Methodology for Determining Potential Locations of Illegal Graffiti in Urban Spaces Using GRA-Type Grey Systems

Abstract

This paper defines the term “graffiti” and outlines the origins of this concept. The terminological arrangement allowed for the subject of this research, i.e., illegal graffiti, to be situated in reality, i.e., an urban space. It was assumed that the existence of the tag was associated with a disturbance of spatial order and had an impact on safety in a space. This, in turn, is related to whether the principles of sustainable development in the social dimension are applied. This paper makes reference to theories of security in a space (the “broken windows” theory and the strategy of Crime Prevention Through Environmental Design, CPTED) and shows the problem of illegal graffiti against the background of these theories. A new research aspect of the occurrence of illegal graffiti (scribbles and tags) within urban space is the features that determine its emergence in a spatial dimension. The aim of the analyses in this paper is to obtain information on which geospatial features are generators of illegal graffiti. The research field was limited to the space of one city—Olsztyn—with the assumption that the proposed research methodology would be useful for the spaces of other cities. The research methodology consists of several steps: firstly, we determined a list of features in the surroundings of illegal graffiti using direct interviews, and secondly, we analyzed the frequency of occurrence of these features in the researched locations in space. The next step was to standardize the obtained results using the quotient transformation method with respect to a reference point, where the reference point is the sum of all observations. After that, we assigned ranks for standardized results. The last stage involved an analysis using the GRA type of grey systems to obtain a sequence of strengths of relationships. This sequence allowed us to determine which of the features adopted for analysis have the greatest impact on the creation of illegal graffiti in a space. As indicated by the strength of the relationship, in the analyses conducted, geospatial features such as poor sidewalk condition and neglected greenery have the greatest impact on the occurrence of illegal graffiti. Other features that influence the occurrence of illegal graffiti in a given space include a lack of visibility from neighboring windows and the proximity of a two-way street. It can be assumed that these features are generators of illegal graffiti in the studied area and space. The poor condition of the facade has the least impact on the possibility of illegal graffiti occurring in a given space.

1. Introduction

The term “graffiti” was first used in 1856 by archaeologist Raphael Garrucchi during his exploration of the ruins of the city of Pompeii by the eruption of the volcano Vesuvius, which occurred on 24 August, 79 CE [1]. The term is derived from the Italian word graffito. Literally translated, graffiti is an inscription or drawing on the wall of a house, wall, fence, etc., and today is most often made with spray paint [2]. Archaeologists and art historians use the term graffiti to describe drawings or inscriptions carved on vessels, stones, or walls, based on the Italian words graffito, meaning to shade with lines, and graffirare, meaning to scrape or scratch, as well as the Greek word graphein, meaning to scrape, engrave, draw, or write [3,4,5,6]. According to a definition by another author, graffiti is an image painted on the walls of houses, other walls, and fences, generally in public places [7].

A dictionary of the English language defines graffiti as words or drawings on walls and other surfaces in public places [8]. There are positive terms used to refer to this type of creation, for example, spray art or street art. Therefore, graffiti is often considered a type of artistic creation that involves creating images in public places [9]. It has become customary to use the word graffiti to describe any forms of on-wall art created using different techniques from ancient or even prehistoric times to the present day [5]. In colloquial terms, graffiti means writing or a drawing placed on a house wall, a fence, or pavement. Such an inscription is usually of a humorous or political nature and is made with spray paint.

The above-mentioned explanations of the term define graffiti as a drawing or inscription made using various techniques (painting, scratching, engraving, scraping), executed on different surfaces (a wall, a fence, pavement, stones, other vessels), of a decorative nature, or conveying a message of a different nature, e.g., humorous, artistic, or political.

The custom of writing on walls in order to convey specific messages had its origins in ancient times. Among the most common motifs of the Nakum graffiti, as in other Mayan centers, there are representations of human figures, animals, deities, buildings, and objects of ceremonial significance, as well as patolli game boards, digits, or glyphs. Most of them were made using the engraving technique; there are also a dozen or so representations painted in black and red paint. From the perspective of their subject matter, they demonstrate direct links to the life of the elites of the classical period. Another significant fact is that approx. 80% of Nakum graffiti was made on residential buildings and the residences of the ruling class, with only 20% made within temples [10]. Ancient sources report that after the Battle of Chaeronea, numerous inscriptions ridiculing Philip II and the Macedonians appeared on the buildings of the city of Athens. Inscriptions ridiculing or criticizing certain politicians and even the Caesars (e.g., Nero) were also common in Rome. These inscriptions, however, did not always refer to politics; the anonymous authors often expressed in them their adoration for certain athletes, hetaeras, or other individuals [11]. Thousands of inscriptions and drawings from ancient times have been discovered on walls in Pompeii and Herculaneum, cities of the Roman Empire destroyed by the volcanic eruption of Mount Vesuvius in the year 79. They are mostly of a vulgar and obscene nature, but there are also manifestations of political satire among them [5]. Equally often, when searching for examples of early graffiti, drawings with political or entertaining content found in Pompeii or in the area of the site known as Hadrian’s Villa are also reported [1].

Graffiti also existed in early Christian art. It was painted on everyday objects, gravestones, house walls, places of worship, and in the immediate vicinity of martyrs’ graves. These forms of graffiti are among the sources of historical and theological knowledge of the early Christian period, as they show the times of creation of artistic monuments and enable the identification of the graves of martyrs and saints [12].

In more recent times (1795–1831), there lived Josef Kyselak—a low-ranking Viennese civil servant, tourist, and vandal, traveling through Austro–Hungarian territory. He used to scratch and paint his name or the phrase “Kyselak was here” in ink on walls, rocks, sculptures, and other surfaces. His tags are still in existence today and have become a specific tourist attraction [1].

Graffiti, in the modern sense, dates back to the late 1960s and early 1970s, when stylized writings, made using markers or paint, of the names or nicknames of young people, who wanted to make their mark on an urban space and marked the area in this way, became popular. According to researchers, as early as the 1960s, there were two graffiti writers active in Philadelphia, namely Cornbread and Cool Earl, who painted their names on the walls of tenement houses [1]. Graffiti writers are regarded as forerunners of street art, and their inscriptions are referred to as tags [7].

However, it is the 17-year-old New Yorker of Greek origin named Demetrius, living on 183rd Street, the first to sign his nickname of TAKI 183 on the New York underground, who is usually considered the modern global precursor of graffiti art. After a while, imitators appeared, and soon, one could already see tags by Che 159, Elsie 134 or Julio 204 on the street walls. An interview conducted in 1971 in the New York Times with TAKI 183 unintentionally created him as an urban hero, sparking an avalanche of graffiti as more and more New York teenagers began to follow his example. Historians working on the subject very often assume this moment as the beginning of, if not graffiti in general (a broad understanding of the term), then at least of modern graffiti [1,5,7,13]. The travels of New York graffiti writers led to the graffiti phenomenon spreading throughout the United States and then Europe. By the early 1980s, graffiti had already appeared in all major European cities, and a movement of graffiti artists, derived from the punk movement, emerged in Amsterdam and Madrid. The art of graffiti in Europe developed under the influence of hip-hop, inspired by the American model [14].

The United States, with the main center initially being the city of New York, has become the birthplace of graffiti. It was in the New York underground system that “battles” took place between rebellious youth and the New York police who were fighting their activities [15].

Graffiti writers know perfectly well that their actions are illegal, but they are also perfectly aware that they are not facing serious criminal responsibility for their deeds, or perhaps they are simply unaware of this responsibility. The surroundings and the state of their development often result in graffiti artists perceiving a space as being nobody’s, without an administrator who cares about it, and therefore appropriating it to commit vandalistic acts [1,13].

Behind the act of illegally writing on walls, there is a complex set of perceptions of space, which may sometimes be one of the motives for action, reasons, and rationalization. A certain way of thinking due to the perception of the existing state of space causes the graffiti writer, roaming through the city, to hunt for places to commit their vandalistic act. A graffiti writer searching for a place knows what they are looking for and has certain qualities encoded in their mind that influence this choice. They have a kind of imaginary map of the space in their head, created from features that delimit a useful fragment from the general urban space and help select a site for the execution of illegal graffiti.

The organization of a space affects the way people behave when they are in it. We can distinguish spaces that attract desirable behaviors, referred to by Hall as sociopetal spaces or, according to Russel, positive and pleasant spaces. The second, radically different type of spaces are those that repel desirable behaviors or attract negative ones, termed by Hall as sociofugal spaces and, by Russel, negative and unpleasant spaces [16,17].

The behavior in a space, in the context of its appropriation for tagging, is influenced by numerous factors. There are spaces that attract illegal graffiti writers and those that repel them. Certain places discourage graffiti writers from creating illegal works, while others are of interest to vandals. A graffiti writer reads a space as they move through the city and classify it as either suitable for graffiti or not. Identifying the elements in a space that stimulate illegal graffiti will help identify potential sites for the emergence of graffiti. In this aspect, one should look for elements of a space that make it attractive to the graffiti artist.

There are certain qualities in the minds of graffiti writers that make a particular place attractive for tagging. Based on the observation of the tags occurring in a space, it is possible to determine what characteristics influence a graffiti writer to choose a certain place. Specific features filling the space influence the choice of a site for making a tag. An analysis of the surroundings of places in a city that are marked by tags will enable the classification of the features that contribute to the emergence of this unfavorable phenomenon within the space, which will allow the places favorable to illegal graffiti to be identified.

The phenomenon described in urban criminology and sociology as the “broken windows” theory, developed by G. L. Kelling and C. M. Wilson, assumes that if a vandal encounters a broken window, this may prompt them to break another one or inflict other damage. Tolerance of minor offenses encourages the vandal to commit more serious ones in the manner of an epidemic that starts with breaking a window in a house and ends with the gradual degeneration of an entire neighborhood. This is because one broken window is a signal that no one really cares; therefore, breaking another window poses no threat whatsoever, while a space where damage is quickly repaired deters hooligans because they feel the space has an administrator [1,18,19].

The broken windows theory is reflected in the occurrence of tags in a space. It has been observed that an emerging tag is a signal that the particular space belongs to no one since nobody reacts to the incident. This fragment of space is, in the graffiti writer’s opinion, uncared for, which becomes a kind of permission for the vandal to develop the space in their own way, which is why more and more tags emerge exponentially. On the other hand, it is to be expected that where a space is protected against graffiti or a tag is quickly removed, it is a sign that the space will deter potential vandals.

As Professor Loidl wrote, “the quality of the space stretching between the houses constitutes the soul of the city” [20]. In 1971, Jeffery’s Crime Prevention Through Environmental Design (CPTED) strategy was introduced. The concept is based on the belief that the physical shape of the surroundings evokes, in the potential offender, pleasant or unpleasant sensations that either stimulate or constrain their will to commit an offense. The CPTED model is based on a stimulus–response model in which the human mind receives either reinforcing or grossly discouraging stimuli from the surrounding environment. Practical solutions for applying the CPTED strategy are generally based on four simple principles: natural observation (the offender feels as though they are being watched), natural supervision (a clear demarcation between private and public spaces, which has a positive effect on reducing crime), separation of an area (creating a feeling of identification with the designated space in the inhabitants), and management and maintenance (an area that is clean, well maintained, and in a good state of repair shows that it has an owner, and repels a potential offender) [19,20,21].

The main point of the CPTED concept was that if the reinforcing stimuli are eliminated, the crime will not be committed. Similarly, as regards the creation of tags, if the factors stimulating the choice of space for tagging are eliminated, the tag will not emerge in the space.

The substantive issue of the undertaken research is the view presented in many studies, according to which the elements creating the conditions for the development of crime are the characteristics of the physical space in which the criminal commits their act and the elimination of hazards through the appropriate shaping of physical space, which is among the basic forms of ensuring security [21,22,23,24,25].

The graffiti writer’s choice to occupy locations in a space for expressing their own particular aesthetics by creating tags is certainly determined by the surroundings of the place. Hence, this study inventoried the features found in the surroundings of illegal graffiti within the urban space.

2. Materials and Methods

2.1. Determination of Features Contributing to the Occurrence of Illegal Graffiti Within the City Space

The main assumption behind this study is the possibility of diagnosing the spatial problem of the spread of vandalism in the form of illegal graffiti within the city space based on messages carried by the state of spatial development. This paper is concerned with the features that are found in the surroundings of illegal graffiti, which arouse vandals’ interest in specific places in a space.

It also addresses the problem of the occurrence of the phenomenon of illegal graffiti in urban spaces, with the main aim of this paper being to identify the features that are the generators of this phenomenon in a space. The analysis was divided into stages performed in the following order:

• An inventory of illegal graffiti in selected areas of the city of Olsztyn (Poland)—a quantitative analysis;
• The identification of the factors surrounding a place in a space that is marked with tags;
• The determination of the importance of the features forming a spatial wasteland using the GRA-type grey system method.

2.2. Identification of the Factors Surrounding a Place in a Space That Is Marked with Tags

One of the most important principles in geography is that elements that are close to each other have more similarities than objects that are far apart from each other. This idea is often referred to as “Tobler’s First Law of Geography” and can be summarized as “everything is related to everything else, but things that are close to each other are more related than distant things” [26].

As already written in an earlier section of this paper, the condition of a space influences a graffiti writer’s selection of a particular place to commit their vandalistic act. The very existence of specific elements in a space directly contributes to the hazard of tagging. In line with the assumption of the inventory, the tagged sites were classified along with their surroundings, and the features surrounding the sites were identified. This study is an attempt to identify factors in a space that stimulate the execution of illegal graffiti in the space. During the face-to-face field interview, it was determined what features accompanied the tags existing in a space. In their surroundings, there were geospatial features such as the poor condition of facades, poor condition of the pavement, neglected greenery, lack of visibility from private windows, and proximity to a two-way road.

The poor condition of the facades indicates clear signs of technical degradation of the buildings, such as surface dirt, structural cracks, flaking plaster, bulges, and traces of mold and moisture, as well as visible defects in insulation materials. Similarly, the poor condition of the sidewalks is manifested by numerous damages and deformations of the surface, including cracks, gaps, unevenness, and protruding elements, sometimes overgrown with ruderal vegetation, indicating a lack of systematic maintenance. Neglected greenery was also noticeable in the surroundings of the studied buildings, defined as areas lacking care and maintenance. This was evidenced by weedy gardens, untidy shrubs, chaotically growing roadside vegetation, and degraded, littered, and trampled lawns. Another significant feature was the lack of visibility from private windows, which, in line with the CPTED concept, refers to residents’ limited ability to naturally observe public spaces. In the cases studied, this particularly concerned marked walls that were located out of sight of neighboring buildings, reducing the potential for social control. The final feature inventoried was the proximity of a two-way street, identified by its presence in the immediate vicinity of the wall. This parameter is important because it influences the exposure of the space, the traffic density in a given area, and the degree of accessibility of the space to illegal graffiti artists.

2.3. Grey System Against the Background of Static Analyses

Spatial analyses are carried out to obtain new information from the input data accepted for the analysis. The analyses in this study aim to find out which geospatial features are generators of illegal graffiti.

There are many ways to solve problems using spatial data analyses. The first group is represented by statistical methods that enable the valuation of features and the determination of the strength of the relationship between its individual elements accepted for research. These include correlation methods, variance analysis, location quotient [27,28,29,30,31,32], and direct comparisons [33].

The second group of methods includes decision support systems used for optimization, classification, or problem-solving purposes [34]. They are used in areas where spatial data or data based on the experience and knowledge of experts is needed. In these cases, the analysis is used to solve particularly complex tasks and different spatial problems. When analyzing spatial data, information on their boundaries, internal structure, and interaction with surroundings is needed. More often than not, however, such data do not exist, while the available data are incomplete and uncertain [35]. The methods by which they can be analyzed and evaluated include probabilistics, fuzzy sets, and rough sets [36,37].

Another group of data analyses includes the statistical techniques known as regression analysis, which determines the effect of independent variables on the course of phenomena. Regression is, therefore, a quantitative description of the dependence of phenomena on certain independent variables [38]. Multiple regression analysis finds numerous applications in socio–economic geography and spatial economics and enables the determination of general relationships between the factors under study. The interpretation of the results obtained focuses on determining which variable or group of independent variables explains the variation in the phenomenon under study to the greatest extent [39]. In order to obtain a model describing these relationships, an entire statistical analysis needs to be carried out, starting from determining the number of observations by testing the assumptions (linearity, normality) and ending with considering the limitations of the method [40]. In the course of the analysis, this is not always possible to accomplish, which makes the analytical process complex or even unfeasible.

As an alternative to the spatial data analysis methods cited above, especially to the regression analysis, Juo-Long Deng’s grey systems theory can be used. This theory has been developed specifically for the analysis of modern systems while taking into account the sparse information of an uncertain and incomplete nature [41,42,43,44].

This extremely effective method of modeling and forecasting short-term time series can be applied to all fields that rely on quantifiable models with little (even several) incomplete and uncertain data, from social sciences, economics, and economy to technical sciences [45,46]. The grey system theory has proved itself in economic forecasting [47], agriculture [48], medicine [49,50], demand forecasting [35], tourism enterprise development [51], and noise source location [52]. In practice, the Grey Relational Analysis (GRA) is most commonly used. It uses information on the similarities and differences between the series of data describing the objects under consideration that can be ranked [44].

Thanks to the application of appropriate procedures, the grey system theory allows (based on only partially known information) additional, previously non-disclosed, useful information to be generated, searched for, reached, and extracted. This facilitates both the modeling and monitoring of the behavior of real systems and the description of the rules that govern their changes [44]. Hence, a GRA-type grey system was selected in order to learn about opinions as to which geospatial features result in the emergence of illegal graffiti within a space. The analysis was carried out based on the analysis of features in the vicinity of illegal graffiti obtained from face-to-face interviews. The advantage of the grey system over regression analysis is that a small amount of necessary data can be taken for analysis. In the regression method, it is recommended that the amount of data to be analyzed should be at least 10 to 20 times as many cases (observations, measurements, respondents) as there are variables (questions) in it. Otherwise, the ratings of the regression lines will be unstable and will change significantly as the number of cases increases (Handbook of Statistics). On the other hand, the minimum number of observations that enables the construction of a grey system model, regardless of the number of features taken for analysis, amounts to four [53]. It was demonstrated that a stable sequence of relationship strength for five features was achieved for 20 observations [54].

The aim of the analysis in this study is to explore the relationships between multiple independent variables (the occurrence of geospatial features) and the dependent variable (the occurrence of illegal graffiti in a space). The result of the analysis will be the establishment of a relationship strength sequence that enables the determination of which features accepted for analysis have the greatest effect on the emergence of illegal graffiti in a space. The method selected for analysis is an alternative to the regression method, as it allows for the same information to be obtained in a much simpler way.

2.4. Characteristics of the Grey System Theory

When observing and considering the functioning of systems, information on their boundaries, internal structure, and interaction with surroundings is needed. In practice, information about complex systems is most often incomplete, uncertain, and, sometimes, even scarce [46].

According to the theory of grey systems, which was developed in 1982 in China and originated from Huazhong University professor Juo-Long Deng, the following systems are distinguished:

• White (white box), of which we have full knowledge—certain information;
• Black (black box), of which we know nothing, as we only have the opportunity to observe the input and (or) output of a complex system—uncertain information;
• Grey (grey box), of which we have limited information—information of an intermediate character between certain and uncertain [55].

Most of the time, the world is described by grey information, and many phenomena occurring in it are uncertain—for example, the weather, earthquakes, or even agricultural yields—even though we know what has been sown, in what quantity, and how it has been cultivated. Moreover, since observations (measurements, market research results, opinions, etc.) are scarce, the obtained information on the system behavior is incomplete. In practice, however, it is precisely this incomplete and uncertain information that provides the basis for the need to assess the performance of the system, predict its behavior, and make various functional, operational, and strategic decisions of great technical and social importance [44]. Considering information of such a diverse nature facilitates the application of modeling using grey systems. The fundamental idea behind the application of the theory is to extract additional white and grey information from the available uncertain and incomplete information at the expense of grey and black information. This is equivalent to a reduction in the proportion of black, i.e., uncertain information. For revealing information, whitening operators are used. Grey systems are used when imperfect information is dealt with in the analytical process. The advantage of grey systems over the other commonly used methods cited above is that no specific internal form is required here, with the identification of the limits of the numbers being sufficient. The absence of the need to determine the internal form of grey numbers results in the processing of imperfect information being performed in a simple, accurate, and unambiguous manner [44].

2.5. Analysis in Terms of the Accepted Input Data Using the Grey Relational Analysis Method

The grey system theory enables the determination of the strength of relationships between the variables of the Grey Relational Analysis (GRA) [44,56]. Using the grey incidence (relation) analysis method, it is possible to determine the absolute degree of grey incidence of the observed system factors and characteristics. The research procedure relating to GRA is described in Refs. [35,53] and comprises several stages: defining the observation vectors, calculating the reflection of the observation vectors, calculating the measures of behavior, calculating the value of the absolute degree of grey incidence (the similarity coefficient), and determining the order of influence of the studied system factors on the system characteristics.

The first step is to define the vectors of system observations, which contain information on the system characteristics (X₀) and the factors of system behavior (X₁, X₂, ..., X_k). The number of system behavior factors is determined by the assumed number of observed variables. Each vector contains information on a particular variable obtained from a specified number of respondents. The essence of grey modeling is to describe the behavior of the system observed in reality in the form of a forecast (endogenous) variable: X⁽⁰⁾(k), where k = 1, 2, ..., and n is a set of explanatory variables that are the determinants of the forecast variable condition. Therefore, an endogenous process observable in reality, given as X⁽⁰⁾(k), is explained over time by the number n of independent (explanatory) variables [53].

The general vector of system observations has the following form, as seen in Equations (1) and (2):

$$X_0= \left(x_0\left(1\right),x_0\left(2\right),\dots ,x_0\left(n\right)\right)$$

(1)

$$X_k=\left(x_k\left(1\right),x_k\left(2\right),\dots ,x_k\left(n\right)\right)$$

(2)

where

k—the number of variables observed (system’s behavior factors);

n—the number of respondents.

The next step is to calculate the so-called reflection of the observation vectors by zeroing the initial vector values. This operation enables the smoothing of incidental disturbances and highlights the evolutionary tendency of the grey system’s behavior [53]. This operation is performed according to the following Equations (3) and (4):

$$X_i^0=\left(x_i^0\left(1\right), x_i^0\left(2\right),\dots ,x_i^0\left(n\right)\right)$$

(3)

$$x_i^0=x_i\left(k\right)-x_i\left(1\right)$$

(4)

The next step is to calculate the behavior measures obtained by means of summing and subtracting their vector values, as shown in Equations (5)–(7) [35,53]:

$$\left|s_0\right|=\left|{\sum }_{k=2}^{k=n-1}{x}_0^0\left(k\right)+{\displaystyle \frac{1}{2}}{x}_0^0\left(n\right)\right|$$

(5)

$$\left|s_1\right|=\left|{\sum }_{k=2}^{k=n-1}{x}_i^0\left(k\right)+{\displaystyle \frac{1}{2}}{x}_i^0\left(n\right)\right|$$

(6)

$$\left|s_0-s_1\right|=\left|{\sum }_{k=1}^{k=n-1}\left[x_0^0\left(k\right)-x_i^0\left(k\right)\right]+{\displaystyle \frac{1}{2}}\left[x_0^0\left(n\right)-x_i^0\left(n\right)\right]\right|$$

(7)

The next step is to calculate the absolute degree of grey incidence, i.e., the similarity coefficient ε between the observation vectors X₀ and X₁, X₂,… X_n, as seen in Equation (8) [35]:

$${Ɛ}_{0i}={\displaystyle \frac{1+\left|s_0\right|+\left|s_i\right|}{1+\left|s_0\right|+\left|s_i\right|+\left|s_0-s_i\right|}}$$

(8)

Using this measure, one can assess well the similarity of behavior of a pair of vectors and also assess their degree of interrelation if it is known that one of them represents a factor affecting the grey system and the other represents the responses of the system [53].

The following variables were adopted to investigate the features that are generators of illegal graffiti in a space:

• Poor condition of the facades (X₁);
• Poor condition of the pavement (X₂);
• Neglected greenery (X₃);
• Lack of visibility from neighboring windows (X₄);
• Proximity to a two-way road (X₅).

3. Results and Discussion

3.1. Inventory of the Occurrence of Features in the Research Sample

The inventory was aimed at determining the geospatial features that are found in the surroundings of a tagged site. The sites for the study were randomly selected and included 134 locations. For the detailed investigation, walls (multi-family houses, tenement houses, fences, and other structures) covered by illegal graffiti were taken into account. During field interviews, geospatial features were identified in the vicinity of illegal graffiti.

The frequency analysis aimed to determine which geospatial features occur most frequently in the vicinity of a site marked with illegal graffiti. The task was to determine the occurrence of a particular feature and, subsequently, its intensity at locations that have proved attractive to graffiti writers for the execution of illegal graffiti.

The results of the frequency analysis are expected to indicate the cause of the emergence of illegal graffiti in the form of tags by identifying features in their surroundings. An analysis of the frequency of illegal graffiti in quantitative terms on 134 building walls showed that 133 of them were located near a two-way road in the study area. The next most common characteristic in the vicinity of illegal graffiti was the lack of visibility from private windows (130 of 134 cases analyzed).

In terms of the frequency of the occurrence and impact on the emergence of the phenomenon of tagging, the subsequent features are those resulting from poor management of the space: neglected greenery, poor condition of the facades, and poor condition of the pavement, respectively (102, 90, and 84 out of 134 cases analyzed) (

Table 1. The importance of a feature for the existence of tags and scribbles in a space. Source: own elaboration.

Feature Name	Number of Places with Tags from the Inventory	The Frequency of the Occurrence of a Feature in the Examined Objects
Proximity to a two-way road	133	99%
Lack of visibility from neighboring windows	131	97%
Neglected greenery	102	73%
Poor condition of the facades	90	67%
Poor condition of the pavement	84	62%

).

This study determined the frequency of the occurrence of particular features in percentage terms in the 134 cases under analysis. The most frequently noted feature in the sites under study was the proximity to a two-way road, followed by the lack of visibility from private windows (approx. 99% and 97% of the analyzed sites). The least frequently observed feature was the poor condition of the pavement (62% of the inventoried sites) (Table 1).

In order to plan a space so as to eliminate the occurrence of illegal graffiti from it or to take action to eliminate the hazard of the phenomenon of illegal graffiti from a space, it is necessary to learn about the elements that generate this phenomenon. In addition to the quantitative inventory, the surroundings of the graffiti under assessment enabled the examination of what spatial elements surround the site of graffiti occurrence. Based on the results obtained, an analysis was conducted to find out which features make a site in a space a target of illegal graffiti artists. To this end, the GRA-type grey system was used. The results obtained in the form of a sequence of feature significance will enable the determination of which features are most related to the existence of illegal graffiti in a space.

3.2. Input Data Analysis

The analysis conducted at the first stage of the research selected features from the research using face-to-face interviews in the field on a sample of 134 sites. This study relied on the quantitative identification of features surrounding illegal graffiti in a space (X_i). The data obtained were then standardized using the quotient transformation method in relation to a reference point, i.e., the sum of all observations (X_s) (9) [26].

$$Y={\displaystyle \frac{X_i}{X_s}}$$

(9)

where

Y—standardized results;

X_i—the frequency of occurrence of features in the studied space;

X_s—the sum of the numbers of feature occurrences in the examined space.

The standardized results were then assigned ranks [56]. A scale from 1 to 5 was adopted, where 1 was the least important and 5 was the most important for the occurrence of illegal graffiti in a space (

Table 2. Standardized and ranked results from face-to-face interviews for 134 observations. Source: own elaboration.

Feature Name	Poor Condition of the Facades	Poor Condition of the Pavement	Neglected Greenery	Lack of Visibility from Neighboring Windows	Proximity to a Two-Way Road
The number of occurrences of a feature in the examined space	84	90	102	131	133
Standardized results	0.16	0.17	0.19	0.24	0.25
Rank	1	2	3	4	5

).

Another aim of this study was to examine how the ε similarity coefficient values develop in terms of the number of observations considered in the construction of the model. The similarity coefficient values were presented for the observed system characteristics, where (X₀) is the existence of illegal graffiti in a space with the system behavior factors, and (X₁, X₂, X₃, X₄, X₅) are the features found in the surroundings of illegal graffiti that were adopted for this study. The conducted analyses yielded values of the epsilon similarity coefficients, where models were built for 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, and 134 observations, each time determining values for the absolute degree of similarity ε (

Table 3. ε similarity coefficient values in terms of the number of observations for 134 sites. Source: own elaboration.

Number of Observations of Similarity Factor	ε1	ε2	ε3	ε4	ε5
5	0.50926	0.50595	0.50649	0.50610	0.50909
10	0.50463	0.50287	0.50311	0.50305	0.50435
20	0.50231	0.50140	0.50153	0.50154	0.50213
30	0.50151	0.50092	0.50099	0.50102	0.50138
40	0.50115	0.50068	0.50074	0.50078	0.50104
50	0.50093	0.50054	0.50059	0.50064	0.50083
60	0.50078	0.50045	0.50050	0.50053	0.50069
70	0.50067	0.50038	0.50043	0.50046	0.50059
80	0.50059	0.50033	0.50037	0.50041	0.50052
90	0.50052	0.50030	0.50033	0.50036	0.50045
100	0.50047	0.50027	0.50030	0.50033	0.50041
110	0.50043	0.50024	0.50027	0.50030	0.50038
120	0.50039	0.50022	0.50024	0.50027	0.50035
130	0.50036	0.50021	0.50022	0.50025	0.50032
134	0.50035	0.50020	0.50022	0.50024	0.50031

).

Relationship order sequences were then determined for individual observations. It is noted that the relationship strength order is stable for five of the studied features at 20 observations and is as follows: ε₂ > ε₃ > ε₄ > ε₅ > ε₁ (

Table 4. Relationship strength sequences for 134 observations. Source: own elaboration.

Number of Observations	Relation Strength Order
5	ε2 > ε4 > ε3 > ε5 > ε1
10	ε2 > ε4 > ε3 > ε5 > ε1
20	ε2 > ε3 > ε4 > ε5 > ε1
30	ε2 > ε3 > ε4 > ε5 > ε1
40	ε2 > ε3 > ε4 > ε5 > ε1
50	ε2 > ε3 > ε4 > ε5 > ε1
60	ε2 > ε3 > ε4 > ε5 > ε1
70	ε2 > ε3 > ε4 > ε5 > ε1
80	ε2 > ε3 > ε4 > ε5 > ε1
90	ε2 > ε3 > ε4 > ε5 > ε1
100	ε2 > ε3 > ε4 > ε5 > ε1
110	ε2 > ε3 > ε4 > ε5 > ε1
120	ε2 > ε3 > ε4 > ε5 > ε1
130	ε2 > ε3 > ε4 > ε5 > ε1
134	ε2 > ε3 > ε4 > ε5 > ε1

).

The obtained results lead to the conclusion that for the five analyzed features, it would be sufficient to carry out an inventory of 20 locations where illegal graffiti occurs in the space. In order to confirm the thesis that 20 sites are sufficient to obtain a stable relationship strength sequence for the five features under study, an additional analysis was performed. It was assumed that the positions may differ depending on their location within the urban area, their affiliation with different housing associations, and different property management policies. Therefore, the random selection of 20 sites was abandoned, and one site each from the 20 districts of the city under study was accepted for further analysis. As in the first analysis, the occurrence of features in the area under study was standardized using the quotient transformation method in relation to a reference point, i.e., the sum of all observations. The standardized results were then assigned ranks from 1 to 5 (

Table 5. Standardized and ranked results from face-to-face interviews for 20 observations. Source: own elaboration.

Feature Name	Poor Condition of the Facades	Poor Condition of the Pavement	Neglected Greenery	Lack of Visibility from Neighboring Windows	Proximity to a Two-Way Road
The number of occurrences of a feature in the examined space	10	11	15	19	20
Standardized results	0.13	0.15	0.20	0.25	0.27
Rank	1	2	3	4	5

).

In the next step, the values of the epsilon similarity coefficients were determined for the models built based on 5, 10, and 20 observations (

Table 6. Epsilon similarity coefficient values in terms of the number of observations for 20 sites. Source: own elaboration.

Similarity Factor Number of Observations	ε1	ε2	ε3	ε4	ε5
5	0.50943	0.50575	0.50617	0.50633	0.50909
10	0.50472	0.50272	0.50292	0.50329	0.50435
20	0.50231	0.50135	0.50143	0.50164	0.50206

).

Finally, relationship order sequences were determined for 5, 10, and 20 observations (

Table 7. Relationship strength sequences for 20 observations. Source: own elaboration.

Number of Observations	Relation Strength Order
5	ε2 > ε3 > ε4 > ε5 > ε1
10	ε2 > ε3 > ε4 > ε5 > ε1
20	ε2 > ε3 > ε4 > ε5 > ε1

).

For the analysis of features obtained from the observation of 20 sites, a stable relationship strength sequence was obtained with five observations. It should be noted that the same sequence of relationship strength, namely ε₂ > ε₃ > ε₄ > ε₅ > ε₁, was obtained for the 134 and 20 field sites under study.

The conducted analyses enable the conclusion that using the Grey Relational Analysis method for the five features adopted for the analysis, a stable model—i.e., a sequence of the ε similarity coefficient relationship order—is obtained with a relatively small amount of observation data, namely twenty with 134 observations and five with 20 observations. The obtained research results confirmed the conclusions reached in the authors’ earlier publication, cited in Chapter 2.3. Hence, when examining five traits, the optimal number of observations should be 20.

The result of the conducted analyses is a relationship strength sequence that enables the determination of which features adopted for analysis contribute the most to the emergence of illegal graffiti in a space. As indicated by the relationship strength sequence, for both analyses, the features that have the greatest impact on the occurrence of illegal graffiti include X₂ (poor condition of the pavement) and X₃ (neglected greenery). The next features contributing to the occurrence of illegal graffiti within a space are X₄ (lack of visibility from neighboring windows) and X₅ (proximity of a two-way road). It can be assumed that the above features are generators of the emergence of illegal graffiti in a space. The feature having the least impact on the possible emergence of illegal graffiti in a space is X₁, i.e., the poor condition of facades. The results are presented in a table where the first column lists the similarity coefficients in the order of the strength of the relationship and the second column contains the appropriate names of the features (

Table 8. Similarity coefficients according to the sequence of relation strength and trait. Source: own elaboration.

Similarity Coefficients	Feature Name
ε2	poor condition of the pavement
ε3	neglected greenery
ε4	lack of visibility from neighboring windows
ε5	proximity to a two-way road
ε1	poor condition of the facades

).

4. Conclusions

This paper proposes a methodology for identifying places in the city space exposed to illegal graffiti. The methodology allows for determining a list of features surrounded by illegal graffiti using direct interviews. After analyzing the frequency of the occurrence of these features in the studied locations and standardizing the obtained results, we obtain data that, appropriately ranked, constitute the input material for conducting the analysis of grey GRA-type systems. The goal is to obtain a sequence of relationship strengths that allows for determining which of the features adopted for analysis have the greatest impact on the creation of illegal graffiti in the studied space.

The spatial features that are generators of illegal graffiti can vary. Spaces are also characterized by a variety of development methods. The demand for information relates to a particular place and a specific time. The identification of spatial features in the vicinity of illegal graffiti involves conducting costly and labor-intensive research. This paper proposes a simple-to-implement method for obtaining information that can be applied to any area of research. GRA-type analysis enables the identification of interrelationships between different factors and their impact on the system under study. The information processed by this method allows for the interdependence of observation vectors to be assessed, the effectiveness of responses to possible situations to be evaluated, and optimal decisions to be made in this respect in an uncomplicated manner. In addition, the results obtained are reliable after analyzing uncertain, sparse, and incomplete data.

This paper describes the strategies shaping safe spaces in the city, outlines the statistical methods used in spatial data analysis, and cites the grey system theory, which enables the analysis of sparse, incomplete, and uncertain data. As recent research and applications have shown, grey systems allow for many assumptions about statistical methods to be omitted, with the results obtained being reliable despite the small number of observations accepted for analysis.

The argument in favor of applying a method based on grey systems is that the method does not require quantitative restrictions on representative samples of data and that these do not have to meet the formal requirements imposed by statistical sampling. The use of a methodology that includes the analysis of grey systems allows for the determination of minimal data sets (data minimization). For the five features adopted for this study using a GRA-type system, obtaining a stable order sequence of the strength of the ε similarity coefficient relationship was achieved for twenty observations with 134 research sites and for five observations with 20 research sites included in the model. This method, compared to commonly employed methods such as regression, is easier to implement and carry out because having test results from a few or several objects in a space can yield a sequence of significance for the features adopted for the analysis.

The example discussed in this publication is a proposal for the application of Grey Relational Analysis-type systems to optimize the management of urban spaces in terms of eliminating features that are generators of illegal graffiti. This, in turn, is related to the application of the principles of sustainable development, mainly in the social dimension. A number of features were identified in the studied space, indicating its degradation and low utility quality. The most significant were the poor technical condition of the facades and sidewalks, manifested by structural damage, dirt, and lack of infrastructure maintenance. Another significant element was the neglected greenery, whose lack of maintenance diminished the aesthetic appeal of the surroundings and intensified the impression of abandonment. Another characteristic was the lack of natural observation of a space from private windows, which limited the potential for social control and aligned with the issues analyzed within the CPTED concept. Additionally, the proximity of a two-way road was a significant spatial context, affecting the accessibility and visibility of the studied spaces. The features whose presence in a space is conducive to the emergence of graffiti should be transformed in such a manner that they discourage a potential graffiti writer from carrying out their intended activity. Neglected elements of space—for example, a lawn, pavement, or uncontrolled greenery—should be regenerated, as proposed in the “broken windows” theory by G. L. Kelling and C. M. Wilson and presented in an earlier section of this paper. Not all features can be subject to change, such as the form of a space, for example, the type of road, which is an environment conducive to the creation of graffiti. The features can be described as permanent, yet they should be made subject to an appropriate procedure to ensure that the space is protected against vandalism. The preventive forms for these features can include monitoring, intensified patrols by security services, the use of fences, or the use of graffiti-proof paints. The possibility of observation from private windows is also a feature that is difficult to change, but during the design phase, it should be taken into account that the walls of buildings should be visible from the windows of other buildings.