Click here to see the cartographic model of this project .

The first step in analyzing this problem it to calculate the distance from each pixel to each of the 9 criteria for evaluation.  To calculate this, the DISTANCE function was run on each layer.  Here is a sample of the results:

Distance from Bike routes:                                                                                                                            Distance from a firehall:
       


Distance from Shopping area:


For the first kind of MCE, I decided to find all of the areas that contained at least 5 of the 9 criteria.  To do this, I converted each distance coverage to a boolean image, based on my (somewhat arbitrary) conditions, and then added the images together using the OVERLAY function.  The conditions that I used are as follows:

•  The site must be between 100 and 1000 meters from a main road
•  The site must be less than 20m from a side road
•  The site must be within 100m of a bike route
•  The site must be between 100 and 500 meters from the Skytrain route
•  The site must 50 and 700 meters from a park
•  The site must be within 200 meters of a shopping district
•  The site must be between 50 and 1500m from a fire department
•  The site must be between 50 and 500 meters from a bus route
•  The site must be between 50 and 500m from the water

Here are some results of applying these conditions to the distance coverages.  They were obtained by using RECLASS to assign the desired values 1, and the undesirable values 0.

Suitable distance from water:                                                                                            Suitable distance from a bus route:
           

Suitable distance from a side road:



I then used the following macro to perfrom the OVERLAY addition to add the layers together:

overlay x 1*mainroadbool*sideroadbool*temp1
overlay x 1*temp1*bikebool*temp2
overlay x 1*temp2*skytrnbool*temp3
overlay x 1*temp3*parkbool*temp4
overlay x 1*temp4*shopbool*temp5
overlay x 1*temp5*firebool*temp6
overlay x 1*temp6*busbool*temp7
overlay x 1*temp7*waterbool*overlay-final

The result of the operation is below.  I then did another RECLASS operation to reassign a new value of 1 to all squares where the boolean add resulted in a value of 5 or more.

Original overlay:




Reclassed Overlay to show most suitable areas:



For the next type of MCE I performed, I needed to reclassify the distance images using the FUZZY command.  The specific functions that I used are outlined below.  The main difference between J shaped functions and Sigmoidal functions is that Sigmoidal functions reach 0 at one of the control points, while J-shaped functions are asymtotic to 0 (they never actually reach 0), and the control points represent the point where suitability is 0.5 on a 0 - 1 scale.

• Mainfuzz - decreasing Sigmoidal - control points (c, d) at 100m, 1000m
• Sidefuzz - decreasing J-shaped - control points at 20m, 40m
• Bikefuzz - decreasing J-shaped - control points at 100m, 300m
• Skytrnfuzz - Symmetric Sigmoidal - control points at 0m ,250m, 250m, 500m
• parkfuzz - Symmetric J-shaped - control points at 35m, 50m, 500m, 550m
• shopfuzz - J-Shaped - control points at 200m, 300m
• firefuzz - decreasing Sigmoidal - control points at 50m, 1500m
• busfuzz - J-shaped - control points at 35m, 50m, 300m, 350m
• waterfuzz - Symmetric Sigmoidal - control points at 35m, 50m, 500m, 1000m

All the functions were rescaled on the byte scale, to give a value of 0 - 255.  Here are some selected results:

FUZZY applied to the Main road distance coverage:                                        FUZZY applied to the park distance coverage:
       

FUZZY applied to the Skytrain distance coverage:



After all of the FUZZY images were created, used the WEIGHT function to determine the wieghts on the various criteria.  I generated 2 different weight files, based on 2 different types of theoretical people, who are looking to move into the city.  The first person is an outdoorsy-type, and had preferences as follows:

• Must live near a bike route, since she commutes by bike to work
• Likes to walk in the park, so distance to that is also important
• Doesn't own a car, so close to transit is also important
• Would prefer to live away from a main road and shopping areas, to cut down on noise/crowds/pollution
• Wants to be a reasonable distance from a firehall, for safety's sake

Based on these preferences, the weights turned out like this:

The eigenvector of weights is :
mainfuzz : 0.0471 
sidefuzz : 0.0695 
bikefuzz : 0.2393 
skytrnfuzz : 0.0965 
parkfuzz : 0.1624 
shopfuzz : 0.0436 
firefuzz : 0.0962 
busfuzz : 0.1505 
waterfuzz : 0.0949 

Consistency ratio =   0.09
Consistency is acceptable.

Running MCE with these weights produces the following output file, which I think is neat-looking:


For the second evaluation, I adjusted the weights to more suit the following hypothetical person:

• Is a shopaholic, so proximity to a main shopping center is paramount
• Needs to live near a main route to get to work/mall
• Would like to be close to a firehall, for safety's sake, just like the other person
• Doesn't use transit or ride a bike, so those things are not important

Based on these preferences, the following weights resulted:

The eigenvector of weights is :
mainfuzz : 0.1886 
sidefuzz : 0.1087 
bikefuzz : 0.0442 
skytrnfuzz : 0.0500 
parkfuzz : 0.0630 
shopfuzz : 0.2278 
firefuzz : 0.1762 
busfuzz : 0.0620 
waterfuzz : 0.0795 

Consistency ratio =   0.05
Consistency is acceptable.

Running MCE with these weights produced the equally compelling image below:


My final step was to RECLASS both of these images to identify spots where the suitibility was above a certain value.  I choose 175 out of 256 as this value and reclassified the images as such.  Here are the results:

RECLASS of the Outdoor person's map:                                                                                                    RECLASS of the Indoor person's map:
                                           

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