temperature
Fuzzy
Elevation
Feasibility Map
Fuzzy
Slope
Fuzzy
Soil PH
Fuzzy
Distance to River
Fuzzy
Soil Depth
Fuzzy
Sunshine hour
Fuzzy
Soil Drainage
Methodology
3. Weight Determine
--- How important is each factor?
--- We can give different weights to different factors, and all the weights must add up to 1
Determine the weight intuitively BUT it requires looking at all criteria together, this will
not allow for negotiation or compromise looking at criteria two at a time.
 Analytic Hierarchy Process (AHP)
• It lets you compare criteria two at a time.
• The user specifies the relative importance of one criteria compared to another and does
this for all possible combinations of criteria.
• The procedure will then tell you how consistent are all of your comparisons and it will
develop weights for you for each criteria.
Methodology
3. Weight Determine
 Analytic Hierarchy Process (AHP)
Steps: 1. Estimate the pertinent data
2. Create pairwise comparison decision matrix
3. Calculate the weights and check consistency（CR<0.1)
Table1. The fundamental scale
Intensity of
Definition
Explanation
1
Equal importance
Two activities contribute equally to the objective
3
Moderate importance
Experience and judgments slightly favor one activity over another
5
Strong importance
Experience and judgment strongly favor one activity over another
7
Very strong or demonstrated importance
9
Extreme importance
2，4，6，8
Intermediate value between the two adjacent judgments
Importance
An activity is favored very strongly over another and dominance is
demonstrated in practice
The evidence favoring one activity over another is of the highest
possible order of affirmation
When compromise is needed
Methodology
3. Weight Determine
* By hand
* Idrisi --- “Weight” module
* Klaus D. Goepel, Singapore
http://bpmsg.com/
*
……
Methodology
3. Weight Determine
* Klaus D. Goepel, Singapore http://bpmsg.com/
Ratio
1 Weather
0.46
2 Hydrology
3 Topography
0.07
0.32
4 Soil
Ratio
1.1 accumulated temperature
0.56
1.2 sunshine
0.09
1.3 annual precipitation
0.35
2.1 distance to river
1
3.1 elevation
0.25
3.2 slope
0.75
Rank
1
4
2
Texture
0.15
4. 1 PH
0.12
4.2 Depth
0.23
4.3 Drainage
0.65
3
Methodology
4. Weighted Overlay
apply weights to several inputs and combine them into a single output.
𝑛
𝑎𝑖 ∗ 𝑏𝑖
S =
0
ai: pixcel value of factor i； bi: weight of pixel i；
n: numbers of factors
2.2
2.2
3.3
3
3
2
2.2
1.1
1.1
1
3
1
1.1
2.2
2.2
2
1
1
Factor 1
( Weight = 0.75)
=
Factor 2
( Weight = 0.25)
 Output (top left cell = 2.4) = 2.2*0.75 + 3* 0.25
2.4
2.4
3.0
1.9
1.6
1.1
1.3
2.4
1.9
Output
Methodology
4. Weighted Overlay
Weather
Hydrology
……
*0.46
*0.07
feasibility map
*Wn
Overview
Criteria layer
……
Standardize
criteria
……
*W’1
*W’n
Suitability ratings
from different
hierarchy
……
*W1
Final feasibility map
*W2
*Wn
Result
Summary
• There are a variety of possible answers to one suitability problem.
• Different answers for the same problem result from:
– Considering criteria to be a factor or constraint
– How the factor is standardized (what function, what thresholds)
– How each factor is weighted
Limitation
1. Different fuzzy functions apply to different crop production areas.
2. Not considering seasonal influence.
3. Lack of data, such as soil texture.
Thank You !
Questions and Comments?