Classification of security quality level using Fuzzy Logic study case: Balikpapan City

A liveable city is a city with a comfortable environment that gives its residents a sense of perfection to live and ease to do various activities. Balikpapan is one of major cities whose has the third-largest population in the province of East Kalimantan consisting of 6 districts namely, South Balikpapan, East Balikpapan, North Balikpapan, West Balikpapan, Central Balikpapan, and Balikpapan City. The consequence that arises from the large population is the increase in crime that affects the liveability in terms of security quality. In this study, Mamdani Fuzzy Logic is used to investigate the level of security quality of each sub-district in this city based on the crime figures. Moreover, the types of criminalities are categorized into four kinds, namely fraud, theft, immoral violence, and other crimes. Based on the result, it was found that the order of sub-districts with the best level of security is Central Balikpapan which is followed by Northern and Eastern Balikpapan with fairly good security status. Meanwhile, sub-districts with lax security are Western Balikpapan, Balikpapan City and Southern Balikpapan.


Introduction
Study of the sustainable and liveable city has received increased attention since it has multi aspects to consider [1]. Liveability of a city has become an essential concept in the field of planning by both researchers and government since it is requisite to have a comfortable environment such that the residents feel a sense of perfection to live and can do various activities. Yadav and Patel in [2] stated that the city's functions for boosting economy, well-providing employment, better health service, and many more things have been perceived as a solution for the community. Many previous researchers had conducted studies of the liveable city toward sustainable development which can be found in [3], [4], and [5].
In deciding whether a city is categorized as liveable or not, one of the methods that can be used is the Fuzzy Inference System (FIS). Rizki and Tipa in [6] employed this method to find the criminality level in Batam City, while Yenni and Utnasari in [7] used Fuzzy Logic to predict the city's criminality rate. Meanwhile, the inconsistent result of the liveability of a city can be occurred according to the variables that are used in the research. Hence, Chen in [8] proposed to use the Multi-MCDM and Hopfield Neural Network which combines some methods to measure the sustainable liveable city. The other results can be seen in [9] and [10].
According to this topic, on the other hand, Balikpapan is one of the most crowded city with the third-largest population in East Kalimantan Province, Indonesia. Based on the data in [11], this city consists of six sub-districts which has been occupied by 667,118 people in 2019. The number of residents' growth implies not only increasing demand for living space but also some unfavorable side impacts such as the decrease of socio-economic quality and the rise of criminality number. Regarding criminality, Hardianto in [12] stated that the insufficient wage rate may have a negative strong correlation to this problem. Additionally, the supporting data from [13] stated that there were 11,509 number of crime in Balikpapan. Although there was a slight decrease in 2017, the main types of criminality in the city which need utmost attention are fraud, theft, and (immoral) violence. These problems surely bring impact to the liveability of Balikpapan City. The study of liveable in the city was previously done by [14] who investigated the rating level of each sub-district by the education sector. Therefore, it is interesting to investigate further this liveability based on another sector. Hence, this research is aimed to implement the Mamdani Fuzzy Logic that focuses on the number of criminality to derive the rank of sub-district based on its security quality.

Fuzzy Logic implementation
In this section, the rank of security quality of each sub-district in Balikpapan City is processed using Mamdani Fuzzy Logic method as follow:

Data collection
Data was acquired from the Report of Police Office which includes criminality reports in Balikpapan City along 2019. This data, then, is classified into four classes of criminality as shown as in table 1.

Fuzzification
In this step, the crisp value is transformed into a fuzzy set. The variable inputs which are used in this research are fraud, theft, immoral violence, and other crimes, while the fuzzy set contains three categories, namely high, fair, and low. Firstly, the number of theft of each sub-district from table 1 is categorized into three types of membership function, those are low theft ( ), fair theft ( ), and high theft ( ), which defined as : Three are three types of membership function for fraud, those are low fraud ( ), fair fraud ( ), and high fraud ( ): As the previous type of criminality, the number of immoral violence of each sub-district is then classified into three types of membership function, those are low immoral violence ( ), fair immoral violence ( ), and high immoral violence ( ): Moreover, the three types of membership function for the other crimes of each sub-district are low other crimes ( ), fair other crimes ( ), and high other crimes ( ): Lastly, the quality of security is also classified as bad ( ), fair ( ), and good ( ) as follow: After defining the membership function, the number of criminality in Table 1 is substituted into the defined membership functions. Hence, the result is summarized in table 2.  1. If one of criminality is high, except for the other crime, then the security quality is bad; 2. If one of criminality is fair and low, except for the other crime, then the security quality is fair; 3. If there are three types of criminality which are fair, and the rest is low, then the security quality is bad; and 4. If there are two types of criminality which are fair, and the rest is low, then the security quality is fair. Therefore, all the rules are explicilty listed in table 3.
For example, since indicates "low" for all type of criminality, so it gives ( ) ( ) for Southern Balikpapan. In this article, we enlist only the values which are not zero. Consequently, Table 2 and 3 altogether yield table 4.   (13) to (15), then we derive new functions which figure out the solution region of each sub-district. First of all, since the quality of security for Subdistrict of Eastern Balikpapan is fair, so we define a new function ( ) as follow: Then, the function for Sub-district of Southern Balikpapan which has a bad quality of security is ( ) as shown in (18).
After that, the function for Sub-district of Balikpapan City which has a bad quality of security is ( ) which is given in (19).
Moreover, the function for Sub-district of Western Balikpapan which has the bad quality of security is ( ) which can be seen in (20).
The next is the function for Sub-district of Northern Balikpapan which has the fair quality of security is ( ) .
All figures for each sub-district are presented in Figure 2.

Defuzzification
Defuzzification is a process to produce a quantifiable result in crisp from the corresponding membership function. In this research, the centroid method is used to find the center of the area ( ̅) from the derived function in (18) to (22). Let ( ) is a function defined on the interval , -, then the center this area is given by From the figure 2 (a), it is evident that the centroid of Sub-district of Eastern Balikpapan based on (17) is 5 which mean that it has a fair quality of security (see figure 1). Furthermore, the centroid of the Southern Balikpapan using the function in (18) is which infer that the security in this sub-district is bad. The rest scores and level of each sub-district are given in table 6.