Priority Modeling for Public Urban Park Development in Feasible Locations Using GIS, Intuitionistic Fuzzy AHP, and Fuzzy TOPSIS

As feasible locations of public urban park in Bogor Municipality have been acquired in a previous study, decision makers are urgently needed to be informed on which locations should be prioritized for public urban park (PUP) development. Therefore, this study aggregates four multi-spatial criteria for PUP development priority modeling, namely distance to slum neighborhood, accessibility, slope, and land value. These four criteria in form of vector datasets were weighted using intuitionistic fuzzy analytical hierarchy process (IF-AHP) to consider the hesitancy, vagueness, and fuzziness might arise from experts’ judgement as well as from multi-spatial data processing. Resulted criteria weights from IF-AHP show that accessibility weight 0.261, land value weight 0.259, distance to slum weight 0.255, and slope weight 0.225, respectively. Criteria weights were inputted into fuzzy technique for order preference by similarity to the ideal solution (TOPSIS) and geographic information system (GIS) to rank location priority. Results from fuzzy TOPSIS show that very high priority class which has the biggest CCi values range (>0.654-0.76) provides 0.14 km2 area of feasible PUP development scattered in 10 locations. The biggest area for feasible PUP development is generated by medium priority class (CCi values >0.439-0.546) in 26 locations and approximately area of 0.38 km2.

achieved using combined technique for order preference by similarity to the ideal solution (TOPSIS), analytical hierarchy process (AHP) and geographic information systems (GIS) [3].
In Bogor Municipality, choosing the primary locations of feasible PUP depends on the available budget, therefore land value inevitably is the main criteria. In addition, PUP construction cannot be implemented without adequate access to the locations. A PUP also serves as a social interaction place for the visitor, and this is not happening in slum neighborhood when crowded houses occupy spaces. Hence, development goal in Bogor Municipality is to construct PUP near the slum area. PUP projects depend on the slope, where locations with extreme slope will increase construction cost. Consequently, this article uses four main criteria to rank feasible PUP locations for development namely distance to slum neighborhood, accessibility, slope, and land value. Since the criteria used in this study were extracted in linguistic classes from original sources such as land value and slope, therefore triangular fuzzy number (TFN) was applied so that all criteria can be inputted commensurably into fuzzy TOPSIS.
Considering these four criteria for weighting and integration, AHP is suitable since it has been combined previously with GIS to search suitable location for urban green space development [4]. In addition to AHP, [5] combined intuitionistic fuzzy sets (IFS) with AHP which fits with judgement involving hesitancy, vagueness, dan intuition found in real world problem solving.
However, not all criteria have the same polarity, three criteria used in this study have negative polarity or the less the better, namely distance to slum, slope, and land value. On the other hand, accessibility criterion has positive polarity or the bigger the better. Speaking of multi-criteria ranking methods involving several public urban park location candidates with different unit of measurement, TOPSIS has the benefit to prioritize them based on the positive and negative ideal solutions [6]. It means that ranks resulted from TOPSIS, has put the top priority close to benefit criteria and far away from cost criteria, and this fits to solve the different polarity of involved criteria in this study.
Integration of all these criteria to prioritize locations for PUP development rank is crucially needed for the decision makers in Bogor Municipality to formulate the future budget and planning. Considering all of earlier mentioned benefits of GIS, intuitionistic fuzzy AHP (IF-AHP), and fuzzy TOPSIS to integrate multi-spatial criteria for location ranking, therefore the objective of this paper is to develop a model for PUP development priority in Bogor Municipality's feasible locations using GIS, IF-AHP, and fuzzy TOPSIS.

II. Methods
Overview of the methodology used in this paper can be observed in Fig. 1. For preparation, four spatial criteria in form of vector maps were created using ArcGIS. Land value and slope maps were originally available in linguistic classes from original sources, while distance to slum area was computed using network analysis tools in ArcGIS. Access to PUP was represented by the length of the adjacent road of PUP locations. Road length values were measured using path tool in Google Earth, after confirmed through the Google Earth's street view to observe whether a PUP location can be accessed by four-wheel vehicles. In fuzzy TOPSIS process, access was classified as benefit criterion while land value, slope, and distance to slum area as cost criteria. These criteria were processed to calculate their positive and negative ideal solutions.
These four spatial criteria were weighted using IF-AHP, where three landscape architects from Housing Agency in Government of Bogor Municipality were asked to provide expert judgment in form of pair-wise comparison matrix. The weights then used to generate weighted fuzzy positive and negative ideal solutions, and computed to provide distance to fuzzy positive (d i + ) and fuzzy negative (d i -). Final calculation gives relative closeness coefficient value (CC i ) to each feasible PUP location so it can be ranked.

A. Study Area
Bogor Municipality consists of six sub-districts with 68 villages in lower level than sub-district. It is located approximately 97.26 km from Bandung, the capital city of West Java Province. In September 2020, it has comparatively dense population of 1,043,070 people in area of 118.5 km 2 [7]. The city is located on the terrain with elevation between 190-330 m. Lowest averaged daily temperature is 20 o -34.2 o C. Monthly average rainfall is 267.9 up to 385.3 mm. Fig. 3 [8] was used to convert four spatial criteria into fuzzy vector maps. PUP locations and slum neighbourhood were converted into centroids using ArcGIS to estimate the closest distance from each PUP to reach nearest slum neighborhood. Distance to slum neighborhood was regarded as the less the better, therefore when it bigger it will serve as the cost criteria. PUP locations in form of centroids were stored into a kml file and then uploaded into Google Earth software. In street view mode in Google Earth, actual road length can be observed in 3D photos and if the photos indicated a location can be accessed by four-wheel vehicles then road length was computed using path menu. This road length of each PUP location was input into ArcGIS spatial attribute and then converted into fuzzy value using TFN. For road length access, acquired crisp values were normalized using max method.

C. Intuitionistic Fuzzy AHP
According to [9] the intuitionistic fuzzy set (IFS) has the form: where ∀x ∈ E in a set A. Here, π A (x) represents the hesitancy degree of membership of element x. For implementation of IFS within AHP, this study uses following steps according to [5]: 1. Identification of the goal and the criteria that serve to the goal, the goal of this study is to prioritize feasible PUP locations for development in Bogor Municipality, hence four spatial criteria are needed to serve this goal, namely land value, accessibility, slope, and distance from slum neighborhood. 2. Determination the weights of the DMs, Let D={D 1 , D 2 , D 3 , …D k } be the set of decision makers (DMs) where k indicates the number of DMs and l k denotes the influence weights of the DMs. In a previous study, [10] categories to weight experts' importance whom came from different backgrounds. Therefore, this study uses experts' importance weighting modified from [10]. For details, scoring values and categories can be observed in Table 1.
In order to process each score of each category commensurably among DMs, every score in each row was normalized using the following equation: where x' = normalized score of each category in each DM while x = score of each category in each DM and max i is the maximum score in each i-th row. Once weight of  Table 1, it will be classified according to linguistic terms according in Table 2.
The yielded linguistic terms for every expert from Table 2 will the basis to compute expert' influence weight (l k ) using the following equation: where and (µ k , v k , π k ) are from IFNs in Table 2.

Construction of the pairwise comparison matrices
where the value is given by each expert using linguistic terms referred to IFNs in Table 3. 4. Develop aggregated intuitionistic fuzzy decision matrix (IF-DM) using decision makers weight evaluation in equation 4. The following equation represents IFWA operator: j=1,2,…,n).

Consistency check with Consistency ratio (CR) and
Random Index (RI) are conducted in this checking. The formula of CR is described in the equation 5: .
In addition, RI value is referred to [11] where its values varied according to specific number of criteria (n). RI values are described in Table 4. 6. Weights computation using entropy approach as described in the following equations:   For this study all of the fuzzy TOPSIS computation was performed using various function within attribute table menu in ArcMap 10.3, the following steps of fuzzy TOPSIS are described based on [12]: 1. Define the fuzzy decision matrix X :

2.
Establish the normalized fuzzy decision matrix R using linear scale normalization: , , Calculate the weighted normalized fuzzy decision matrix: ij m x n 13

Compute the distance of feasible PUP location from the fuzzy A + and fuzzy A − using the following equations: Distance from fuzzy positive ideal solutions A + :
( ) 14 where, j = 1, 2, 3, . . . , m.

A. Criteria Maps
Based on mentioned methods earlier to prepare criteria maps needed for this study, all of PUP locations in form of  Fig. 5. In Fig. 5(a), classes of distance to slum neighborhood are displayed in five colors. Moreover, map of accessibility classes is shown in Fig.  5(b), where interestingly there is no very low accessibility class in Central Bogor sub-district.
It can also be added that all sub-districts but Central Bogor sub-district have locations with very low accessibility though it does not mean that very low accessibility cannot be accessed by four-wheel vehicle as explained in criteria preparation. As for the slope classes, a map in Fig. 5(c) shows that nearly all locations have very gently slope. In addition, the land value of feasible locations for PUP development is displayed in four classes within Fig. 5(d). For Fig.s 5(c) and 5(d), displayed classes are not five but depend on where the locations fall within class range, for example in Fig. 5(d), there is no location within the best land value or in other words no feasible location for PUP development has lowest value range.

B. Criteria Weights from IF-AHP
Firstly, all DMs importance weights were scored using categories from Table 1. In each category, the score for each DM was normalized using equation 3. For instance, DM A has master degree level of education therefore DM A had a score of 2 but because it was normalized using equation 3, hence DM A has normalized score of 1 as can be seen in Table 5. The final result indicates that DM A is very important followed by DM B with important, and DM C has medium importance weight.
For further computation, influence weight of each DM (l k ) is needed to be calculated using equation (4). As DM A is very important therefore according linguistic terms in Table 2, DM A has IFN of (0.90,0.05,0.05). When its IFN of DM A was inputted into equation 4, therefore l A = 0.9+(0.05*(0.9/(0.9+0.05))) = 0.95. When normalized with the sum other experts' influence weight, hence the final l A weight become 0.41. The next step is to gather experts' preference number for pairwise comparison. Herein, three DMs were sent forms to be filled with preference numbers and later converted into IFNs according to Table 3.
All of experts' preference numbers in pairwise comparison within Table 6 were integrated using IFWA in equation 4. For example to determine r 12 within R matrix, the value from Table 6 for each DM in designated for first column and second row where DM A (1/7), DM B (1/3), and DM C (1/9). Hence, their IFNs can be linked with Table 3, and be converted as DM A (0.18, 0.62, 0.20), DM B (0.27, 0.13, 0.60), and DM C (0.00, 1.00, 0.00). These values were computed using equation (4) to yield µ ij between C 2 in second row and C 1 in first column, and the computation process can be described as  Table 7 that the µ ij in r 12 is 0.17. The whole resulted matrix R can be observed in Table 7.
Furthermore, by applying equation 6 and 7 the weights of criteria for prioritizing PUP development in feasible location can be determined. Hence, w accessibility = 0.261, w land value = 0.259, w distance to slum = 0.255, and w slope = 0.225. These weights are used for further computation within fuzzy TOPSIS.
The fact that IF-AHP method in this study yields in highest weight for accessibility, it indicates that experts from urban park planners put access to feasible location as prerequisite before starting procurement or even development. From several previous studies, accessibility is emphasized as factors to determine suitable locations for urban green space or urban park ( [3], [13]). Hence, it is acceptable for this study that accessibility has the highest weight considering its vital role to access the PUP locations.
As land value criterion gains second place weight based on IF-AHP, it indicates that feasible locations for PUP development need to be purchased first by the Government of Bogor Municipality. The land value for PUP development is very important because budget to purchase feasible location needs to be planned first and consulted with people's representatives in the parliament. This can be a major constraint for urban park planners and decision makers in Bogor Municipality considering that according to [14] the land value in Jabodetabek has extremely high growth when compared to other cities in Indonesia and some other cities in Asia.
As one of the ultimate goals for PUP development in Bogor Municipality to serve closer to the mostly needed communities such as slum neighborhood and poor Land value 1/9 1/9 1/5 1

C. PUP Development Priority
The spatial distribution of PUP feasible locations development priority based on CC i value is displayed in Fig. 6. The priority classes were generated using equal interval method in ArcMap 10.3, namely very high, high, medium, low, and very low. Very high priority means that feasible locations within this class are very urgently to be constructed for PUP based on closesnest to slum neigborhood, better accessibility, gentle slope, and better land value. Interestingly, as it can be observed in Fig. 6 there is no feasible location for PUP development in Central Bogor sub-district with CC i value within very high priority class. It can be caused by its distance to slum areas where it is farther than other locations, not to mention the higher land value. Furthermore, some of very low priority locations in the northern Bogor Municipality in Fig. 6 correspond with distance from slum neighborhoods in Fig.  5(a).
Since most of the feasible locations have similar value range in accessibility and slope criteria as can be seen in Fig.s 5(b) and 5(c), it can be interpreted that these two criteria give no substantial change for PUP development priority. On the contrary, distance to slum and land value criteria shown in Fig.s 5(a) and 5(d) have more different values among feasible locations. It can be sumarized that distance to slum and land value are two criteria which provide more influential to CC i value in each feasible location when compared to accessibility and slope.
For area calculation in each priority class, very high priority class has around 0.14 km 2 , while high priority class has approximately 0.12 km 2 . As it can be observed in Fig. 7(a), medium priority class has the biggest area around 0.38 km 2 , followed by low priority class with 0.29 km 2 . Based on the official area of Bogor Municipality around 118.5 km 2 , the total area of feasible location for PUP development is around 1.076 km 2 or 0.91% of the Bogor Municipality.
It can be observed in Fig. 7(b) that very high class priority provides 10 locations for PUP development, while medium class priority consists of 26 locations. In total, there are 77 feasible locations for PUP development.

IV. dIscussIons
Results gained in form of priority classes for PUP development in feasible locations within this study have given decision makers a clear map for options. Plus, it gives decision makers abundance of location alternatives for PUP development in Bogor Municipality. When problems might arise within locations of very high priority which can prevent PUP construction, decision makers have choices of feasible locations in high or medium priority classes. And since its locations are scattered in all of six sub-districts, the development of PUP in these feasible locations might satisfy the population in each subdistrict. From the perspective of tackling the problems in slum areas, these feasible locations of PUP development add to the existing efforts performed by the Government of Bogor Municipality and central government to improve slum areas such as KOTAKU (Kota tanpa kumuh) and BSPS (Bantuan stimulan perumahan swadaya).
The superiority of applied fuzzy TOPSIS in this study is reflected by the results of this study where priority ranks for the feasible locations of PUP development approach the closest distance for positive solutions such as accessibility and stay away from negative solutions such as land value. Though in previous studies ( [15], [3]), combination of AHP and TOPSIS with multi-criteria of GIS has successfully provided alternatives in searching location of urban parks and green spaces, but further special technique is needed when tackling the fuzziness of multi-spatial criteria found such as in this study. Furthermore, this study considers hesitancy and vagueness of experts' judgement through IF-AHP method beside the fuzziness of multi-spatial criteria which processed using GIS and fuzzy TOPSIS.
However, for further implementation of this result an updated ground checking is needed to anticipate recent land use changes. In addition, real construction development program should be based on available budget and therefore further study related to actual size of each location should be performed to plan the detail engineering design and eventually construction budget.

V. conclusIon
The combination of GIS, IF-AHP, and Fuzzy TOPSIS has succesfully resulted five priority classes of feasible locations for PUP development in Bogor Municipality. The very high priority class which has the biggest CC i values range (>0.654-0.76) provides 0.14 km 2 area of feasible PUP development with 10 locations. The biggest area for PUP development is generated by medium priority class with 26 feasible locations and approximately area of 0.38 km 2 .