heliportos - IJiETAP

International Journal of Industrial Engineering, 21(1), 40-51, 2014ISSN 1943-670X © INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING EFFICIENT DETERMINATION OF HELIPORTS IN THE CITY OF RIO DE 1 JANEIRO FOR THE OLYMPIC GAMES AND WORLD CUP: A FUZZY 2 LOGIC APPROACH 3 4 Claudio S. Bisso a , Carlos Patricio Samanez b 5 a Production Engineering Program 6 Federal University of Rio de Janeiro (UFRJ), COPPE, Brazil 7 b Industrial Engineering Department 8 Pontifical Catholic University of Rio de Janeiro PUC-Rio, Brazil 9 10 The purpose of this study was to determine a method of evaluation for the use and adaptation of Helicopter Landing 11 Zones (HLZs) and their requirements for registered public-use for the Olympic Games and the World Cup. The 12 proposed method involves two stages. The first stage consists of clustering the data obtained through the Aerial and 13 Maritime Group/Military Police of the State of Rio de Janeiro (GAM/PMERJ). The second stage uses the weighted 14 ranking method. The weighted ranking method was applied to a selection of locations using fuzzy logic, linguistic 15 variables and a direct evaluation of the alternatives. Based upon the selection of four clusters, eight HLZs were obtained 16 for ranking. The proposed method may be used to integrate the air space that will be used by the defense and state 17 assistance agencies with the locations of the sporting events to be held in 2014 and 2016. 18 19 Significance: In this paper we proposed a model for evaluating the use and adaptation of Helicopter Landing Zones. 20 This method involves clustering data and the selection of locations using fuzzy logic and a direct evaluation of the 21 alternatives. The proposed method allowed for precise ranking of the selected locations (HLZs) contributing to the 22 development of public policies aimed at reforming the local aerial resources. 23 24 Keywords: Fuzzy logic, Site selection, Transport, Public Policy. 25 26 1. INTRODUCTION 27 28 The city of Rio de Janeiro will host the 2014 World Cup and 2016 Olympic competitions. Thus, the development of 29 more effective and technical mapping is urgently needed to rationalize the use of aerial resources (helicopters) that 30 belong to the state of Rio de Janeiro. Consequently, the helicopters will meet the demands for human health and safety 31 better, as well as actively participate in these large sporting events. 32 The main objective of this study was to determine a method that could be used to justify potential investment 33 opportunities in registered public-use heliports based on their requirements and their locations relative to points of 34 public interest. To accomplish this task, Helicopter Landing Zones, or HLZs, were mapped and identified by the Aerial 35 and Maritime Group (Grupamento Aéreo e Marítimo (GAM)) of the Military Police of the State of Rio de Janeiro 36 (Polícia Militar do Estado do Rio de Janeiro (PMERJ)). 37 In the city of Rio de Janeiro, various zones were identified by the GAM as HLZs. Yet, these zones do not have the 38 appropriate identification, illumination or signage. Thus, these HLZs do not meet the appropriate technical standards 39 that would define them as zones being appropriate for helicopter landing. Here, several aspects, including the proximity 40 of the HLZs to hospitals, PMERJ (Military Police of the State of Rio de Janeiro) units, Fire Department (CBMERJ), 41 Civil Police (PCERJ) and the major sporting competition locations, were used to identify the most relevant HLZs in the 42 city of Rio de Janeiro (according to these criteria). In addition, this study serves to stimulate the use of the HLZs and 43 provide subsidies for developing public policies for streamlining the existing aerial resources (helicopters) that belong 44 to corporations within the state of Rio de Janeiro. 45 Considering that is not likely that the city will have a fitting conventional terrestrial transport that can handle the 46 numerous tourists and authorities, Rio de Janeiro will face an increased demand for air transport via helicopter to move 47 between the different sports facilities, integrated with the local assistance and defense agencies. 48 Today, Rio de Janeiro faces a challenge that it has never face before. The burden of investments in various sectors – 49 led by the oil and gas industry – sum, according to the Federation of Industries of the State of Rio de Janeiro (FIRJAN), 50 $ 76 billion during the period from 2011 to 2013. This is one of the largest concentrations of investment in the world, 51 given the volume of investments in relation to the small territorial dimension of the state. 52 Air transport demand brought by those investments, combined with the fact that the city will host the 2014 World Cup 53 and the 2016 Olympic Games, requires a focused technical mapping that allows streamlining the aerial resources 54 Determination of Heliports in The City of Rio De Janeiro 41 (helicopter) and the helicopter landing zones (HLZ). In this sense, the present study contributes by showing a method 55 that identifies and assesses those HLZs, justifying public and/or private investment in adaptation, reform and creation of 56 helipads in the city of Rio de Janeiro. 57 Another contribution stems from the size of the problem faced, because of the large amount of ZPHs and existing 58 places of interest, the proposed method adopts a clustering method to delimit the original data, which allows restricting 59 the analysis to a smaller and simpler sub problem to be solved. The method incorporates the analysis, among other 60 relevant factors, the distance and the ease of access between the HLZs and the locations of the sports competitions. This 61 is crucial given the large amount of people who are expected to these sporting events. The identification and appropriate 62 choice of HLZs arising from this study, optimizes the logistics of transportation by air and minimizes costs. 63 64 2. ORIGIN OF THE DATA 65 66 The data that was used for choosing the locations for implementing the heliports for public use in Rio de Janeiro was 67 obtained from a database that was prepared by the GAM of the PMERJ (GAM/PMERJ 2010-2016 Multi-year plan, 68 2009). The GAM identified existing, viable Helicopter Landing Zones (HLZs) based on the helicopter flights over Rio 69 de Janeiro. These HLZs include soccer fields, parking areas, unsheltered areas, unregistered heliports and locations 70 where helicopter landing is feasible. 71 The quality of these HLZs was based upon how closely they met the predicted standard requirements for becoming a 72 registered heliport. Overall, the quality of the HLZs was highly variable. Although several HLZs met all of the 73 requirements, others were extremely restricted by obstacles, such as high buildings, trees, posts, and electrical 74 transmission lines. 75 In addition to the HLZs, the database provided by the GAM contains the hospitals of interest and the PMERJ, 76 CBMERJ and PCERJ units in separate spreadsheets. The locations of the major sporting competitions were obtained by 77 consulting the GAM/PMERJ 2010-2016 Multi-year Plan and were mapped by the authors with the Google Earth ® 78 software. A succinct description of these data is provided in Table 1. 79 80 Table 1: Data description 81 82 Category Quantity Helicopter landing zones 436 Hospitals 10 Fire Department (CBMERJ 63 Military Police (PMERJ) 76 Civil Police (PCERJ) 14 Sport events location 18 TOTAL 617 Source: GAM-PMERJ. 83 84 3. BIBLIOGRAPHIC REVIEW 85 86 Several approaches have been reported in the literature for solving location problems (Aikens, 1985; Hamacher & 87 Nickel, 1998). Agrawal, 2010, presents a hybrid approach, using the features of the Taguchi technique with Artificial 88 Immune Systems (AIS), to optimize an integrated supply chain design problem with multiple shipping. Sun et al. 89 (2008), present a bilevel programming model for the location of logistics distribution centers. Multi-criteria facility 90 location models have been investigated by researchers in Lee et al., 1981 and Ross & Soland, 1980. 91 The most commonly used approaches can be classified as continuous location models, network location models and 92 integer programming models (Awasthi et al., 2010). In continuous location models, every point on the plane is a 93 candidate for facility location and a suitable distance metric is used for selecting the locations. In network location 94 models, distances are computed as shortest paths in a graph. The integer programming models start with a given set of 95 potential sites and use integer programming to identify best locations for facilities. 96 It is worth noting that most of the works mentioned above study the location problem within a certain environment, in 97 Bisso and Samanez 42 other words, the parameters in the problem are fixed and known in advance. To deal with parameters that cannot be 98 obtained with certainty, location problems have been extensively studied in the literature by using multi-criteria 99 decisions, fuzzy logic methods and other mathematical tools (Chi & Kuo, 2001). The majority of these models seek to 100 maximize revenue or to minimize expenses. In addition, the majority of these approaches only provide systematic 101 procedures for resolving the problem without considering the global aspects that can affect the system, such as decision- 102 making factors (Chen & Qu, 2006). 103 It is important to introduce “uncertainties” in the ratings and weights of various factors that are associated with 104 determining locations. Uncertainty emerges primarily from a lack of precise or reliable information and from the need 105 to evaluate a series of factors that are frequently intangible. Regarding the application of fuzzy logic, Terano (1992) 106 states, “the preeminent characteristic of the fuzzy sets is the ability to express the quantity of ambiguity present in 107 human thought and the subjectivity (including natural language) in a manner relatively free from distortions”. 108 The Fuzzy Sets Theory was introduced by Zadeh (1965) to handle a problem with ambiguity. Thus, linguistic values 109 could be used to approximate rationale based on the fuzzy sets theory to handle data evaluation ambiguity effectively. 110 Regarding the vague properties of the linguistic expressions, normal triangular fuzzy numbers were used to characterize 111 the fuzzy values of the quantitative data and linguistic terms that were used in the approximate rationale (Lee, 1996 and 112 Zadeh, 1975). Ambiguity is one characteristic of human thought. The Fuzzy Sets Theory is an effective tool for 113 incorporating subjectivity into decision-making processes (Wei et al., 2008) 114 The use of fuzzy theory for location selection projects allows decision makers to incorporate non-quantifiable 115 information into the decision making model. In new location selection studies, the fuzzy-multi-criteria decision-making 116 method was considered. 117 Vahidinia et al. (2009) used the AHP (Analytical Hierarchy Process) fuzzy method to determine the optimal location 118 for a new hospital in the city of Tehran. In addition, Soltani & Marandi (2011) approached the same problem using a 119 two-stage fuzzy multi-criteria decision-making method. 120 Furthermore, Wu et al. (2007) used the Delphi method, the AHP and sensitivity analysis to develop an evaluation 121 method for selecting the ideal location for a regional hospital in Taiwan and for determining the hospital efficiency. Rao 122 (2010) proposed a methodology based on fuzzy diagraphs and matrix for evaluation of alternative plant locations, using 123 characteristic expressions that are useful comparing alternative plant locations. 124 There are more recent works using fuzzy logic as an efficient method for site selection. Shahmoradi & Isalou (2013) 125 used an integrated fuzzy logic and multicriteria decision model to select a suitable site for establishing wastewater 126 treatment plant in Kahak, Iran. Isalou et al. (2013) developed an integrated fuzzy logic and analytic network process to 127 locate a suitable location for landfilling municipal solid wastes generated in Kahak Town, Qom, Iran. Barros et al. 128 (2013) developed an application of fuzzy logic, supporting the Selection Process of Nuclear Sites established by the 129 concepts and criteria of the Electric Power Research Institute EPRI-Siting Guide 130 Narasimhan (1979) applied fuzzy subsets to a problem that involved selecting gas station locations by proposing a 131 model with linguistic variables and by directly evaluating feasible alternatives with fuzzy variables. 132 Additionally, Narasimhan (1979) aimed to define the degree of preference when dealing with unreliable and imprecise 133 information based on conversations with decision makers. Thus, this method consisted of two criteria, including 134 scenario criteria (which seek to filter and remove locations that do not meet the essential requirements as indicated by 135 the decision makers) and evaluation criteria (which seek to evaluate the selected locations). 136 This modeling was suggested by Narasimhan and was used here due to its simplicity and potential for assigning 137 numbers to rate each factor associated with a location. 138 139 4. REAL-LIFE EXAMPLE 140 141 This study was conducted in two stages. The first stage involved the use of a clustering method and the second stage 142 involved the application of a weighted ranking method (described by Narasimhan (1979)). 143 Clustering was used to group the data (the HLZs and locations of public interest) and to select the clusters that contain 144 both HLZs and locations of public interest. Clusters that contained only HLZs were discarded and clusters that 145 contained only points of public interest were used to represent areas with large concentrations of public resources 146 without current helicopter access. 147 In addition, due to the size of the problem- the large number of HLZs and locations of public interest that were 148 selected by the GAM- clustering was used to delimit the original data, which restricted analysis to a simpler sub- 149 problem. This delimitation was performed by selecting points that were contained in a few clusters with specific 150 characteristics. 151 The weighted ranking method from Narasimhan (1979) was used to define preferential HLZs based on the ease of 152 Determination of Heliports in The City of Rio De Janeiro 43 terrestrial access to the points of interest. The ease of terrestrial access to these sites is important because the HLZs that 153 do not have easy terrestrial access, or any type of possible access, are not suitable for loading and unloading people or 154 the general population. 155 The location analyses for this problem have frequently concentrated on accessibility and on the impacts of activities 156 through the application of accessibility indicators. Accessibility is defined as "the relative proximity of one place to 157 another” (Tsou et al., 2005). The concept of accessibility is used to explain the availability of one product, device, 158 service or environment. 159 In addition, the degree of relative importance between points of interest was also considered. In this case, different 160 weights were used do define the ease of access for each type of point of interest. 161 162 4.1 Clustering and computational resources 163 The geographical coordinates for all of the points (HLZs and locations of interest) were obtained in decimal coordinates 164 using the Google Earth® software. In addition, the R statistical and data mining software (version 2.11.1) was used with 165 the editor/compiler of the R® language (Tinn-R®, version 2.3.7.0). 166 The simple K-means clustering method (MacQueen, 1967) was used in this study. The K-means method is potentially 167 one of the most intuitive clustering methods. In this method, each object belongs to only one cluster, and all of the 168 clusters contain at least one element. 169 Various configurations were considered for clustering (that is, various numbers of centroids) in the K-means 170 algorithm. The results from these configurations are discussed in the results section. The Euclidean distance was used to 171 measure the distance between the points. The Euclidean distance between two points a = (a x , a y ) and b = (b x , b y ) is 172 defined as: 173 174 2 2 ( , ) ( ) ( ) x x y y d a b a b a b = ÷ + ÷ (1) 175 176 The first step of the algorithm is initialization. During initialization, the clusters for each element are determined. 177 Usually, this can be accomplished in two different ways. In the first method, one of the centers of each cluster is chosen 178 randomly within the elements. In the second method, each object is placed in a random cluster before calculating the 179 centers. The centers are recalculated at each iteration when the elements are reallocated between the clusters to optimize 180 the cost function with an iterative procedure (Luenberger, 1984). 181 Let x i represent the objects to be clustered. By considering the objects as vectors, the center v j of cluster C j can be 182 calculated as the average of all of the elements in the cluster as follows: 183 184 1 i j j i x C j v x C ¬ e = ¿ (2) 185 186 From this equation, the distance D ij from each element x i to each center v j is calculated. Usually, the Euclidean 187 distance is used. 188 From these distances, each element is reallocated to the closest cluster (based on the cluster center). Next, it is 189 determined if more iterations are needed. The criteria are simple. While changes are occurring, new centers are 190 calculated and the objects are reallocated. When no more changes are occurring, the algorithm stops. 191 192 4.2 Weighted ranking method 193 The weighted ranking method was applied to a selection of locations using fuzzy logic. To apply the model proposed in 194 this study, the HLZs (known as L 1 , L 2 ... L n ) were considered as locations to be selected. 195 For each location L i , five attributes, a 1 , a 2 , a 3 , a 4 and a 5 , were used. These attributes represented the ease of access to 196 the hospitals, PMERJ units, CBMERJ units, PCERJ units and major sporting competition locations, respectively (Table 197 2). The accessibility attributes were chosen to grant air space integration between the defense and state assistance 198 agencies and the locations of the sporting events. 199 The value of each attribute a i for location L j was represented by the fuzzy variable r ij . Five linguistic values were 200 attributed to these fuzzy variables. One of these variables used the modifier “very” r ij {very easy, easy, average, 201 difficult, and not feasible} 202 To decrease the variability of the linguistic values r ij that were attributed by the evaluators to the attributes a i from the 203 Bisso and Samanez 44 locations L j , a table was created to explain the meaning of the linguistic values relative to the attributes. These values 204 are shown in Table 3. 205 206 207 208 Table 2: Accessibility attributes of the HLZ 209 210 Attributes a 1 a 2 a 3 a 4 a 5 Ease of access to hospitals or health care facilities Ease of access to Military Police (PMERJ) units Ease of access to firefighter (CBMERJ) units Ease of access to Civil Police (PCERJ) units Ease of access to sport events locations 211 Table 3: Linguistic values meanings (r ij ) 212 213 Linguistic value Meaning - Very easy - Easy - Average - Difficult - Not feasible - HLZ within or adjacent to the site of interest. - HLZ close to the site of interest, with good quality access, easy traffic throughout the day. - HLZ in an average distance to the site of interest, with reasonable quality pathway access, possibility of some traffic. - HLZ far from the site of interest, with poor quality, many road traffic lights or intersections, possibility of bad traffic. - It is not possible to consider ground transportation between HLZ considered and the site of interest. 214 Each linguistic value was represented with triangular fuzzy numbers by the authors (Table 4). 215 216 Table 4: Linguistic values r ij 217 218 Triangular fuzzy numbers for the linguistic values r ij Very easy Easy Average Difficult Not feasible (0.7, 0.9, 0.9) (0.5, 0.7, 0.9) (0.3, 0.5, 0.7) (0.1, 0.3, 0.5) (0.1, 0.1, 0.3) 219 These values were chosen to represent the authors’ consensus with the best reliability. The graphical representation of 220 the fuzzy numbers of the r ij linguistic values is provided in Figure 1. 221 To allow for the compositions of the various r ij values that the evaluators attributed to each attribute a i from the 222 locations L j , weights were assigned to quantify the relative importance between the a i attributes (with W j as the weight 223 associated with the attribute a i ). 224 The weight W j was defined as a fuzzy linguistic variable. Four linguistic values were attributed to this variable. One 225 of these values used the modifier “very” and another used the modifier “less” as follows: 226 227 W j {very important, important, average, less important} 228 229 Determination of Heliports in The City of Rio De Janeiro 45 230 Figure 1: Graphical representation of the linguistic values (r ij ) fuzzy numbers. 231 232 The triangular fuzzy numbers that represent the linguistic values of W j are shown in Table 5. 233 234 Table 5: Linguistic values W j 235 236 Triangular fuzzy numbers for W j Very important Important Average Less important (0.75, 1.0, 1.0) (0.5, 0.75, 1.0) (0.25, 0.5, 0.75) (0.0, 0.25, 0.5) 237 Finally, the problem structure was established as shown in Table 6 and was similar to the problem structure proposed 238 by Narasimhan (1979). 239 240 Table 6: Problem structure. Adapted from Narasimhan, 1979. 241 242 L 1 L 2 L 3 ................................................ L n a 1 W 1 r 11 r 12 r 13 r 1n a 2 W 2 r 21 r 22 r 23 r 2n a 3 W 3 r 31 r 32 r 33 r ij r 3n a 4 W 4 r 41 r 42 r 43 r 4n a 5 W 5 r 51 r 52 r 53 r 5n 243 To classify the HLZs in a way that permits the visualization of the relative suitability of each HLZ relative to its 244 location near a point of interest (by respecting the relative weights between their various types and indicating the HLZs 245 that best serve the points of interest), the coefficient i r was determined as follows: 246 5 1 5 1 j ij j i j j W r r W = = = ¿ ¿ . (3) 247 Bisso and Samanez 46 Where the coefficient i r from the point i L is given by equation (3) based on fuzzy operations. 248 249 1 1 2 2 3 3 4 4 5 5 1 2 3 4 5 i i i i i i Wr W r W r W r W r r W W W W W © © © © = © © © © (4) 250 251 From the i r coefficients related to each of the HLZs, the coefficient i p was calculated (named the normalized general 252 rating (Narasimhan, 1979)) for the alternative location i. 253 1 1 - -1 m i i k k k i p r r n = = = ¿ (5) 254 The definitions of the attribute weights and the degrees of non-quantitative weighting for each linguistic variable and 255 for each attribute are determined through a consensus process that applies the Delphi Technique to all of the decision 256 makers that are involved in the process. Thus, this method is based on information from key people in the decision- 257 making process and aims for quality. In addition, the largest possible consensus is gained by weighting this treatment 258 (Levine, 1984). 259 The Delphi Technique (Pill, 1971) was used in all of the model stages proposed in this study. This technique included 260 the following steps. 261 - Ask the decision makers to categorize the importance of the attributes associated with the three selected 262 locations. 263 - Ask each decision maker to indicate on a scale from zero to one where to allocate each qualitative description 264 of the weights corresponding to each attribute associated with the analyzed location. 265 - Ask each decision maker to provide a qualitative evaluation for each linguistic variable relative to each 266 attribute associated with the selected location. 267 - Ask each decision maker to indicate a degree of weighting for each qualitative evaluation of each linguistic 268 variable relative to each attribute associated with the selected location (on a scale from zero to one). 269 The values given by the decision makers in the Delphi Technique were very reasonable approximations. The 270 functions developed empirically by the decision makers were used to compute the preferability of the locations through 271 a fuzzy evaluation of the relative degrees of the superimposed alternatives. In addition, one location was not emphasized 272 in detriment of another given the approximated values. However, in the absence of a consistent scheme for resolving the 273 uncertainty in the location evaluations, methods based on judgment and experience can subsidize a non-optimal choice 274 or accepted location. 275 276 5. RESULTS 277 278 5.1 Clustering results 279 The clusters obtained from the R® software represent a geographical agglomeration of points (HLZs and locations of 280 interest). However, the geographical proximity does not indicate that an HLZ will serve as a transport terminal for a 281 point of interest. 282 An HLZ positioned on an island near the continent can be geographically closer to a point of interest on the coast than 283 another HLZ on the continent. However, if no connecting bridge is present between the island and the point of interest, 284 the more distant HLZ may serve the point of interest better than the closer HLZ. 285 In order to avoid a comparison between distant points that would produce useless results, the obtained clusters served as 286 a starting point for the analysis of the points that belonged to the same cluster. When more than one location of public 287 interest of the same nature was found in the same cluster, only the best access was used to define the values attributed to 288 each HLZ. 289 Clusterings with 50, 80, 90, 100 and 124 clusters were attempted. Clusterings that contained 50, 80 and 90 clusters 290 with many HLZs and only a few public interest locations were obtained. By using a larger number of clusters, a better 291 balance was achieved between the number of HLZs and these locations. In addition, based on the data bank 292 characteristics, a larger number of clusters permitted the neglect of a portion of the HLZs. This result occurred because 293 a larger number of clusters were formed by these landing zones, which were not important for this study. 294 Determination of Heliports in The City of Rio De Janeiro 47 Finally, clusterings with 100 or more clusters provided the lowest sum of quadratic distances from the points in each 295 cluster to their respective centroids. 296 Thus, a clustering of 124 clusters was selected as the best tradeoff between the number of clusters (and the number of 297 HLZs per cluster) and the variability of the categories involved in the clusters (that is, an appropriate variety of public 298 interest locations together with few HLZs per cluster). 299 Table 7 shows the total number of elements in each cluster. 300 301 302 Table 7. Number of elements in each cluster (124 clusters). 303 304 8, 8, 16, 9, 2, 9, 7, 1, 1, 11, 9, 5, 2, 21, 2, 2, 10, 7, 5, 6, 3, 3, 24, 6, 1, 5, 4, 9, 5, 6, 1, 6, 1, 4, 4, 3, 3, 6, 5, 3, 18, 15, 14, 305 9, 6, 1, 5, 4, 2, 4, 1, 10, 5, 9, 7, 4, 4, 8, 5, 4, 13, 3, 1, 7, 1, 4, 1, 9, 7, 3, 7, 7, 8, 4, 12, 1, 4, 18, 6, 1, 7, 3, 3, 4, 6, 2, 15, 9, 306 3, 9, 19, 7, 8, 5, 7, 6, 3, 14, 4, 4, 2, 9, 2, 1, 1, 31, 6, 7, 2, 2, 4, 7, 3, 3, 4, 2, 9, 6, 4, 10, 4, 4, 1, 4 307 308 For example, cluster 1 has 8 elements, cluster 2 has 8 elements and cluster 124 has 4 elements. Within the 124 clusters 309 considered in this analysis, only four clusters were selected for consideration. 310 As previously mentioned, due to the size of the initial problem (the original databank had more than 500 HLZ 311 locations), it was necessary to restrict its scope to a smaller and simpler sub-problem. This restriction was necessary to 312 illustrate the application of the proposed method. In addition, the inclusion of all of the determined clusters is proposed 313 for future studies. 314 The four selected clusters united some interesting characteristics for illustrating the proposed methodology. For 315 example, 316 - They represented diverse public interest locations, 317 - They had a relatively balanced number of public interest locations and HLZs, and 318 - They did not have large numbers of HLZs. 319 Table 8 shows the selected clusters and the categories to which the points contained in these clusters belong. 320 The first and second columns of Table 8 refer to the latitude and longitude of the points in decimal coordinates, 321 respectively. The third column shows the descriptive codes for the selected points. These codes are formed by two 322 components. The first component is formed by three literal characters that represent a category in which a point belongs 323 (CBM, representing the fire department; PMR representing Military Police battalions, OLP representing points that will 324 host sporting events; HLZ representing helicopter landing zones and HPT representing hospitals). 325 The second component of the code represents the numbering of the points in the original listing of the considered 326 points. The last column represents the number of the selected cluster according to the previous numbering of these 327 clusters. 328 The selected clusters did not contain any Civil Police units. This finding resulted from the small quantity of locations 329 that were mapped by the GAM. In addition, during the evaluation of the points, it was determined that HLZ 449 was 330 within a Civil Police unit. Thus, this datum was considered in the evaluation as proposed in the method. 331 332 5.2 Results from the application of the weighted ranking method 333 Based on the selection of the four previously mentioned clusters, eight HLZs were ranked by the adopted method. 334 Based on this method, the normalized general ratings i r , the ratings k r and the preferability indices i p were calculated. 335 Table 9 illustrates these indices for each of the eight considered helicopter-landing zones. 336 In Table 9, a tie between the preferability indices of p 6 and p 8 was observed . This result was explained by the physical 337 proximity between the points, which resulted in equal attributes. Regarding the p 2 and p 6 indices, the equal values 338 resulted from their similar characteristics, which determined the coincidence of the attribute linguistic values. 339 The preferability index i p of the eight analyzed HLZs were plotted in the graphical form of triangular fuzzy numbers 340 (Figure 2). 341 342 343 344 345 346 Bisso and Samanez 48 Table 8: Selected clusters 347 348 Latitude Longitude Code Cluster number -22,92673 -43,23783 CBM_48 9 -22,92755 -43,25243 HPT_3 9 -22,92547 -43,24368 PMR_65 9 -22,92467 -43,23779 HLZ_173 9 -22,92033 -43,24606 HLZ_94 9 -22,90725 -43,22837 CBM_28 11 -22,91329 -43,23116 CBM_49 11 -22,91043 -43,24149 CBM_9 11 -22,91311 -43,22897 OLP_9 11 -22,91381 -43,22982 PMR_52 11 -22,91763 -43,22904 HLZ_92 11 -22,90929 -43,22724 HLZ_96 11 -22,90919 -43,18756 CBM_29 44 -22,90857 -43,19008 HPT_4 44 -22,90777 -43,18359 PMR_67 44 -22,91012 -43,18443 HLZ_449 44 -22,93378 -43,17973 CBM_30 68 -22,92741 -43,18481 OLP_8 68 -22,92826 -43,18401 PMR_43 68 -22,93056 -43,18510 HLZ_185 68 -22,92823 -43,18379 HLZ_458 68 -22,93027 -43,18544 HLZ_499 68 349 Table 9. i p preferability indices 350 p 1 (-1,3388; -0,1407; 1,0194) p 2 (-1,2407; 0,0000; 1,3028) p 3 (-1,1614; 0,1758; 1,5346) p 4 (-1,3081; -0,0703; 1,0728) p 5 (-1,2325; 0,0352; 1,2795) p 6 (-1,2407; 0,0000;1,3028) p 7 (-1,2549; 0,0000; 1,2028) p 8 (-1,2407; 0,0000; 1,3028) 351 352 353 354 Figure 2. Fuzzy triangular numbers graphic represents the preferability indices. 355 Determination of Heliports in The City of Rio De Janeiro 49 The p 3 index, which refers to the location of HLZ 449, contained in cluster 44, has the greatest degree of preferability 356 (Figure 3). This finding was justified by the fact that its pertinence function resulted in the largest area under the curve 357 in the positive ranges of its support. In addition, the value of the support that corresponded to the maximum pertinence 358 function was furthest from the origin relative to the other maximum points of the other locations. 359 According to this logic, the decreasing ranking of the considered HLZs is established as follows: p 3 (HLZ 449), p 5 360 (HLZ 173), p 2 (HLZ 96) / p 6 (HLZ 185) / p 8 (HLZ 499), p 7 (HLZ 458), p 4 (HLZ 94) and p 1 (HLZ 92). 361 The four clusters with their respective points can be observed geographically in Figure 3. 362 363 364 365 Figure 3: Satellite image obtained by plotting the four selected clusters in Google Earth ®. 366 367 Figure 3 shows that the four clusters correspond to sets of points that are located in the following neighborhoods: 368 Tijuca and Andarai (cluster 9), Maracanã (cluster 11), Downtown Rio de Janeiro (cluster 68) and Catete (cluster 44). 369 Among the HLZs contained in the Tijuca and Andarai cluster, HLZ 173 was ranked the highest. In the Maracanã 370 cluster, HLZ 96 was ranked the highest, and in the downtown Rio de Janeiro cluster, HLZ 449 was ranked the highest. 371 HLZ 449 was located near the Central Headquarters of the Fire Department, the Souza Aguiar Municipal Hospital, the 372 Military Police and a Civil Police Unit. 373 374 6. CONCLUSIONS 375 376 The motivation behind this work came from the need to have an alternative to ground transport for locomotion of 377 tourists, citizens, authorities and athletes who will be in Rio de Janeiro for the Olympic Games and the World Cup. A 378 integration based model, which allows allocating the HLZs considering points of public interest, was proposed for this 379 very reason. 380 The results obtained from applying the proposed methodology resulted in several conclusions that were relevant to the 381 main objective of the study. Thus, a method for evaluating HLZs relative to their locations near public interest points 382 (hospitals, PMERJ units, firefighter units, Civil Police units and sporting event locations) was created. The use of the 383 proposed method allowed for precise ranking of the selected locations (HLZs) based on their subjective attributes, 384 which were valued through linguistic variables. 385 In the future, studies that incorporate a method for considering the costs of the proposed method should be conducted 386 regarding the transformation of the mapped HLZs into registered heliports, adapting them to technical standards. 387 The strength of our work is the ability to deal with multiple criteria and model uncertainty in location planning for 388 helicopter landing zones. The practicality demonstrated by this proposed method and the utility and clarity of the 389 obtained results indicates that this method will contribute to the development of public policies that are aimed at 390 streamlining existing aerial resources (helicopters) of agencies in the state of Rio de Janeiro. Thus, these agencies can 391 better meet the health and safety demands of the population and actively contribute to the large sporting events that are 392 predicted to occur in 2014 and 2016 in Brazil. In addition the application of this methodology to other Brazilian cities, 393 is also of interest, for the reasons already mentioned. 394 395 396 Bisso and Samanez 50 7. REFERENCES 397 398 [1] Agrawal, S., Raghavendra, N., Tiwari, M.K., Goyal, S.K. (2010). A hybrid Taguchi-immune approach to optimize 399 an integrated supply chain design problem with multiple shipping. European Journal of Operation Research, 203: 400 95–106. 401 [2] Aikens, C.H. (1985). Facility location models for distribution planning. European Journal of Operational Research, 402 22: 263–279. 403 [3] Awasthi, A., Chauhan, S.S., Goyal, S.K. (2010). A multi-criteria decision making approach for location planning for 404 urban distribution centers under uncertainty. Mathematical and Computer Modelling, 53: 98-109. 405 [4] Barros, C.F., Atalla, D.L and Cosenza, C.A.N. (2013). A Selection System of Brazilian Nuclear Sites based on EPRI 406 Siting Guide Model using Fuzzy Logic: An Exploratory Exercise in Reliability Engineering. 4th International 407 Conference on Integrity, Reliability and Failure (IRF 2013). Funchal, Portugal, June 23-27. 408 [5] Chen, Y. and Qu, L. (2006). Evaluating the selection of logistics centre location using fuzzy mcdm model based on 409 entropy weight. Proceedings of the 6th World Congress on Intelligent Control and Automation. Dailan, China, June 410 21-23. 411 [6] Chi, S.C. and Kuo, R.J. (2001). Examination of the influence of fuzzy analytic hierarchy process in the development 412 of an intelligent location selection support system of convenience store. IFSA World Congress and 20th NAFIPS 413 International Conference. Joint 9th, Vol. 3, pp. 1312-1316. 414 [7] Hamacher, H.W., Nickel, S. (1998). Classification of location models. Location Science, 6: 229–242. 415 [8] Isalou, A. A., Zamani , V., Shahmoradi, B and Alizadeh, H. (2013). Landfill site selection using integrated fuzzy 416 logic and analytic network process (F-ANP). Environmental Earth Sciences, 68: 1745-1755. 417 [9] Lee, H.M. (1996). Group decision making using fuzzy sets theory for evaluating the rate of aggregative risk in 418 software development. Fuzzy Sets and Systems, 80: 261-271. 419 [10] Lee, S.M., Green, G.I., Kim, C. (1981). A multiple criteria model for the location–allocation problem. Computers 420 and Operations Research, 8: 1–8. 421 [11] Levine, A. (1984). A model for health projections using knowledgeable informants. World Health Statistics 422 Quarterly, 37: 306-317. 423 [12] Luenberger, D.G. (1984). Introduction to Linear and Nonlinear Programming (2 nd ed). Addison-Wesley. 424 [13] MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In: Proceedings of 425 the fifth Berkley Symposium on Mathematical Statistics and Probability. Berkley, CA. University of California 426 Press. 427 [14] Narasimhan, R. (1979). A fuzzy subset characterization of a site-selection problem. Decision Sciences, 10: 618– 428 628. 429 [15] Pill, J. (1971). The Delphi method: substance, context, a critique and an annotated bibliography. Socio-Economic 430 Planning Sciences, 5: 57-71. 431 [16] Rao, R. (2010). Plant location selection using fuzzy digraph and matrix methods. International Journal Of Industrial 432 Engineering: Theory, Applications And Practice, 13: 166-176. 433 [17] Rio de Janeiro. Office of Public Safety. Military Police. GAM/PMERJ 2010-2016 Multi-year plan. [Rio de 434 Janeiro]: Aerial and Maritime Group, [2009]. 435 [18] Ross, G.T., Soland, R.M. (1980). A multicriteria approach to location of public facilities. European Journal of 436 Operational Research 4: 307–321. 437 [19] Shahmoradi, B and Isalou, A. A. (2013). Site selection for wastewater treatment plant using integrated fuzzy logic 438 and multicriteria decision model: A case study in Kahak. Journal of Advances in Environmental Health Research, 439 1: 51-61. 440 [20] Soltani, A. and Marandi, E.Z. (2011). Hospital site selection using two-stage fuzzy multi-criteria decision making. 441 Journal of Urban and Environmental Engineering, 5: 32-43. 442 [21] Sun, H., Gao, Z., Wu, J. (2008). A bi-level programming model and solution algorithm for the location of logistics 443 distribution centers. Applied Mathematical Modeling, 32: 610–616. 444 [22] Terano, T. (1992). Fuzzy Systems Theory and Its Application. San Diego: Academic Press. 445 [23] Tsou, K.W., Hung, Y.T. and Chang, Y.L. (2005). An accessibility-based integrated measure of relative spatial 446 equity in urban public facilities. Cities, 22: 424-435. 447 [24] Vahidnia, M.H., Alesheikh, A.A., and Alimohammadi, A. (2009). Hospital site selection using fuzzy AHP and its 448 derivatives. Journal of Environmental Management, 90: 3048-3056. 449 [25] Wei, L., Zhen-gang, Z., and Xinpu, W. (2008). Application of multi-objects fuzzy comprehension evaluation in 450 selecting location of coal-fired plant construction project. MMIT, Proceedings of the 2008 International Conference 451 on Multimedia and Information Technology. Washington, USA, Dec 30-31. 452 Determination of Heliports in The City of Rio De Janeiro 51 [26] Wu, C.R., Lin, C.T., and Chen, H.C. (2007). Optimal selection of location for Taiwanese hospitals to ensure a 453 competitive advantage by using the analytic hierarchy process and sensitivity analysis. Building and Environment, 454 42: 1431-1444. 455 [27] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8: 338–353. 456 [28] Zadeh, L. A. (1975). The concept of a linguistic variable and its application to approximate reasoning. Information 457 Sciences, 8: 199-249. 458 459 460 461 462 463