### Tutorial : create an aptitude map with ArcMap, with and without fuzzy criteria (2)

Let’s go back literally to the Spatial Analyst tutorial:
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Creation of an aptitude map

The creation an aptitude map allows you to get an aptitude value for each location on the map.
Once you have created the necessary layers ( in this example , the layers are Slope , Distance to Recreational Facilities , Distance to Schools and Land Use) to your analysis, how do these  created layers combine to create a classified map of the potential surfaces to locate school   ? You must compare the values of classes among layers. To accomplish this task, a method involves assigning numerical values to the classes included in each layer of the map or to re classify them.

Each layer of the map is classified according its aptitude degree as location for the new school.. For example, you can assign a value to each class of each layer, according to a scale from 1 to 10, 10 being the best ranking.
This scale is called an “aptitude scale”. Use the value NoData to rule out areas that should not be taken into consideration. If all measures are affected by the same numerical scale, grants the same importance in the determination of the most adequate locations. Initially, the model is developed this way. Afterwards, when you test other scenarios, weighting factors will be applied to the layers to increase the exploration of data and their relationships.

Creation of aptitude scales

As shown in this example, many scales are synthetic. Usually a ranking, from the most appropriate to the least appropriate is used. This ranking is based on something measurable, such as distance to schools, but in fact, it is a subjective measure that determines the aptitude degree of a certain distance from a school to place another school.
There are natural scales that are commonly associated with certain objectives. The cost is a good example, but must be defined in detail . In a study on the feasibility of a building, a weak cost target would be   measured on a dollar scale. Be sure to define an adequate scale. For an element well known as the dollar other variables must be taken into account, for example whether it is American, Australian dollars or an exchange rate between currencies.
Many scales are not linear relationships nevertheless they are often presented as if they were to save time and money or because all the options have not been considered. For example, if you assign a scale to a travel distance, a displacement of 1.5 or 10 km would not be classified as an aptitude of 10, 5 and 1 if the movement was done on foot. Some people will evaluate that a 5 kilometres walk is only twice more tiring than a 1 kilometre walk while others will evaluate it as tenfold.
When you are developing an aptitude scale, ask the opinion of well-informed people to identify both extremes of a scenario and as many intermediate points as possible. These people must have a good knowledge of the objective under consideration. For example, it is more interesting to ask users their opinion about their preferences about the travel time from their homes to their work, than asking an agent the time brackets when traffic is the worst.

The problem is very well framed. Let’s see how to answer by using the classical tools.

Ranking of nearby areas to recreational facilities with the Re-classification tool

In order to locate a school near recreational facilities, you must know the distance between them. The Spatial Analyst Euclidean Distance tool creates this type of map by calculating the distance in straight line (Euclidean) between a location and the nearest recreational facility. The result is a raster dataset in which each cell represents the distance to the nearest recreational facilities. To rank the map, use the Reclassification tool. Since it is desirable to locate the school near recreational facilities, assign the value 1 to the distant places from these facilities and the value 10 to closer places. Then rank intermediate distances linearly as shown in the next illustration.

We use the Re-classification tool from the toolbox Spatial Analyst-> Classify.

Steps:

• Open the Re-classification tool
• As layer in the entry indicate DistanceToRecSites
• Accept the default value for the parameter reclassification Field to use as Value field.
• Click

• Set the Method to equal Interval (variable number) and the number of Classes out of 10.
• Click
• Click Reverse news values.

The selection of the option Invert the news values attribute a new, higher value to close distances to the leisure centres, as these areas are more desirable.
Give a name for Raster output parameter: DistRecSitesReclass
Click OK.

The result got is the following:

For the geomaticists that we are, this result appears as quite consistent. We have a study area, concentric distances from our targets and a regular gradient of values as we move away from our targets.

But the question is: does it answer the question?

The green areas, i.e. the most suitable areas according to this criterion, depend on the location of the recreational sites. But not only. They depend on our study area: if we would have selected a larger area, they would be bigger, we would have limited our area, they would be smaller. They also depend on our arbitrary choice of 10 zones. If we would have chosen to make 7, they would be bigger, and if we had selected to make 12 of them would be smaller.

The question asked is to find sites, given that parents want the new school to be near a recreational site. As a parent, I want to find that a recreational site is close or far according to many personal criteria, but most likely not as a function of the total area of the planning project!

Ranking of nearby recreational facilities areas using the Fuzzy Criterion tool

The satisfaction of the criterion Proximity to a recreational site must be asked to the actors. Therefore we will be able to understand what is considered “Close”, a site within walking distance with children, or by car but with a maximum traject between 5 to 10 minutes.

If we translate the latter in distance, we can say that the optimum satisfaction is between 0 and 1,000 m (route distance) and, from 7 km (route 10 ‘ by car) is considered as “Far”.

We use the command Criterion flexible on the layer DistanceRecre

We select the attribute Gridcode and define a maximum satisfaction up to 1000m (a) and a zero satisfaction from 5000 m (b).

We click Calculate, and obtain the following result:

Of course we could do something similar with the Reclassify tool. For the time being, what is important, is the reasoning used.

We have two different results, not just because we are using two different tools, but because we have two different reasoning.

Ranking of remote areas from existing schools, using Spatial Analyst

We have created a raster dataset in which each cell represents the distance to the nearest school (DistToSchools). To rank the map, use the Reclassification tool. Since it is desirable to locate the school away from existing schools, assign the value 1 to the distances close to these schools and the value 10 to the distances far away. Then rank intermediate distances linearly as shown in the next illustration.

As for the distance to the recreational sites,   we use the Re-classify tool of the toolbox Spatial Analyst-> Classify .

Steps :

• Open the Re-classification tool
• As layer in entry indicate DistSchoolsReclass
• Accept the default value for the parameter re-classification Field to use the field Value.
• Click
• Set the Method to Equal Interval ( variable number ) and the number of Classes out of 10.
• Click

You want to locate the school away from existing schools; therefore you assign increasing numbers to ranges of values that represent more remote locations, because these locations are most desirable. Since the default affects New high values (more suitable locations) to Old high values (locations further away from existing schools), you do not need to change the values at this stage.

The result is as follows:

The remarks stated for the remoteness of recreational sites are applicable to the result of this criterion. The distance of existing schools is not a concept related to the size of our study area.

Ranking of remote areas from existing schools   with the tool   Fuzzy Criterion tool

If we apply the same reasoning as previously, a user will consider that the school is “Far” if  it takes more than 10 ‘ by car and   “Close” if can go walking (1000m).

We select the attribute Gridcode and define zero satisfaction   up to 1000m (a) and maximum satisfaction   from 5000 m (b).

We click Calculate, and we get the following result:

This result matches better our notion of “Far”: from a certain distance, one is far, not far-far or far- very distance, etc.

In the next article, we will classify the slopes and the type of land use, before facing the aggregation of all these criteria for obtaining the final result: our aptitude map.

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