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# Y. Meng & J. Malczewski
A GIS-based multicriteria decision making approach for
evaluating accessibility to public parks in Calgary,
Alberta
a b
Yunliang Meng *, Jacek Malczewski
a Central Connecticut State University, USA
b , CanadaWestern University
This paper presents a Geographic Information System based Multicriteria Decision Making
approach for evaluating accessibility to public parks in Calgary, Alberta. The approach
involves the weighted linear combination with the for obtaining entropy weighting method
the criterion (attribute) weights. The paper demonstrates a core-periphery pattern of
accessibility to public parks in Calgary. Furthermore, the pattern has shown tendency to be
more polarized between the year of 2006 and 2011. The results of this research can help the
park planning authorities in identifying the needs for improving the accessibility to public
parks, monitoring the changes of accessibility patterns over time, and locating new public
parks. The results can also help the general public to better understand the spatial relation-
ship between their neighbourhoods and public parks in the city.
Key Words: GIS, MCDM, Accessibility Evaluation, Public parks.
Article Info: Received: February 22, 2015; Revised: May 15, 2015; Accepted: May 22, 2014;
Online: May 30, 2015.
Introduction
Public parks are considered as amenities representing desirable land-use to urban
residents when they are assessed in the context of environmental planning. They
can provide urban residents with the leisure opportunities and aesthetic enjoy-
ment (Kong et al., 2007). T public parkshe accessibility to is directly related to the
life quality of urban residents (Pred, 1977). Moreover, proximity to public parks
has been proved to have positive effects on human health by lowering the rates of
mortality, cardiovascular disease, diabetes, and obesity (Gordon-Larsen et al.,
Human Geographies – Journal of Studies and Research in Human Geography
Vol. 9, No. 1, May 2015 | www.humangeographies.org.ro
ISSN-print: 1843–6587 | ISSN-online: 2067–2284
©2015 Human Geographies; The authors DOI:1 5 91 30.5719/hgeo.201 . .
* Corresponding author
Address: Yunliang Meng, Assistant Professor, Central Connecticut State University, 1615
Stanley Street, New Britain, Connecticut, 06053, USA.
P + | hone: 1-860-832-2789 Email: mengy@ccsu.edu
30 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 31
2006; Berke et al., 2007; Rundle et al., 2008; Rundle et al., 2013). However, these
benets are lack of a clear market price. Consequently, the importance of public
parks is usually underestimated by planning authorities. In reality, some public
parks are gradually encroached upon and transformed into residential or com-
mercial land use over time as a result of urban land shortage. Therefore, the
ongoing evaluation of accessibility to public parks for urban neighbourhoods is
needed to provide empirical evidence to support urban planning.
Geographic Information Systems (GIS) has widely been applied for analyzing
accessibility to public parks (Talen, 1998; Talen and Anselin, 1998; Chakraborty et
al., 1999; Nicholls, 2001; Maantay, 2002; Maroko et al., 2009; Weiss et al., 2011;
Zhu et al., 2011). However, those studies do not typically consider park characteris-
tics (e.g., type, size, and facilities). In addition, the population size of the affected
neighbourhoods is often ignored. Consequently, the inducted conclusions based
on accessibility to public parks are questioned by some researchers (Maroko et al.,
2009). Therefore, the rst objective of this paper is to include the park characteris-
tics – park type and neighbourhood population into the procedure for measuring
accessibility.
There are also other drawbacks of the research on accessibility to public parks.
Although the spatial relationship between the distribution of public parks and
characteristics of affected residents can be determined, it is unclear where exactly
improvements in accessibility should be implemented. Residents living in a
neighbourhood may have high levels of accessibility to some types of parks (e.g.,
mini park), but not others (e.g., community park). In addition, the residents may
have high levels of accessibility in terms of the number of parks surrounding their
neighbourhood, but not in terms of the distance to parks. Therefore, it is necessary
to trade off between the benets and limitations of having access to various types of
parks to determine the accessibility levels to public parks for different neighbour-
hoods. In the trade-off procedure, the neighbourhoods need to be evaluated,
classied and prioritized according to the overall accessibility levels. This type of
problems can be tackled using GIS-based Multicriteria Decision Making (GIS-
MCDM) procedures (Malczewski, 1999; Malczewski and Rinner, 2015). Therefore,
the second objective of this paper is to use GIS-MCDM procedures to evaluate the
overall accessibility to public parks for neighbourhoods in different years, so that
the areas with low levels of accessibility to public parks could be identied and
compared spatially and temporally. The two objectives will be investigated by
conducting a case study in Calgary, Alberta.
The paper is organized as follows. Section 2 provides a brief review of accessibil-
ity and GIS-MCDM. Section 3 presents a case study of accessibility to public parks
in Calgary, Canada. The case study outlines a description of the study area, data
source, variables used in this study, and analysis results, followed by a discussion
and conclusions in Sections 4 and 5.
Accessibility and GIS-MCDM
Accessibility Measures
Accessibility refers to the ease with which any land-use activity can be reached
from a particular location, using a particular transportation system (Dalvi, 1978).
It is a measure quantifying the relative opportunity for interaction with a given
element of urban system, such as a park (Gregory, 1986). The accessibility to
public parks can be operationalized in terms of the following three models: (i) the
covering model (Hodgart, 1978), (ii) the travel cost model (McAllister, 1976;
Morrill and Symons, 1977), and (iii) the minimum distance model (Talen, 1998).
In the covering model, accessibility to a park can be measured according to the
park service area, represented by a circle drawn around a park (Hodgart, 1978).
The circle radius (Euclidean distance) equals to the maximum distance the users
have to travel to get to the park facility. This method assumes that the facility is
equally enjoyed by residents living within its service area, even if its utility is
diminished or vanishing beyond the border of the service area. It should be noted
that different types of public parks, such as mini, neighbourhood, and community
parks, have different sizes of service areas. The size of various types of public parks
and their service areas can be determined according to the public park and open
space classication scheme dened by U.S. National Recreation and Park
Association (Table 1). In this study, the number of public parks located within a
critical distance (road network based distance) surrounding a DA is used to
quantify the accessibility level for residents living in the DA (see Figure 1A. as an
example). The larger number of public parks within the critical distance, the
higher the level of accessibility.
The concept of accessibility can also be operationalized using the travel cost
method (e.g., McAllister, 1976; Morrill and Symons, 1977). This method of
measuring accessibility originates from a normative perspective on location
analysis, in which the most often used objective is to minimize the total travel cost
for customers. In this study, the average distance between each origin (e.g. the
centroid of a DA) and destinations (e.g. public parks within the service area) is
used as a measure of accessibility (see Figure 1B as an example). It should be noted
that the average distance is measured based on the actual road network in Calgary.
Since the goal of improving accessibility is to minimize the travel cost, the shorter
is the average distance, the higher is the level of accessibility.
In addition, the minimum distance between each point of origin (e.g., the
centroid of a DA) and the nearest park facility is used as a measure of accessibility
(see Figure 1C as an example). The rationale behind this approach is that resi-
dents would most often visit the closest park to conduct daily leisure activities. In
this study, the minimum distance is a measure based on the road network. Some
neighbourhoods are always closer than others to any given park facility, so the
smaller the minimum distance, the better.
Table 1. Public Park and Open Space Classification Scheme (Mertes and Hall 1995)
Type of park Location criteria Site criteria Population served
Mini Park Service area usually less
than 0.25 mile or 0.4 km
Usually between 2,500
square feet and 1 acre;
maximum 5 acres
500 to 2,500
Neighbourhood
Park
Service area usually no
more than 0.5 mile or 0.8
km
Minimum of 5 acres, 7
to 10 acres optimal,
maximum 20 acres
2,500 to 10,000
Community Park Usually serves 2 or more
neighbourhoods within 3
mile or 4.83 km
Between 20 and 50
acres
10,000 to 50,000
30 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 31
2006; Berke et al., 2007; Rundle et al., 2008; Rundle et al., 2013). However, these
benets are lack of a clear market price. Consequently, the importance of public
parks is usually underestimated by planning authorities. In reality, some public
parks are gradually encroached upon and transformed into residential or com-
mercial land use over time as a result of urban land shortage. Therefore, the
ongoing evaluation of accessibility to public parks for urban neighbourhoods is
needed to provide empirical evidence to support urban planning.
Geographic Information Systems (GIS) has widely been applied for analyzing
accessibility to public parks (Talen, 1998; Talen and Anselin, 1998; Chakraborty et
al., 1999; Nicholls, 2001; Maantay, 2002; Maroko et al., 2009; Weiss et al., 2011;
Zhu et al., 2011). However, those studies do not typically consider park characteris-
tics (e.g., type, size, and facilities). In addition, the population size of the affected
neighbourhoods is often ignored. Consequently, the inducted conclusions based
on accessibility to public parks are questioned by some researchers (Maroko et al.,
2009). Therefore, the rst objective of this paper is to include the park characteris-
tics – park type and neighbourhood population into the procedure for measuring
accessibility.
There are also other drawbacks of the research on accessibility to public parks.
Although the spatial relationship between the distribution of public parks and
characteristics of affected residents can be determined, it is unclear where exactly
improvements in accessibility should be implemented. Residents living in a
neighbourhood may have high levels of accessibility to some types of parks (e.g.,
mini park), but not others (e.g., community park). In addition, the residents may
have high levels of accessibility in terms of the number of parks surrounding their
neighbourhood, but not in terms of the distance to parks. Therefore, it is necessary
to trade off between the benets and limitations of having access to various types of
parks to determine the accessibility levels to public parks for different neighbour-
hoods. In the trade-off procedure, the neighbourhoods need to be evaluated,
classied and prioritized according to the overall accessibility levels. This type of
problems can be tackled using GIS-based Multicriteria Decision Making (GIS-
MCDM) procedures (Malczewski, 1999; Malczewski and Rinner, 2015). Therefore,
the second objective of this paper is to use GIS-MCDM procedures to evaluate the
overall accessibility to public parks for neighbourhoods in different years, so that
the areas with low levels of accessibility to public parks could be identied and
compared spatially and temporally. The two objectives will be investigated by
conducting a case study in Calgary, Alberta.
The paper is organized as follows. Section 2 provides a brief review of accessibil-
ity and GIS-MCDM. Section 3 presents a case study of accessibility to public parks
in Calgary, Canada. The case study outlines a description of the study area, data
source, variables used in this study, and analysis results, followed by a discussion
and conclusions in Sections 4 and 5.
Accessibility and GIS-MCDM
Accessibility Measures
Accessibility refers to the ease with which any land-use activity can be reached
from a particular location, using a particular transportation system (Dalvi, 1978).
It is a measure quantifying the relative opportunity for interaction with a given
element of urban system, such as a park (Gregory, 1986). The accessibility to
public parks can be operationalized in terms of the following three models: (i) the
covering model (Hodgart, 1978), (ii) the travel cost model (McAllister, 1976;
Morrill and Symons, 1977), and (iii) the minimum distance model (Talen, 1998).
In the covering model, accessibility to a park can be measured according to the
park service area, represented by a circle drawn around a park (Hodgart, 1978).
The circle radius (Euclidean distance) equals to the maximum distance the users
have to travel to get to the park facility. This method assumes that the facility is
equally enjoyed by residents living within its service area, even if its utility is
diminished or vanishing beyond the border of the service area. It should be noted
that different types of public parks, such as mini, neighbourhood, and community
parks, have different sizes of service areas. The size of various types of public parks
and their service areas can be determined according to the public park and open
space classication scheme dened by U.S. National Recreation and Park
Association (Table 1). In this study, the number of public parks located within a
critical distance (road network based distance) surrounding a DA is used to
quantify the accessibility level for residents living in the DA (see Figure 1A. as an
example). The larger number of public parks within the critical distance, the
higher the level of accessibility.
The concept of accessibility can also be operationalized using the travel cost
method (e.g., McAllister, 1976; Morrill and Symons, 1977). This method of
measuring accessibility originates from a normative perspective on location
analysis, in which the most often used objective is to minimize the total travel cost
for customers. In this study, the average distance between each origin (e.g. the
centroid of a DA) and destinations (e.g. public parks within the service area) is
used as a measure of accessibility (see Figure 1B as an example). It should be noted
that the average distance is measured based on the actual road network in Calgary.
Since the goal of improving accessibility is to minimize the travel cost, the shorter
is the average distance, the higher is the level of accessibility.
In addition, the minimum distance between each point of origin (e.g., the
centroid of a DA) and the nearest park facility is used as a measure of accessibility
(see Figure 1C as an example). The rationale behind this approach is that resi-
dents would most often visit the closest park to conduct daily leisure activities. In
this study, the minimum distance is a measure based on the road network. Some
neighbourhoods are always closer than others to any given park facility, so the
smaller the minimum distance, the better.
Table 1. Public Park and Open Space Classification Scheme (Mertes and Hall 1995)
Type of park Location criteria Site criteria Population served
Mini Park Service area usually less
than 0.25 mile or 0.4 km
Usually between 2,500
square feet and 1 acre;
maximum 5 acres
500 to 2,500
Neighbourhood
Park
Service area usually no
more than 0.5 mile or 0.8
km
Minimum of 5 acres, 7
to 10 acres optimal,
maximum 20 acres
2,500 to 10,000
Community Park Usually serves 2 or more
neighbourhoods within 3
mile or 4.83 km
Between 20 and 50
acres
10,000 to 50,000
32 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 33
GIS-MCDM
GIS-MCDM can be dened as a process that transforms and combines geographical
data (criterion maps) and value judgement to obtain overall assessment of the
decision alternatives (Laaribi, 2000; Chakhar and Martel, 2003; Malczewski, 2006;
Malczewski and Rinner, 2015). The rationale behind the integrating GIS and
MCDM is that these two distinct areas of research can benet from each other. GIS
plays an important role in storing, manipulating, analyzing and visualizing spatial
data for decision-making. MCDM provides systematic evaluation procedures and
algorithms for structuring decision problems, and designing, evaluating and
prioritizing alternatives (e.g., Eastman et al., 1995; Jankowski, 1995; Malczewski,
1999; Thill, 1999; Feick and Hall, 2004; Malczewski and Rinner, 2015).
Central to GIS-MCDM is a decision (or aggregation) rule, which can be consid-
ered as a procedure that allows decision makers to select one or more alternatives
from a number of alternatives. The most often used decision rules in GIS-MCDM
have been limited to a few well-known methods, such as Boolean overlay and
weighted linear combination (WLC) (Eastman et al., 1995; Malczewski, 2006;
Malczewski, 2011). When using Boolean overlay, all attributes are rst transformed
into logical statements of suitability (e.g., 1 or 0), and then combined by means of
logical operators such as intersection (Logical AND) and union (Logical OR). In
the process of WLC, continuous attributes are rst standardized to a common
numeric range, and then aggregated through a weighted average function. The
WLC model has often been used together with the Boolean operators (Malczewski,
2006). The outcome of such integration is a continuous map of overall perfor-
mance masked by one or more Boolean constraints. In this research, the WLC
integrated with Boolean operators is applied for evaluating the accessibility to
public parks for neighbourhoods in Calgary, Alberta.
Accessibility to Public Parks in Calgary, Alberta
Study Area
The City of Calgary is located at the foothills of Alberta's Rocky Mountains, at the
junction of the Bow and Elbow Rivers. Its land area is about 726.5 square kilome-
ters. Calgary is the energy capital of Canada and an important transportation hub.
Due to the oil boom, Calgary becomes a rapidly developing and expanding city. It
has experienced major population growth over the last decade or so. According to
the 2011 national census, the Calgary Census Metropolitan Area (CMA) reached a
population of 1,214,839 and its population grew at a rate of 12.6% between 2006
and 2011 (Statistics Canada, 2012a). Calgary grew almost two and half times faster
than the national growth rate of 5.4%, and also had a higher growth rate than
Alberta, 10.6%. In 2014, Calgary's metropolitan population was estimated at
1,360,000, raising its rank to fourth-largest city in Canada and the largest city in
Alberta.
Data
A variety of datasets were utilized in this research (see Table 2 and Figure 2). The
2006 and 2011 census data, aggregated at the dissemination areas (or DA) level (see
Figure 2), were used to analyze the spatial distribution of residents in the City. Both
datasets were obtained from Statistics Canada. In this study, dissemination areas (or
DA), the smallest geographic unit of population measurement used by Statistic
Canada (Statistics Canada, 2012b), were chosen to represent different neighbour-
hoods in Calgary. Although DA boundaries were not explicitly considered neigh-
bourhoods, they have been widely used in extant research as units of analysis that
correspond to actual neighbourhoods (e.g. Edwardh et al., 2011; Hou, 2014).
A road network data of Calgary and park boundaries in the City, created in 2006
and 2011 by DMTI Canada were used in this study (see Figure 2). Between 2006
and 2011, the total area and number of public parks have decreased from 12869 to
12793 acres and 278 to 213, respectively. Over the ve year period, the largest drop
Figure 1. Three GIS-based Techniques for Measuring Accessibility to Public Parks
Table 2. Data Type and Source
Data Type Source
Calgary DA Boundaries Statistics Canada
Calgary Population Census Statistics Canada
Calgary Street Network DMTI Canada
Calgary Park Boundaries DMTI Canada
32 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 33
GIS-MCDM
GIS-MCDM can be dened as a process that transforms and combines geographical
data (criterion maps) and value judgement to obtain overall assessment of the
decision alternatives (Laaribi, 2000; Chakhar and Martel, 2003; Malczewski, 2006;
Malczewski and Rinner, 2015). The rationale behind the integrating GIS and
MCDM is that these two distinct areas of research can benet from each other. GIS
plays an important role in storing, manipulating, analyzing and visualizing spatial
data for decision-making. MCDM provides systematic evaluation procedures and
algorithms for structuring decision problems, and designing, evaluating and
prioritizing alternatives (e.g., Eastman et al., 1995; Jankowski, 1995; Malczewski,
1999; Thill, 1999; Feick and Hall, 2004; Malczewski and Rinner, 2015).
Central to GIS-MCDM is a decision (or aggregation) rule, which can be consid-
ered as a procedure that allows decision makers to select one or more alternatives
from a number of alternatives. The most often used decision rules in GIS-MCDM
have been limited to a few well-known methods, such as Boolean overlay and
weighted linear combination (WLC) (Eastman et al., 1995; Malczewski, 2006;
Malczewski, 2011). When using Boolean overlay, all attributes are rst transformed
into logical statements of suitability (e.g., 1 or 0), and then combined by means of
logical operators such as intersection (Logical AND) and union (Logical OR). In
the process of WLC, continuous attributes are rst standardized to a common
numeric range, and then aggregated through a weighted average function. The
WLC model has often been used together with the Boolean operators (Malczewski,
2006). The outcome of such integration is a continuous map of overall perfor-
mance masked by one or more Boolean constraints. In this research, the WLC
integrated with Boolean operators is applied for evaluating the accessibility to
public parks for neighbourhoods in Calgary, Alberta.
Accessibility to Public Parks in Calgary, Alberta
Study Area
The City of Calgary is located at the foothills of Alberta's Rocky Mountains, at the
junction of the Bow and Elbow Rivers. Its land area is about 726.5 square kilome-
ters. Calgary is the energy capital of Canada and an important transportation hub.
Due to the oil boom, Calgary becomes a rapidly developing and expanding city. It
has experienced major population growth over the last decade or so. According to
the 2011 national census, the Calgary Census Metropolitan Area (CMA) reached a
population of 1,214,839 and its population grew at a rate of 12.6% between 2006
and 2011 (Statistics Canada, 2012a). Calgary grew almost two and half times faster
than the national growth rate of 5.4%, and also had a higher growth rate than
Alberta, 10.6%. In 2014, Calgary's metropolitan population was estimated at
1,360,000, raising its rank to fourth-largest city in Canada and the largest city in
Alberta.
Data
A variety of datasets were utilized in this research (see Table 2 and Figure 2). The
2006 and 2011 census data, aggregated at the dissemination areas (or DA) level (see
Figure 2), were used to analyze the spatial distribution of residents in the City. Both
datasets were obtained from Statistics Canada. In this study, dissemination areas (or
DA), the smallest geographic unit of population measurement used by Statistic
Canada (Statistics Canada, 2012b), were chosen to represent different neighbour-
hoods in Calgary. Although DA boundaries were not explicitly considered neigh-
bourhoods, they have been widely used in extant research as units of analysis that
correspond to actual neighbourhoods (e.g. Edwardh et al., 2011; Hou, 2014).
A road network data of Calgary and park boundaries in the City, created in 2006
and 2011 by DMTI Canada were used in this study (see Figure 2). Between 2006
and 2011, the total area and number of public parks have decreased from 12869 to
12793 acres and 278 to 213, respectively. Over the ve year period, the largest drop
Figure 1. Three GIS-based Techniques for Measuring Accessibility to Public Parks
Table 2. Data Type and Source
Data Type Source
Calgary DA Boundaries Statistics Canada
Calgary Population Census Statistics Canada
Calgary Street Network DMTI Canada
Calgary Park Boundaries DMTI Canada
34 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 35
was recorded in the number of mini parks (about 37% decrease), followed by the
number of neighbourhood parks (about 18% decrease). The number of commu-
nity parks has not changed over the ve years (see Figure 3).
Measuring Accessibility
The three methods for measuring accessibility (see Chapter 2) were applied to
quantify accessibility to each type of parks. The covering model involves specifying
the critical travel distance allowed for each park type (see Table 1). The distance was
then measured outwards from each DA's centroid along the streets using the
“Network Analysis” module of ArcMap (ESRI, 2010a). Specically, the distances of
0.25, 0.5, and 3 miles (0.4, 0.8, 4.83 km) from the centroids of DAs were used to
create the reaching (or covered) areas for residents living in each DA for different
types of parks. The “spatial join” and “summarize” functions provided by ArcMap
(ESRI, 2010b) were then used to identify the number of different types of parks
located within the specied distances. Finally, the measure of accessibility for each
DA was calculated by dividing the total number of parks of a given type by the DA's
population (see Table 3).
The travel cost and minimum distance methods involve measuring the travel
distance between each DA centroid and centroids of a given type of parks (e.g., the
mini, neighbourhood, or community parks). These measurements were performed
with the “Network Analysis” module of ArcMap (ESRI, 2010a). The average
distance was calculated using the sum of the travel distance divided by the total
number of a specic type of parks. The minimum distance was quantied by
adopting the shortest travel distance between a DA and its nearest park. It should be
noted that both the average and minimum distances were weighted by the DA's
population before they were used for calculating accessibility measures (see Table 3)
The GIS-MCDM Procedure
The GIS-MCDM procedures involve two steps: (i) dening the evaluation problem
in terms of hierarchical structure, and (ii) evaluating the overall accessibility score
by means of a decision (evaluation) rule. The hierarchical structure consists of three
levels: goal, attributes, and decision alternatives (or DAs) to be evaluated in terms of
accessibility to public parks (see Figure 4). Nine attributes of the DAs were consid-
ered to measure the levels of accessibility to public parks in Calgary in 2006 and
2011. Each attribute has been weighted using the number of residents living in
DAs. Consequently, eighteen attribute maps (nine maps for each of the two years)
have been generated using the “Spatial Analyst” module of ArcMap (ESRI, 2010b).
The maps have then been converted into 30m resolution raster data layers. The
raster maps have been used as the input dataset for evaluating accessibility.
Figure 2. Geographical Distribution of Parks in Calgary, Alberta
Figure 3. The Number of Different Types of Parks in 2006 and 2011
Table 3. Methods for measuring accessibility to parks in Calgary, Alberta
Measure of
accessibility
Equation
The covering
measure DAth - theof population the
distance specified an park withith - theofnumber total the
j
i
The average
distance measure
distance specified a within park typeth - theofnumber totalthe
parks) all DA toth - thefrom distance totalthe(
DA)th - theof population (the
i
j
j´
The minimum
distance measure DA)th - thefrompark nearest th - the todistance (the
DA)th - theof population the(
ji
j´
Note: DA = Dissemination Area; i = 1, 2, ..,m; j = 1, 2, …, n)
34 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 35
was recorded in the number of mini parks (about 37% decrease), followed by the
number of neighbourhood parks (about 18% decrease). The number of commu-
nity parks has not changed over the ve years (see Figure 3).
Measuring Accessibility
The three methods for measuring accessibility (see Chapter 2) were applied to
quantify accessibility to each type of parks. The covering model involves specifying
the critical travel distance allowed for each park type (see Table 1). The distance was
then measured outwards from each DA's centroid along the streets using the
“Network Analysis” module of ArcMap (ESRI, 2010a). Specically, the distances of
0.25, 0.5, and 3 miles (0.4, 0.8, 4.83 km) from the centroids of DAs were used to
create the reaching (or covered) areas for residents living in each DA for different
types of parks. The “spatial join” and “summarize” functions provided by ArcMap
(ESRI, 2010b) were then used to identify the number of different types of parks
located within the specied distances. Finally, the measure of accessibility for each
DA was calculated by dividing the total number of parks of a given type by the DA's
population (see Table 3).
The travel cost and minimum distance methods involve measuring the travel
distance between each DA centroid and centroids of a given type of parks (e.g., the
mini, neighbourhood, or community parks). These measurements were performed
with the “Network Analysis” module of ArcMap (ESRI, 2010a). The average
distance was calculated using the sum of the travel distance divided by the total
number of a specic type of parks. The minimum distance was quantied by
adopting the shortest travel distance between a DA and its nearest park. It should be
noted that both the average and minimum distances were weighted by the DA's
population before they were used for calculating accessibility measures (see Table 3)
The GIS-MCDM Procedure
The GIS-MCDM procedures involve two steps: (i) dening the evaluation problem
in terms of hierarchical structure, and (ii) evaluating the overall accessibility score
by means of a decision (evaluation) rule. The hierarchical structure consists of three
levels: goal, attributes, and decision alternatives (or DAs) to be evaluated in terms of
accessibility to public parks (see Figure 4). Nine attributes of the DAs were consid-
ered to measure the levels of accessibility to public parks in Calgary in 2006 and
2011. Each attribute has been weighted using the number of residents living in
DAs. Consequently, eighteen attribute maps (nine maps for each of the two years)
have been generated using the “Spatial Analyst” module of ArcMap (ESRI, 2010b).
The maps have then been converted into 30m resolution raster data layers. The
raster maps have been used as the input dataset for evaluating accessibility.
Figure 2. Geographical Distribution of Parks in Calgary, Alberta
Figure 3. The Number of Different Types of Parks in 2006 and 2011
Table 3. Methods for measuring accessibility to parks in Calgary, Alberta
Measure of
accessibility
Equation
The covering
measure DAth - theof population the
distance specified an park withith - theofnumber total the
j
i
The average
distance measure
distance specified a within park typeth - theofnumber totalthe
parks) all DA toth - thefrom distance totalthe(
DA)th - theof population (the
i
j
j´
The minimum
distance measure DA)th - thefrompark nearest th - the todistance (the
DA)th - theof population the(
ji
j´
Note: DA = Dissemination Area; i = 1, 2, ..,m; j = 1, 2, …, n)
36 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 37
The second step of the GIS-MCDM procedure combines the raster maps by
means of WLC. Specically, the overall accessibility score, S of the j-th alternative
j
(DA) is calculated as follows:
where w is the weight associated with the k-th attribute (∑w = 1; k = 1,2,...,h);
k k
p is the normalized attribute value for j-th DA (0< P < 1; ∑ p = 1; j = 1,2, ..,n);
jk jk jk
g is the criterion score of the g-th Boolean constraint which excludes DAs without
population from the analysis (g = 1,2, ..., q). The attribute weights, , are esti-
mated by means of the entropy method (Shannon and Weaver, 1947; Hwang and
Yoon, 1981; Zeleny, 1982). This method requires that the attribute values be
normalized as follows.
where is the attribute value of the k-th attribute for j-th DAs. Given the
jk
normalized attribute values, one can estimate attribute weights based on the
amount of decision information contained in each attribute, , measured by the
jk
entropy value, , as:
k
The degree of diversity of the information contained by each criterion can be
calculated as: d = 1– . Thus, the attribute weight is given by:
k k
Equation (1) has been applied to calculate the overall accessibility to public
parks for each DA in Calgary in 2006 and 2011 (see Figure 5). The WLC values were
reclassied into ve categories based on the “Quantile” classication scheme (see
Figure 6).
Results
The results of this research show that the residents of the central and eastern parts
of Calgary tend to have higher levels of accessibility to public parks than those living
in the peripheral neighbourhoods (see Figures 5 and 6). As expected, the spatial
inequalities are related to the locational pattern of parks in the City (see Figure 2).
However, several areas in the north and south sections of the City had relatively
high levels of accessibility to the public parks in 2006, while they were located
relatively far from the public parks (see Figure 6). This can be related to the fact that
these areas had comparatively small populations in 2006.
A comparison of the accessibility patterns in 2006 and 2011 reveals that the DAs
having high levels of accessibility shifted from the north and south edges of the City
to the center and east sections (Figure 6). The decline in accessibility in the periph-
ery of Calgary over time can partially be attributed to the decreasing size and
number of the public parks. The other factor contributing to the shift in accessibil-
ity to public parks is associated with the changes in the population distribution
between 2006 and 2011. The total number of people living in the neighbourhoods
with at least medium residential density (30 residents per hectare) has decreased by
5.0 %, while the population of the Calgary CMA has increased by 12.6% (Statistics
Canada, 2012a). Most of the population growth occurred in the neighbourhoods
with low residential density along the City edge.
The population in some peripheral areas of Calgary grew more than ten times
as the result of urban expansion. However, these areas are lack of newly-founded
parks. Therefore, the lower levels of accessibility in the peripheral sections of the
City can be attributed to the large increase in populations of these areas. The
higher levels of accessibility in the central and eastern parts of Calgary should be
seen in relative terms. It is not an outcome of an increase in the size and number of
the public parks. It is rather a result of relative decrease in population of the central
and eastern parts of the City as compared the peripheral sections of Calgary.
Discussion
This paper has presented a GIS-MCDM approach for evaluating spatial accessibil-
ity to the public parks in Calgary, Alberta. The approach provides a useful tool for
those involved in the planning of public parks. It offers a novel method of visualiz-
ing and measuring the levels of accessibility to public parks. Specically, the paper
has demonstrated an improved method of measuring distance using the street
network rather than the straight-line distance. This method provides more realistic
representation of the service areas. The proposed GIS-MCDM approach can be
used by park planning authorities to indentify the areas where there are needs for
improving accessibility to public parks as well as to monitor changes in the accessi-
bility over time. The approach can also be used for identifying the best locations for
new public parks, since identifying areas with low accessibility to public parks can
be considered as a stimulus for planning activities (e.g., adding new parks).
The general public has a natural tendency to more readily accept analyses that
Figure 4. Hierarchical structure of the DAs accessibility to the public parks in Calgary
(Note: DA = Dissemination Area)
e
e
x
x
c
k
w
Õ
å
=
=
=
q
g
g
h
k
jkkj cpwS
1
1
)ln(
)ln(
1
n
pp
e
n
jjkjk
k
å=
-=
å=
=h
kk
k
kd
d
w
1
å=
=n
jjk
jk
jk x
x
p
1
36 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 37
The second step of the GIS-MCDM procedure combines the raster maps by
means of WLC. Specically, the overall accessibility score, S of the j-th alternative
j
(DA) is calculated as follows:
where w is the weight associated with the k-th attribute (∑w = 1; k = 1,2,...,h);
k k
p is the normalized attribute value for j-th DA (0< P < 1; ∑ p = 1; j = 1,2, ..,n);
jk jk jk
g is the criterion score of the g-th Boolean constraint which excludes DAs without
population from the analysis (g = 1,2, ..., q). The attribute weights, , are esti-
mated by means of the entropy method (Shannon and Weaver, 1947; Hwang and
Yoon, 1981; Zeleny, 1982). This method requires that the attribute values be
normalized as follows.
where is the attribute value of the k-th attribute for j-th DAs. Given the
jk
normalized attribute values, one can estimate attribute weights based on the
amount of decision information contained in each attribute, , measured by the
jk
entropy value, , as:
k
The degree of diversity of the information contained by each criterion can be
calculated as: d = 1– . Thus, the attribute weight is given by:
k k
Equation (1) has been applied to calculate the overall accessibility to public
parks for each DA in Calgary in 2006 and 2011 (see Figure 5). The WLC values were
reclassied into ve categories based on the “Quantile” classication scheme (see
Figure 6).
Results
The results of this research show that the residents of the central and eastern parts
of Calgary tend to have higher levels of accessibility to public parks than those living
in the peripheral neighbourhoods (see Figures 5 and 6). As expected, the spatial
inequalities are related to the locational pattern of parks in the City (see Figure 2).
However, several areas in the north and south sections of the City had relatively
high levels of accessibility to the public parks in 2006, while they were located
relatively far from the public parks (see Figure 6). This can be related to the fact that
these areas had comparatively small populations in 2006.
A comparison of the accessibility patterns in 2006 and 2011 reveals that the DAs
having high levels of accessibility shifted from the north and south edges of the City
to the center and east sections (Figure 6). The decline in accessibility in the periph-
ery of Calgary over time can partially be attributed to the decreasing size and
number of the public parks. The other factor contributing to the shift in accessibil-
ity to public parks is associated with the changes in the population distribution
between 2006 and 2011. The total number of people living in the neighbourhoods
with at least medium residential density (30 residents per hectare) has decreased by
5.0 %, while the population of the Calgary CMA has increased by 12.6% (Statistics
Canada, 2012a). Most of the population growth occurred in the neighbourhoods
with low residential density along the City edge.
The population in some peripheral areas of Calgary grew more than ten times
as the result of urban expansion. However, these areas are lack of newly-founded
parks. Therefore, the lower levels of accessibility in the peripheral sections of the
City can be attributed to the large increase in populations of these areas. The
higher levels of accessibility in the central and eastern parts of Calgary should be
seen in relative terms. It is not an outcome of an increase in the size and number of
the public parks. It is rather a result of relative decrease in population of the central
and eastern parts of the City as compared the peripheral sections of Calgary.
Discussion
This paper has presented a GIS-MCDM approach for evaluating spatial accessibil-
ity to the public parks in Calgary, Alberta. The approach provides a useful tool for
those involved in the planning of public parks. It offers a novel method of visualiz-
ing and measuring the levels of accessibility to public parks. Specically, the paper
has demonstrated an improved method of measuring distance using the street
network rather than the straight-line distance. This method provides more realistic
representation of the service areas. The proposed GIS-MCDM approach can be
used by park planning authorities to indentify the areas where there are needs for
improving accessibility to public parks as well as to monitor changes in the accessi-
bility over time. The approach can also be used for identifying the best locations for
new public parks, since identifying areas with low accessibility to public parks can
be considered as a stimulus for planning activities (e.g., adding new parks).
The general public has a natural tendency to more readily accept analyses that
Figure 4. Hierarchical structure of the DAs accessibility to the public parks in Calgary
(Note: DA = Dissemination Area)
e
e
x
x
c
k
w
Õ
å
=
=
=
q
g
g
h
k
jkkj cpwS
1
1
)ln(
)ln(
1
n
pp
e
n
jjkjk
k
å=
-=
å=
=h
kk
k
kd
d
w
1
å=
=n
jjk
jk
jk x
x
p
1
38 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 39
are technical, scientic, and/or quantitative, and assume that such studies are less
prone to deliberative biases (Comer and Skraastad-Jurney, 2008). However, the
results of scientic research are usually hard to be understood by the general
public. As with any public presentation, how the park accessibility information is
presented can be as important as the content of the information. This research
demonstrates that the GIS-MCDM procedures provide park planners and admin-
istrators with useful tools to create and disseminate well-designed accessibility
maps to the general public, so that the local residents to can better visualize and
understand the spatial relationship between their neighbourhoods and public
parks in the city.
The neighbourhood population and the size of public parks have often been
ignored by previous research on accessibility to public park facilities. This paper
has demonstrated that these are essential factors in evaluating accessibility to public
parks. It has emphasized the importance of using different measures of accessibility
such as the weighted average distance, the weighted minimum distance, and the
weighted number of public parks to represent different aspects of accessibility in
relation to the spatial patterns of population distribution.
The results of this research have shown a core-periphery pattern of accessibility
to public parks in Calgary. Specically, the neighbourhoods with higher levels of
accessibility to public parks tend to be concentrated in the core and eastern parts of
the City, while the neighbourhoods with lower levels of accessibility tend to be
located in the peripheral areas. The core-periphery pattern polarizes over time.
The high accessibility areas located in the center and east sections of Calgary have
become larger, while the level of accessibility to public parks has tended to decrease
in the peripheral areas. These results provide support for growing concerns about
the lack of infrastructure (e.g., public parks) in the newly developed neighbour-
hoods in the fast growing peripheral areas of Calgary (Couroux et al., 2006).
Finally, it should be noted that park accessibility, by nature, is a multiple dimension
concept, including: physical proximity to neighbourhoods, park safety, and park
attractiveness (Zhang et al. 2011).
The method employed in this case study is only concerned with which areas and
populations have different levels of physical access to public parks and it does not
take into account the safety and attractiveness of public parks, such as levels of
development and physical condition. Inclusion of the park's safety and attractive-
ness information could add a more qualitative dimension to the analysis. In
addition, cultural and perceptual barriers should also be taken into account when
measuring accessibility to parks (Maroko et al., 2009). Furthermore, diverse public
opinions could allow planning authorities to make better decisions. The involve-
ment of interest groups (e.g., local residents) in the planning and decision making
process is an important step toward a sustainable park design approach.
Conclusions
This research provides a GIS-MCDM method for evaluating the overall accessibil-
ity to various types of public parks in Calgary, Canada. The GIS-MCDM proce-
dures are particularly useful for park planning experts to interact with and analyze
all possible alternative scenarios, so that they can better improve accessibility to
Figure 5. Accessibility to the public parks in Calgary, Alberta
Figure 6. Accessibility patterns of DAs: The reclassied results of WLC
38 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 39
are technical, scientic, and/or quantitative, and assume that such studies are less
prone to deliberative biases (Comer and Skraastad-Jurney, 2008). However, the
results of scientic research are usually hard to be understood by the general
public. As with any public presentation, how the park accessibility information is
presented can be as important as the content of the information. This research
demonstrates that the GIS-MCDM procedures provide park planners and admin-
istrators with useful tools to create and disseminate well-designed accessibility
maps to the general public, so that the local residents to can better visualize and
understand the spatial relationship between their neighbourhoods and public
parks in the city.
The neighbourhood population and the size of public parks have often been
ignored by previous research on accessibility to public park facilities. This paper
has demonstrated that these are essential factors in evaluating accessibility to public
parks. It has emphasized the importance of using different measures of accessibility
such as the weighted average distance, the weighted minimum distance, and the
weighted number of public parks to represent different aspects of accessibility in
relation to the spatial patterns of population distribution.
The results of this research have shown a core-periphery pattern of accessibility
to public parks in Calgary. Specically, the neighbourhoods with higher levels of
accessibility to public parks tend to be concentrated in the core and eastern parts of
the City, while the neighbourhoods with lower levels of accessibility tend to be
located in the peripheral areas. The core-periphery pattern polarizes over time.
The high accessibility areas located in the center and east sections of Calgary have
become larger, while the level of accessibility to public parks has tended to decrease
in the peripheral areas. These results provide support for growing concerns about
the lack of infrastructure (e.g., public parks) in the newly developed neighbour-
hoods in the fast growing peripheral areas of Calgary (Couroux et al., 2006).
Finally, it should be noted that park accessibility, by nature, is a multiple dimension
concept, including: physical proximity to neighbourhoods, park safety, and park
attractiveness (Zhang et al. 2011).
The method employed in this case study is only concerned with which areas and
populations have different levels of physical access to public parks and it does not
take into account the safety and attractiveness of public parks, such as levels of
development and physical condition. Inclusion of the park's safety and attractive-
ness information could add a more qualitative dimension to the analysis. In
addition, cultural and perceptual barriers should also be taken into account when
measuring accessibility to parks (Maroko et al., 2009). Furthermore, diverse public
opinions could allow planning authorities to make better decisions. The involve-
ment of interest groups (e.g., local residents) in the planning and decision making
process is an important step toward a sustainable park design approach.
Conclusions
This research provides a GIS-MCDM method for evaluating the overall accessibil-
ity to various types of public parks in Calgary, Canada. The GIS-MCDM proce-
dures are particularly useful for park planning experts to interact with and analyze
all possible alternative scenarios, so that they can better improve accessibility to
Figure 5. Accessibility to the public parks in Calgary, Alberta
Figure 6. Accessibility patterns of DAs: The reclassied results of WLC
40 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 41
public parks and monitor changes in accessibility over time. For the general public,
the well-designed accessibility maps can help them to better understand the spatial
relationship between their neighbourhoods and public parks in the city. With the
GIS-MCDM tool, interpretable quantitative results, and visually appealing maps,
the research procedure described in this paper can lead to less biased, more
transparent, more up-to-date and more informative decision making for park
planning and operations.
References
Berke, E, Koepsell, T & Moudon, A 2007, 'Association of the built environment with physical
activity and obesity in older persons', American Journal of Public Health, vol. 97, no. 3, pp.
486-492.
Chakhar, S & Martel, JM 2003, 'Enhancing geographical information systems capabilities
with multi-criteria evaluation functions', Journal of Geographic Information and Decision
Analysis, vol. 7, no. 2, pp. 47-71.
Chakraborty, J, Schweitzer, L & Forkenbrock, D 1999, 'Using GIS to assess the environmen-
tal justice consequences of transportation system changes', Transactions in GIS, vol. 3, no. 3,
pp. 239-258.
Comer, JC & Skraastad-Jurney, PD 2008, 'Assessing the locational equity of community
parks through the application of geographic information systems', Journal of Park and
Recreation Administration, vol. 26, no. 1, pp. 122-46.
Couroux, D, Keough, N, Miller, B & Row, J 2006, Overcoming barriers to sustainable develop-
ment: Toward s s m a r t g rowt h in Cal ga r y , v i ewed on 21 Fe b r u ary 2015 ,
www.pembina.org/reports/Smart_growth_Calgary.pdf
Dalvi, MQ 1978, 'Behavioural modelling, accessibility, mobility and need: concepts and
measurement', in DA Hensher & PR Stopher (eds), Croom Behavioural travel modelling,
Helm, London.
Eastman, JR, Jin, W, Kyem, P & Toledano, J 1995, 'Raster procedures for multicriteria multi-
objective decisions', , vol. 61, no. 5, pp. 539-Photogrammetric Engineering and Remote Sensing
547.
Edwardh, J, Hildebrandt, T & Lau, R 2011, Incomes and Poverty Report, viewed on 15 May
2015, www.cdhalton.ca/pdf/Burlington-Incomes-and-Poverty-Report.pdf
Esri 2010a, ArcGIS Network Analyst: An ArcGIS for Desktop Extension, viewed on 15 May 2015,
www.esri.com/software/arcgis/extensions/networkanalyst.
ESRI 2010b, ArcGIS Spatial Analyst: An ArcGIS for Desktop Extension, viewed on 15 May 2015
www.esri.com/software/arcgis/extensions/spatialanalyst.
Feick, RD & Hall, BG 2004, A method for examining the spatial dimension of multicriteria
weight sensitivity, International Journal of Geographical Information Science, vol. 18, no. 8, pp.
815-40.
Gregory, D 1986, 'Accessibility', in RJ, Johnston, D, Gregory & DR Stoddart (eds), The
Dictionary of Human Geography, Blackwell, Oxford.
Gordon-Larsen, P, Nelson, M, Page, P & Popkin, B 2006, 'Inequality in the built environ-
ment underlies key health disparities in physical activity and obesity', Pediatrics, vol. 117,
no. 2, pp. 417-424.
Hodgart, RL 1978, 'Optimizing access to public services', , vol. 2, Progress in Human Geography
pp. 17-48.
Hou, F 2014, Life Satisfaction and Income in Canadian Urban Neighbourhoods, Catalogue
no. 11F0019M – no. 357, ISSN 1205-9153.
Hwang, CL & Yoon, KS 1981, Multiple Attribute Decision Making: Methods and Applications,
Springer, New York.
Jankowski, P 1995, 'Integrating geographical information systems and multiple criteria
decision making methods', International Journal of Geographical Information Systems, vol. 9,
no. 3, pp. 251-273.
Kong, F, Yin, H & Nakagoshi, N 2007, 'Using GIS and landscape metrics in the hedonic
price modeling of the amenity value of urban green space: a case study in Jinan City,
China', Landscape and Urban Planning, vol. 79, no. 3-4, pp. 240-252.
Laaribi, A 2000, SIG et Analyse Multicitere, Hermes Sciences Publications, Paris.
Maantay, J 2002, 'Mapping environmental injustices: Pitfalls and potential of geographic
information systems in assessing environmental health and equity', Environmental Health
Perspectives, vol. 110, no. 2, pp. 161-171.
Malczewski, J 1999, GIS and Multicriteria Decision Analysis, John Wiley and Sons, New York.
Malczewski, J 2006, 'GIS-based multicriteria decision analysis: A survey of the literature',
International Journal of Geographical Information Science, vol. 20, no. 7, pp. 249-268.
Malczewski, J 2011, 'Local weighted linear combination', Transactions in GIS, vol. 15, no. 4,
pp. 439-455.
Malczewski, J & Rinner, C 2015, Multicriteria Decision Analysis in Geographic Information
Science, Springer, New York.
Maroko, AR, Maantay, JA, Sohler, N, Grady, K & Arno, P 2009, 'The complexities of
measuring access to parks and physical activity sites in New York City: A Quantitative and
qualitative approach', International Journal of Health Geographics, vol. 8, no. 34, pp. 1-23.
McAllister, DM 1976, 'Equity and efciency in public facility location', , Geographical Analysis
vol. 8, pp. 47-63.
Mertes, JD & Hall, JR 1995, Park, Recreation, Open Space and Greenway Guidelines, National
Recreation and Park Association, Arlington.
Morrill, R & Symons, S 1977, 'Efciency and equity aspects of optimum location',
Geographical Analysis, vol. 9, pp. 215-225.
Nicholls, S 2001, 'Measuring the accessibility and equity of public parks: a case study using
GIS', Managing Leisure, vol. 6, no. 4, pp. 201-219.
Pred, A 1977, City Systems in Advanced Economics, Hutchinson, London.
Rundle, A, Field, S, Park, Y, Freeman, L, Weiss, C & Neckerman, K 2008, 'Personal and
neighborhood socioeconomic status and indices of neighborhood walk-ability predict
body mass index in New York City', Social Science and Medicine, vol. 67, no. 12, pp. 1951-58.
Rundle, A, Quinn, J, Lovasi, G, Bader, MD, Yousefzadeh P, Weiss, C & Neckerman, K 2013,
'Associations between body mass index and park proximity, size, cleanliness, and recre-
ational facilities', The American Journal of Health Promotion, vol. 27, no. 4, pp. 262-269.
Shannon, CE & Weaver, W 1947, The Mathematical Theory of Communication, The University of
Illinois Press, Urbana.
Statistics Canada 2012a, CANSIM, table 051-0056, Statistics Canada, Ottawa.
Statistics Canada 2012b, Census 2011: Geography - Illustrated Glossary, Statistics Canada,
Ottawa.
Talen, E 1998, 'Visualizing fairness: Equity maps for planners', Journal of the American
Planning Association, vol. 64, no. 1, pp. 22-38.
Talen, E & Anselin, L 1998, 'Assessing spatial equity: An evaluation of measures of accessibil-
ity to public playgrounds', Environment and Planning A, vol. 30, no. 4, pp. 595-613.
Thill, JC 1999, Multicriteria decision-making and analysis: A geographic information sciences
approach, Ashgate, New York.
Weiss, CC, Purciel, M, Bader, M, Quinn, JW, Lovasi, G, Neckerman, KM & Rundle, AG
2011, 'Reconsidering access: park facilities and neighborhood disamenities in New York
City', Journal of Urban Health, vol. 88, no. 2, pp. 297-310.
Zeleny, M 1982, Multiple criteria decision making, McGraw-Hill, New York.
Zhang, X, Lu, H & Holt, JB 2011, 'Modeling spatial accessibility to parks: A national study',
International Journal of Health Geographics, vol. 10, no. 31.
40 Y. Meng & J. Malczewski A GIS-based Multicriteria Decision Making Approach 41
public parks and monitor changes in accessibility over time. For the general public,
the well-designed accessibility maps can help them to better understand the spatial
relationship between their neighbourhoods and public parks in the city. With the
GIS-MCDM tool, interpretable quantitative results, and visually appealing maps,
the research procedure described in this paper can lead to less biased, more
transparent, more up-to-date and more informative decision making for park
planning and operations.
References
Berke, E, Koepsell, T & Moudon, A 2007, 'Association of the built environment with physical
activity and obesity in older persons', American Journal of Public Health, vol. 97, no. 3, pp.
486-492.
Chakhar, S & Martel, JM 2003, 'Enhancing geographical information systems capabilities
with multi-criteria evaluation functions', Journal of Geographic Information and Decision
Analysis, vol. 7, no. 2, pp. 47-71.
Chakraborty, J, Schweitzer, L & Forkenbrock, D 1999, 'Using GIS to assess the environmen-
tal justice consequences of transportation system changes', Transactions in GIS, vol. 3, no. 3,
pp. 239-258.
Comer, JC & Skraastad-Jurney, PD 2008, 'Assessing the locational equity of community
parks through the application of geographic information systems', Journal of Park and
Recreation Administration, vol. 26, no. 1, pp. 122-46.
Couroux, D, Keough, N, Miller, B & Row, J 2006, Overcoming barriers to sustainable develop-
ment: Toward s s m a r t g rowt h in Cal ga r y , v i ewed on 21 Fe b r u ary 2015 ,
www.pembina.org/reports/Smart_growth_Calgary.pdf
Dalvi, MQ 1978, 'Behavioural modelling, accessibility, mobility and need: concepts and
measurement', in DA Hensher & PR Stopher (eds), Croom Behavioural travel modelling,
Helm, London.
Eastman, JR, Jin, W, Kyem, P & Toledano, J 1995, 'Raster procedures for multicriteria multi-
objective decisions', , vol. 61, no. 5, pp. 539-Photogrammetric Engineering and Remote Sensing
547.
Edwardh, J, Hildebrandt, T & Lau, R 2011, Incomes and Poverty Report, viewed on 15 May
2015, www.cdhalton.ca/pdf/Burlington-Incomes-and-Poverty-Report.pdf
Esri 2010a, ArcGIS Network Analyst: An ArcGIS for Desktop Extension, viewed on 15 May 2015,
www.esri.com/software/arcgis/extensions/networkanalyst.
ESRI 2010b, ArcGIS Spatial Analyst: An ArcGIS for Desktop Extension, viewed on 15 May 2015
www.esri.com/software/arcgis/extensions/spatialanalyst.
Feick, RD & Hall, BG 2004, A method for examining the spatial dimension of multicriteria
weight sensitivity, International Journal of Geographical Information Science, vol. 18, no. 8, pp.
815-40.
Gregory, D 1986, 'Accessibility', in RJ, Johnston, D, Gregory & DR Stoddart (eds), The
Dictionary of Human Geography, Blackwell, Oxford.
Gordon-Larsen, P, Nelson, M, Page, P & Popkin, B 2006, 'Inequality in the built environ-
ment underlies key health disparities in physical activity and obesity', Pediatrics, vol. 117,
no. 2, pp. 417-424.
Hodgart, RL 1978, 'Optimizing access to public services', , vol. 2, Progress in Human Geography
pp. 17-48.
Hou, F 2014, Life Satisfaction and Income in Canadian Urban Neighbourhoods, Catalogue
no. 11F0019M – no. 357, ISSN 1205-9153.
Hwang, CL & Yoon, KS 1981, Multiple Attribute Decision Making: Methods and Applications,
Springer, New York.
Jankowski, P 1995, 'Integrating geographical information systems and multiple criteria
decision making methods', International Journal of Geographical Information Systems, vol. 9,
no. 3, pp. 251-273.
Kong, F, Yin, H & Nakagoshi, N 2007, 'Using GIS and landscape metrics in the hedonic
price modeling of the amenity value of urban green space: a case study in Jinan City,
China', Landscape and Urban Planning, vol. 79, no. 3-4, pp. 240-252.
Laaribi, A 2000, SIG et Analyse Multicitere, Hermes Sciences Publications, Paris.
Maantay, J 2002, 'Mapping environmental injustices: Pitfalls and potential of geographic
information systems in assessing environmental health and equity', Environmental Health
Perspectives, vol. 110, no. 2, pp. 161-171.
Malczewski, J 1999, GIS and Multicriteria Decision Analysis, John Wiley and Sons, New York.
Malczewski, J 2006, 'GIS-based multicriteria decision analysis: A survey of the literature',
International Journal of Geographical Information Science, vol. 20, no. 7, pp. 249-268.
Malczewski, J 2011, 'Local weighted linear combination', Transactions in GIS, vol. 15, no. 4,
pp. 439-455.
Malczewski, J & Rinner, C 2015, Multicriteria Decision Analysis in Geographic Information
Science, Springer, New York.
Maroko, AR, Maantay, JA, Sohler, N, Grady, K & Arno, P 2009, 'The complexities of
measuring access to parks and physical activity sites in New York City: A Quantitative and
qualitative approach', International Journal of Health Geographics, vol. 8, no. 34, pp. 1-23.
McAllister, DM 1976, 'Equity and efciency in public facility location', , Geographical Analysis
vol. 8, pp. 47-63.
Mertes, JD & Hall, JR 1995, Park, Recreation, Open Space and Greenway Guidelines, National
Recreation and Park Association, Arlington.
Morrill, R & Symons, S 1977, 'Efciency and equity aspects of optimum location',
Geographical Analysis, vol. 9, pp. 215-225.
Nicholls, S 2001, 'Measuring the accessibility and equity of public parks: a case study using
GIS', Managing Leisure, vol. 6, no. 4, pp. 201-219.
Pred, A 1977, City Systems in Advanced Economics, Hutchinson, London.
Rundle, A, Field, S, Park, Y, Freeman, L, Weiss, C & Neckerman, K 2008, 'Personal and
neighborhood socioeconomic status and indices of neighborhood walk-ability predict
body mass index in New York City', Social Science and Medicine, vol. 67, no. 12, pp. 1951-58.
Rundle, A, Quinn, J, Lovasi, G, Bader, MD, Yousefzadeh P, Weiss, C & Neckerman, K 2013,
'Associations between body mass index and park proximity, size, cleanliness, and recre-
ational facilities', The American Journal of Health Promotion, vol. 27, no. 4, pp. 262-269.
Shannon, CE & Weaver, W 1947, The Mathematical Theory of Communication, The University of
Illinois Press, Urbana.
Statistics Canada 2012a, CANSIM, table 051-0056, Statistics Canada, Ottawa.
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