Spatial Analysis :
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The main method used in the spatial analysis portion of this assignment was a multi-criteria evalultion. The Decision Support Wizard in Idrisi was used to facilitate this. The wizard is essentially a GUI that brings together several different Idrisi functions, such as fuzzy and mce, ultimately providing the user with a quick and efficient tool for running a multi-criteria analysis.
The first step in the MCE was to declare the factors and constraints. A constraint is a boolean layer to which all results are bound. In this case, our constraint was the layer consisting of green and open and undeveloped space. A factor is a criterion that alters the attractiveness of different areas on the constraint layer. All factors in this analysis were developed using the fuzzy tool which takes an input dataset, in this case a distance layer, and reclassifies it based on a membership function (sigmoidal,, J-shaped or linear). The end result is a raster layer of byte data with the most attractive areas assigned a value of 255 and the least attractive assigned a value of 0. The following table describes the inputs and membership operations used for each of our fuzzy classifications:
| Factor | Min | Max | Membership Shape | Membership Func. | lower bound | upper bound |
| railwaydist | 0 | 37726.6 | Decreasing | Linear | 0.00 | 2000.00 |
| commercialdist | 0 | 35687.2 | Decreasing | Sigmoidal | 0.00 | 1500.00 |
| roaddist | 0 | 32942.8 | Increasing | Sigmoidal | 0.00 | 1500.00 |
| slope | 0 | 589.69 | Decreasing | Sigmoidal | 0.00 | 15.00 |
**Note that for each of the control points (in meters, except for slope) I assumed that mobility was limited to walking/cycling
This table shows how we defined the fuzzy classification for each of our factors. The railwaydist factor was assigned a decreasing linear function. This means that as distance from the tracks increases, suitability decreases at a linear rate. For this factor, areas beyond 2km were deemed unsuitable. The commercialdist factor was rescaled using a decreasing sigmoidal function. This function rescales the data in such a way that areas closer to commercial land use were given a higher suitability and the suitability of those further away decreases in a non-linear rate. Areas within 1.5km of commercial land use were most desirable in this model. The next factor was roaddist. An increasing sigmoidal function was assigned to this factor given the fact that homeless people like to use roads as transportation whilst maintaining seclusion when not on foot. It was assumed that homeless people preferred to be with 1.5km of a major road. The last factor taken into account was slope. It was assigned a decreasing sigmoidal membership function isolating the flattest areas as most suitable. The range of desirable slope in this model was limited to 15%.
Once all of these fuzzy relationships were defined, the following images were produced in which black is the least suitable and pink is the most suitable:
Railfuzz:
Commercialfuzz:
Roadfuzz:
Slopefuzz:
The last step was assigning weights to our factors. This was an area where I wish I had a little bit more justification on which to base my assumptions. However, based on conversations with local police members as well as the literature sources I am confident in my assumptions. The following table describes the weights given to each factor:
| Factor Name | Factor Weight |
| Railwayfuzz | .25 |
| Commercialfuzz | .40 |
| Roadfuzz | .20 |
| Slopefuzz | .15 |
The reasoning for these factors was based primarily on the needs of the homeless people. Mobility and Nourishment were the two most important factors that I considered. I assigned a weight of 25% to the railwayfuzz layer as this is assumed to be the number one source of transport over long distances for homeless people. The layer roadfuzz was given a weight of 20% as this was deemed as important as railwayfuzz, however roads are more prevalent than rail lines thus access to roads is most likely higher already. In the SPARC BC (2008) homeless count they identified commercial establishments such as convenience stores and fast food restaurants as primary sources of nourishment for many homeless people. These establishments dispose of old or unwanted food and the homeless are seen to take advantage of this. For these reasons I assigned a weight of 40% to the commercialfuzz factor. Lastly, I tried to incorporate a topographical effect into the study. In doing this we can limit the areas of refuge to relatively flat regions which is a fairly straightforward assumption. Therefore, the slopefuzz layer was assigned a weight of 15% to take this factor into account.
With the fuzzy layers produced and the factors weighted, the last step was to run the mce. This tool simply performs a mathematical overlay of each of the fuzzy layers taking the weighting factors into account.