1. Introduction
Various cities that are industrialized and developing across the globe greatly suffer from contaminated air for the greater part of the year [
1]. Dirty air has great impact globally and locally; if not paid attention to, it can become a threat to all living things, especially to humans. From the authors of [
2,
3,
4], many countries in Africa have attained decades of industrialization and development but without a proper plan to handle the air pollution problem.
Many developed countries have tried to make use of current booming technologies to determine strategies and methods to improve air quality and, in the long run, mitigate the issue of air pollution but most countries in Africa still lack air pollution monitoring systems and do not have management strategies in place [
5,
6,
7].
There is a great need to pay attention to air pollution concerns in Africa where urbanization and industrialization continue to increase with the increasing population density. This paper focuses on the geographical area of Kampala City in Uganda East African region where the population numbers keep increasing higher every year. Moreover, industries are being opened and also a big number of second-hand vehicles and motorcycles, which are the major sources of transport, enter into the city at higher rates annually [
8].
According to the Air Visual’s World Air Quality Report, Kampala city is among the cities with the most polluted air in Africa [
9]. Air pollution has a great effect on health, alone causing millions of hospitalizations every year.
Major sources of air pollution in Kampala city include dust from unpaved roads and open burning of waste by individuals as a way of managing uncollected waste, which introduces dangerously large amounts of pollutants into the air via combustion. There are also massive amounts of dirty air coming from many factories and power plants around the Kampala area [
10,
11].
Another big contributing source of air pollution is vehicular emissions coming from many imported second-hand vehicles; the Uganda National Environment Management Authority (NEMA) estimates that more than 140,000 litres of fuel are burnt by idling cars every day in Kampala city because of ever-growing road traffic [
12].
A report compiled by Global Burden of Disease project indicates that exposure to dirty air is the fifth highest ranking risk issue for death, answerable for 4.2 million deaths from heart condition and stroke, carcinoma, chronic respiratory organ unwellness, and metabolic process infections; conjointly, an extra 254,000 deaths were owing to exposure to gas and its impact on chronic respiratory organ disease around the world. In Africa alone, there was an estimated one million deaths [
13].
Therefore, it’s a very important health factor to measure the quality of air. Information on air quality concentrations in a particular region and its health effects is usually presented via the Air Quality Index (AQI). The AQI presents air quality concentrations in a more understandable form to the public. It is a public information tool designed to help individuals in a particular society understand the effects of air quality on both health and the environment; it is a generalized way of describing the quality of air around the universe.
In this paper, the AQI is based on Kampala standards for air quality, which follow the Environmental Protection Agency (EPA) standards [
14]. The values of the Kampala Air Quality Index are divided into six groups: good, moderate, unhealthy for sensitive groups, unhealthy, very unhealthy, and hazardous. Different colors are assigned to each group. Thus, in this paper, the AQI prediction model for Kampala city is designed using the fuzzy logic inference system. In predicting the quality of air, traditional methods, such as clustering analysis, regression analysis and variance analysis, have been greatly used but these methods do not give the desired measurements in predicting the air quality, due to the non-linear relationship between pollutant datasets. The methods that were used in [
15] included the use of an impinge air quality testing apparatus, which is very expensive and requires a huge budget, which makes it heavy and difficult for developing countries governments to fund [
10]. The other approach is that samples of fine particulate matter (2.5) is collected at the end of each sampling period, stored in plastic petri dishes, sealed, and transferred to the U.S.A. for analysis.
Therefore, in this paper, a fuzzy based prediction model for predicting AQI based on the air pollutant concentrations in Kampala city is designed in order to provide the public with information about the quality of air and also the responsible authorities to take the precautions and decisions from an informed point of view of the levels of air pollutants. Fuzzy logic modeling is known to give accurate results in solving non-linear problems.
1.1. Main Air Pollutants
The AQI of Kampala is measured, following the three air pollutant concentrations in Kampala: nitrogen dioxide (NO), sulphur dioxide (SO) and particulate matter (PM) based on the 24 h average of hourly readings.
1.1.1. Nitrogen Dioxide
NO
is mainly produced in internal combustion engines burning fossil fuels, such as cars, power plants and house heaters. Direct exposure to the skin or eyes can cause irritation to the throat and nose, and it also burns. Long-term exposure to relatively low levels of nitrogen dioxide is believed to cause bronchitis and asthma, especially in children [
16]. Kampala has thousands of taxis, basically used for public transport as a major means of transportation around the city.
1.1.2. Sulphur Dioxide
SO
is emitted through the burning of fossil fuels (for vehicles, heating, and power generation) and processing of ores containing sulphur. Exposure to SO
causes irritation of the eyes and lungs, causing coughing and aggravation of chronic bronchitis and asthma. Higher SO
levels are correlated with mortality from cardiac diseases [
17].
Kampala city has a high number of vehicle growth and most of them are old fleets driven with dirty fuel on a poorly planned public transport system and road network [
18].
1.1.3. Particulate Matter (PM)
PM refers to a type of air pollutants which consist of a complex mixture of particles suspended in the air, with various sizes and compositions. They are produced by both natural and anthropogenic activities. The main sources of particulate pollution are industrial activities, power plants, motor vehicles, construction activity, fires and natural windblown dust. The major industries in Kampala include the following: sugar, brewing, tobacco, cotton textiles, cement and steel production [
19]. PM mass concentration is typically tracked as both PM
, the total mass of PM with a diameter of 10 micrometres or less, and PM
, the total mass of PM with a diameter of 2.5 micrometers or below (and a subset of PM
). This paper concentrated mainly on PM
, nitrogen dioxide and sulphur dioxide.
2. Materials and Methods
In this study, a simulation based on fuzzy logic techniques embedded within the MATLAB version R2017b software simulation environment was applied. In order to simulate the proposed model, the MATLAB Fuzzy Logic toolbox was used. Then, the fuzzy prediction model was modeled and its performance behavior was observed, using a set of three input parameters: indices of PM, indices of SO and indices of NO. The estimated Kampala Air Quality Index (KAQI) was considered as the output parameter. In order to process the fuzzy logic model, a rule-based Mamdani’s fuzzy inference system was used and later, defuzzification processes followed.
2.1. Fuzzy Modeling Approach
2.1.1. Description of Fuzzy Logic
In traditional logic, the degree of truth can be represented by either the values of 1 (true) or 0 (false), but this has limitations because some elements’ membership is unclear, thereby rendering traditional methods incapable of handling complex environmental problems that have some kind of vagueness in them. In a crisp set, an element is either a member of the set or not, but also crisp elements can belong to more than one set, for example, height measurements. Therefore, fuzzy logic comes in to cater to fuzziness in solving real-life problems. In fuzzy logic, the degree of truth ranges between 0 and 1, both inclusive. Fuzzy sets allow elements to be partially in a set.
Fuzzy logic helps to compute linguistic variables, that is, variables whose values are not numbers but words or sentences in natural or artificial languages as proposed by Dr. Loft Zadeh of the University of California in the 1960s [
20]. According to Banks [
21], fuzzy logic can efficiently handle soft computing complex issues. Its techniques have been widely applied in all aspects of today’s society, such as industrial manufacturing, diagnosis, automation control, academic education and forecasting. A linguistic variable is a collection of five things represented as <T(x), U, G, M> where
x is a variable name
T(x) is a set of terms;
U is universe of discourse;
G is set of syntax rules;
M is a set of semantic rules.
Fuzzy logic works well in designing non-linear complex control solutions with multiple parameters because of the following [
22]:
Fuzzy logic has the ability to describe systems in terms of a combination of numeric and linguistic means.
Fuzzy logic measures the certainty or uncertainty of the membership of an element of the set.
Fuzzy algorithms are often robust in the sense that they are not very sensitive to changing environments and erroneous or forgotten rules.
In the other words, the fuzzy logic method shows the satisfactory value of air pollutants in a continuous value between 0 and 1. Fuzzy logic uses if–then implication reference rules with suitable linguistic description rules. A fuzzy rule is written as
if situation, then conclusion [
23]. In this case, the situation is also called rule premise or antecedent. The conclusion part is called consequence or conclusion, that is, IF the “antecedent” is satisfied, THEN the “consequent” is inferred.
Therefore, the designed rules are inferred, according to the fuzzy inference knowledge base to generate a generic, fuzzy based algorithm. Then, the model designed as the output represents the fuzzy function to predict the Air Quality Index for Kampala city.
2.1.2. The Proposed Fuzzy Logic Control Model
The proposed prediction model is based on fuzzy control model reasoning to predict the Kampala Air Quality Index as a percentage of the given air pollutant status. For the simulations, we used MATLAB R2017b, an environment where the fuzzy toolbox logic controller is embedded.
The fuzzy control model is designed predict the KAQI based on a set of predefined parameters, which include NO, SO and PM.
To build the fuzzy logic system, the principle steps are followed as shown in
Figure 1. The design steps included during design are as follows: defining the input variables, fuzzyfication, formulation of fuzzy inference rules, defuzzification and model evalutation.
2.2. Defining the Input Variables and Fuzzyfication of the Values
In this paper, the KAQI model is designed on the basis of concentration levels of pollutants based on the Environmental Protection Agency air quality index guidelines.
As shown in
Figure 2, AQI ranges from 0 to 500 and is divided into five levels: good, 0–50; moderate, 51–100; unhealthy for sensitive groups, 101–150; unhealthy, 151–200; very unhealthy, 201–300; and hazardous, 301–500.
The higher the AQI value, the poorer the quality of air; the lower the AQI value, the better the quality of air. The three input crisp parameters used to define air quality in this paper include the following: nitrogen dioxide (NO), sulphur dioxide (SO) and particulate matter (PM). The output of the system is taken as KAQI. The inputs are taken in the form of linguistic variables as well as the output.
2.2.1. Selection of Membership Functions
A membership function (MF) is a function that specifies the degree to which a given input belongs to a set [
25]. The output of a membership function is also known as the degree of the membership function, where its value is always limited to between 0 and 1. Membership functions are used in the fuzzification and defuzzification processes to map the non-fuzzy input values to fuzzy linguistic terms and vice versa.
The Mamdani Fuzzy Logic Toolbox has many inbuilt membership functions.
In this paper, the triangular membership function, known as (trimf), is applied in the design of the proposed fuzzy based prediction model. The triangular membership function is computationally efficient and is used to normalize crisp inputs.
The Mamdani Fuzzy Inference System is suitable for designing AQI prediction models, as both the inputs and outputs of the Fuzzy Inference Systems are represented by the values of linguistic variables [
26]. In order to transform crisp input values into fuzzy values, the membership function for each input is determined.
The corresponding fuzzy membership values in this paper are defined as follows:
The intensity of nitrogen dioxide (NO) = Low, Medium and High
The intensity of sulphur dioxide (SO) = Low, Medium and High
The intensity of particulate matter 2.5 (PM) = Low, Medium and High
The KAQI is defined and estimated as the output by the following membership values: good, moderate, sensitive, unhealthy, very unhealthy, hazardous.
2.2.2. Formulation of Fuzzy Rules
In fuzzy logic, rules play an important role. They determine the input and output membership functions that are later used in inference process. They are represented by a generic form of if–then. A fuzzy rule maps a condition described by linguistic variables and fuzzy sets to a desired output.
To design the model, the boundary values of the universal sets for the input and output variables are determined.
The fuzzy sets to be defined in universes for the fuzzification process are identified. As shown in
Table 1, the boundary values of universal sets are set. Each variable is represented by three different fuzzy sets, ’Low’, ’Medium’, and ’High’ in these universes [
27].
In order to determine the boundary values for ’Low’, ’Medium’ and ’High’ fuzzy sets, the corresponding boundary values of the sets are defined in the form of ’Good’, ’Moderate-Sensitive’, ’Unhealthy-Very-Unhealthy-Hazardous’ and fuzzy set values are defined based on the lower and upper boundary values for the universal sets.
In this work, the values are defined following the boundaries indicated by the Environmental Protection Agency (EPA) standards [
14].
EPA is an international agency that prescribes standards and guidelines relating to air pollution as elaborated in
Figure 2 [
28].
Table 2 shows the boundary values of universal sets and fuzzy sets NO
, SO
, and PM
input variables. The membership functions for the input variables fuzzy sets are defined basing on the boundary values.
The selected output variable is KAQI and is represented by the six fuzzy sets, ’Good’, ’Moderate’, ’Sensitive’, ’Unhealthy’, ’Very Unhealthy’ and ’Hazardous’. The boundary values of these output fuzzy sets are determined by considering the value ranges used by the Environmental Protection Agency standards as indicated in
Table 3.
In
Table 4, the relationship between the input variables and output variables is determined by the rule base.
The fuzzy associative memory method is used to map input fuzzy values to corresponding output fuzzy sets in order to generate the inference rules. In this, the three variables represented by the three fuzzy sets, a total of twenty-seven rules, are generated in the following rule base: for 3 inputs (M) classified into 3 linguistic variables (N). M to the power N rules (M) are generated. Rules are formed based on the highest values of NO, SO and PM. To generate the rule base, we take into consideration all the pollutant concentrations, that is, if one of the pollutants is high, then the resultant KAQI will be Unhealthy, as clearly indicated in the rule base.