Mathematical Problems in Engineering

Volume 2016, Article ID 3534824, 10 pages

http://dx.doi.org/10.1155/2016/3534824

## A Classification Model to Evaluate the Security Level in a City Based on GIS-MCDA

Management Engineering Department, Federal University of Pernambuco, P.O. Box 7462, 50630-970 Recife, PE, Brazil

Received 6 January 2016; Revised 13 April 2016; Accepted 26 April 2016

Academic Editor: Juan C. Leyva

Copyright © 2016 Ciro José Jardim de Figueiredo and Caroline Maria de Miranda Mota. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The aim of this paper is to map the most favorable locations for the occurrence of robberies in the Brazilian city through the multicriteria method Dominance-Based Rough Set Approach. Considering the city divisions with alternatives and evaluating by several spatial criteria, a decision-maker is building a preference model with based previous knowledge. Next, decision rules induced from preference information are introduced to the spatial environment to get the results. The decision rules can be seen as conditional part (represented by criteria) and decision part (assignment to decision classes). The rules classify all the alternatives according to security level. Moreover, the rules help to understand the social dynamics of the city and to assist in the proposition of strategies against violence.

#### 1. Introduction

The issues of public safety and violence are often discussed because they directly affect each person living in society. In general, understanding and explaining the occurrence of violence require significant efforts to collect information on the issue. Information such as crime rates and socioeconomic variables associated with the population is important for the development of new research [1, 2]. Then the data can be used to create strategic options that will help to combat violence.

For Andresen [3], field studies of violence require more than discrete data. It is necessary to assess the evolution of violence over time and space for decision-making in public security. According to Elmes and Roedl [4], the Geographic Information System (GIS) is an important tool to support this decision-making process and formulate strategies to combat crime.

In the literature, the use of GIS in the field of criminality has already been reported in several different contexts. Various studies show themes and applications such as the identification of crime spatial patterns [4], spatial diversity of crimes [5], spatial correlation between crime and inequality [2, 6], and simulation and agent-based models for exploring crime patterns [7]. However, our intention is to provide an alternative technique, using GIS within the context of crime. This technique explores several factors that can help to understand violence.

Therefore, by evaluating different areas as alternatives and the impact of the multiple criteria with respect to violence, we used Multicriteria Decision-Making (MCDM). The primary objective of MCDM is to assist a decision-maker (DM) in choosing, ordering, or sorting a given set of two or more alternative criteria [8]. Moreover, several studies demonstrate the importance of the MCDM in many research fields [9–11]. In our case, we also considered the features of the spatial information supported by GIS. In the literature, there are very few studies of the combined use of MCDM and GIS to criminality. Gurgel and Mota [12] presented a GIS-MCDM model to prioritize regions for allocation resources considering several criteria; and in [13] a multicriteria approach was proposed aimed at setting police patrol sectors.

The focus of this study is to build a GIS-MCDM model to assess the level of security (increase in crime) in a city. The present study can be divided into two main contributions. First, we discuss the classification of the spatial alternatives to evaluate the level of security and its relationship to criminality using a GIS-MCDM approach. Second, we discuss how the results of the model can be used in the formulation of security policies and which criteria are most important.

The rest of the paper is divided as follows. Section 2 presents background information illustrating the importance of GIS-MCDM. Section 3 presents the MCDM method used in the application. In Section 4, we present a model of the problem and describe the procedures used. In Section 5, we apply and discuss the results that were obtained. In Section 6, we present our conclusions and perspectives for future studies.

#### 2. Background on GIS-MCDM

The MCDM approach assists in building an aggregation model based on the preference information sourced by the DM [14]. For Dyer et al. [15], since the 1980s MCDM methods have been implemented in computer systems to support the decision-making process and have subsequently been called Decision Support Systems (DSS). In recent years, authors have explored MCDM methods in different applications [16–18].

Specifically, there has been a growth in the use of GIS with MCDM because of the development computerized systems and improved access by users [19]. This combination is important because spatial decision problems typically involve several alternatives assessed by conflicting multiple criteria. Also, the evaluation is conducted by a DM or group of decision-makers [20]. Afterwards the concept of GIS-based Multicriteria Decision-Making (GIS-MCDM) emerged [19].

In the recent literature, several studies have combined the decision process using GIS and MCDM such as choosing a better route for vehicles [21], identifying sustainable sites for environmental conservation [20, 22], sorting regions to implement energy mixes [23], allocating industries [24], and suitable land use [25].

We also observed that authors have evaluated specific combination MCDM methods with GIS. The adaptation of GIS-MCDM needs to create a synergy that might facilitate the aggregation of information. In this sense, [20, 26, 27] have presented studies using the importance of scales to assess alternatives based on DM preferences or situations involving uncertainty.

On the contrary, authors have shown more traditional methods including both compensatory and noncompensatory methods. In the compensatory methods, AHP was integrated into the GIS environment [28, 29]. Noncompensatory methods present practical applications with ELECTRE and other outranking methods [22, 30]. Also, there are software packages to facilitate the generation of recommendations to decision-makers [30].

Thus, the possibilities are extensive for combining the GIS-MCDM approach to support decision-making processes that directly involve the spatial use. However, there are a few studies that use GIS-MCDM for the public security field [12, 13]. Thus, the gap related with GIS-MCDM and criminality becomes a motivator for building a model to solve specific problems in public safety.

#### 3. DRSA Method

In this section, we present Dominance-Based Rough Set Approach (DRSA) method that was integrated with GIS. We choose a method that allows using the set of reference examples (real or fictitious) for aggregating the information from preference obtained with the DM. Thereafter, each reference alternative of the set is allocated in preordered classes [31, 32]. To arrive in results, the DRSA method consider the preference model in the form of a set of “IF…THEN…” decision rules discovered from the data by inductive learning [14, 32].

Highlighted DRSA method, the absence in weights, and preference thresholds used by DM avoiding a high cognitive effort are required. The reference examples are used as input to get DM’s preference information. Moreover, there is an interactive construction between the DM and the analyst. The rules are transparent and easy to interpret for the DM and give arguments to justify and explain the decision.

##### 3.1. Notations Used

Let set of alternatives be finite, discrete, and nonempty .

Let a finite, discrete, and nonempty set of alternatives assuming , called the set of reference examples where the DM wishes to express his/her preferences for a given problem.

Also, let a collection of finite and nonempty set of criteria , and each alternative has an evaluation criterion for all . Thus, for two alternatives and , we have which means that “ is at least as good in relation to when compared with criteria ”, representing a weak preference relation between both alternatives pairs [32]. We also assume that these criteria are preference ordered with two types: cost criteria (the smaller the better) and gain criteria (the greater the better).

In addition , with , such that must belong to one and only one class . Each class is called decision class. Assuming too that these classes are ordered for all and any and , such as , the actions included in are preferred over the actions contained in *.* The sets to be approximated are called upward and downward unions of decision classes, respectively (see (1) and (2)). Consider

It is assumed that for each evaluation of the alternatives with respect to criteria having a strictly monotonicity relationship with decision class, we can define the dominance relation according to [32]. Let be a subset of condition criteria; we can say that * dominates * in the condition criteria space (denoted by ) if . Assuming, without loss of generality, that the domains of the criteria are numerical and that they are ordered so that the preference increases with the value, we can say that is equivalent to The analogous definition holds in the decision class space [32].

In DRSA, the granules of knowledge used for approximation are dominance cones that are defined as follows in objects that are dominating and dominated, respectively, with respect to :

Finally, the upper and lower approximations of unions of decision classes with respect to are calculated as follows:(i)The -upper approximation of : .(ii)The -lower approximation of : .(iii)The -upper approximation of : .(iv)The -lower approximation of : .

Finally, the -boundaries (doubtful regions) of the unions and are defined, respectively, as follows:

To evaluate the results using the sample of the reference examples, the DRSA apply the accuracy of approximation. For any and for any the accuracy is defined as and by as the respective ratios (see (7) and (8)). Consider

From the accuracy approximation we can obtaining the quality approximation (see (9)). It expresses the ration of all -correctly sorted reference examples to all reference examples in the table. For every minimal we define such that is called a reduct of and denoted by . The intersection of all of the reducts is called the core and denoted by :

The decision rules are the final of the DRSA method and are divided in two parts: condition and decision, where the condition part specifies the values assumed by one or more criteria and the decision part specifies an assignment to one decision class [33].

#### 4. Development of GIS-MCDM Model for Public Safety

The present study shows the usefulness of the GIS-MCDM approach, using DRSA method. In this the section we expose the steps of the GIS-MCDM model for public safety and application performed on a real problem.

##### 4.1. Steps of the GIS-MCDM

The integration between the DRSA method with spatial data is made in two systems. All evaluations for choosing the reference examples are prepared in a GIS environment, which avoids the decision table to realize the same procedure. Moreover, the visualization of data becomes better understood by the DM. However, to execute DRSA, we used the free software called jMAF (available at http://idss.cs.put.poznan.pl/).

The construction of the model comprises two integrated processes. The first is the selection of the reference examples using the maps, which contains the numeric values for each criterion (layers). Each layer is a set of alternatives evaluated by one criterion. The DM chooses the same subset of alternatives considering all criteria. Next, each alternative is allocated to only one predefined class. These procedures are performed in ArcGis 10.1 and exported to the second step.

In second procedure, the alternatives are evaluated for each criterion and each alternative is allocated in only one decision class [34]. Furthermore, we may get the results in relation to and , as well as and for decision classes, and we may obtain the decision rules that are used to map the alternatives. Thereafter, the rules that are exported come back to ArcGis 10.1 and are implemented on the Python environment to classify all the alternatives. The decision rules are divided in the condition criteria part (IF) and decision classes part (THEN). This permits the interactive decision process to be with the DM. Because if the DM does not agree with the results, he/she can change the set. Figure 1 shows the flowchart with the procedures.