**4. Results**

results are expressed in the form of 'if…, then…' decision rules, which are sentences that decision-makers find easier to understand [29–31] and using only the most relevant attri-

In the case of air pollution problem at hand, for example, we can consider some different decision classes of pollution according to an increasing level of some micro-pollutants (SOx, NOx,…). Since some meteorological variables (conditional attributes/criteria) present a monotonic relationship with the degree of pollution (e.g. the air temperature, the degree of humidity) and other no (e.g. wind direction, etc.), it is very important from both the operational and methodological points of view to take into consideration and to exploit in the appropriate way in the description of the objects and in the rule induction attributes and criteria distinctly. Therefore, we have to consider the indiscernibility relation with respect to the former, the dominance relation with respect to the latter, and the assignment to ordered classes with

Greco et al. [26] proposed an approach for this kind of real-life multicriteria problems. This can be easily modeled by introducing some appropriate thresholds to discretize the conditional attributes and to characterize different levels of air pollution, for the decision classes.

Consequently, the rough sets could be very efficiently applied in the case of uncertainty derived from the granularity of information. Actually, granules of condition attributes/criteria (objects having the same descriptions or respectively belonging to the same dominating/dominated sets) are used to approximate granules of decision (assignment to some decision classes). The RSA is therefore very different with respect to the fuzzy sets, where the linguistic imprecision due to the use of natural language is mainly considered, and the membership function aims at indicating in what degree each object belongs to a particular class. Of course, the two approaches are not mutually exclusive, but they can actually be used in a complementary way [32–34]. Using a terminology from image representation, we could say that rough sets are related to the number of pixels of an image (its resolution), while the fuzzy sets represent the number of gray levels between black and white. At an operational level, the implementation of fuzzy sets always requires the definition and specification of particular membership functions, one for each attribute, not easy to specify analytically. Therefore, both classical rough set approach and fuzzy sets are sensitive to the specification of these values and both interesting and useful sensitivity and robustness analysis are actually useful and recommended by moving the level of the thresholds and other parameters [30, 35, 36]. It is not the case of DRSA, where actually no parameter should be elicited, but only some example of decision (from the past experiences of

No discretization is required with respect to criteria, using the DRSA.

6 Emerging Pollutants - Some Strategies for the Quality Preservation of Our Environment

from expert knowledge) is needed to model the preference of the decision-maker.

Air micro-pollution-analyzed data come from an air monitoring network, working since 1975,

ated in the province of Siracusa, in the region of Sicily. This industrial area was declared 'a

, including the towns of Priolo–Melilli–Siracusa, situ-

butes/criteria (i.e. some reduct).

respect to the decision.

**3. Data description**

covering an industrial area of 500 km2

In spite of the fact that data samples used are restricted to a relatively short period of time (each one only 2 weeks), their analysis allowed us to obtain some interesting results, both from methodological and from operational points of view, which give an idea of the knowledge extraction (in terms of decision rules) from available data using the considered approach and the possibility to use this new method to improve air pollution management. As mentioned before, the final results are expressed in the form of 'if…, then…' decision rules, using at any time a particular (relevant) subset of attributes (reducts), according to the season and the micro-pollutant considered at each time.

In the following sections of this chapter, just some examples of decision rules obtained in our study are presented, useful for understanding and describing concisely pollution effects caused by particular combinations of conditional attribute/criteria values. Such rules, as mentioned before, are very useful in explaining the main reasons of some particular pollution events and can be also used in forecast analysis and for decision support too. The rules were chosen as the most representative among those with the highest degree of confidence, indicating the relative frequency of antecedent ('if' part of the rule) also matching the consequent ('then' part of the same rule) of the considered rule. Apart from the analysis of SOx, CH<sup>4</sup> , and NMHC with respect to the January observations (**Tables 1**–**4**), the considered rules have a confidence equal to one, that means that all the objects match both the antecedent and the consequent in each rule [37, 41, 43].

These decision rules are presented in the form of tables which are very easy to read, showing in the first column the number of the rule and in the other columns the values of the conditional attributes/criteria characterizing that rule. These values are expressed as intervals with respect to attributes (corresponding to the partition of their domain) and as real numbers ('vertices' of dominance cones) with respect to criteria. The last columns of **Tables 1**–**3** display the confidence of each rule; in the other tables, the confidence of the rules is one. In particular, **Tables 1**–**4** show results from Melilli Monitoring Station during the month of January, and **Tables 5**–**7** show the results in Melilli Monitoring Station during the month of August. Each table concerns a different micro-pollutant.

The threshold interval values for the conditional attribute were chosen as following: hour: 0, 1, … 23 and wind direction: N (North), S (South), E (East), W (West), as main direction ±45°. On the contrary, the criteria values were automatically determined by the method applied for


them (DRSA). Since the dominance approach is also used for the decisional attribute, pollution is reached 'by definition' depending whether or not the observed value of micro-pollutant is at least equal to the threshold value defined by law and indicated in each table. They are usually some threshold values that it is not allowed to exceed more than three times a year. In each table, the conditional attributes/criteria are the following: Attribute 1: hour of observation; Criterion 1: air temperature (°C); Criterion 2: air relative humidity index (%); Criterion 3: wind speed (m/s); Attribute 2: wind direction; Attribute 6: wind direction (degrees) with

, confidence = 1.

**Rule Hour Air temperature Humidity Wind speed Wind direction Wind speed and direction**

**speed**

8 13–17 ≥9.5 0.21 9 14–17 N 0.21 10 13–17 134.2–190.2 0.21

**speed**

11 ≥11 0.36 12 E 0.40 13 107.3–149.7 0.37 14 E 107.3–149.7 0.42

**Wind direction**

Rough Set Applied to Air Pollution: A New Approach to Manage Pollutions in High Risk Rate…

; threshold = 950 μg/Nm**<sup>3</sup>**

**Wind direction** .

.

**Wind speed and direction**

http://dx.doi.org/10.5772/intechopen.75630

**Wind speed and direction**

**Confidence**

9

**Confidence**

16 66.4–111.5

19 ≥ 9.7 18.8–117.9

21 ≥ 53.8 67.3–111.5

respect to wind speed (measured by SODAR).

15 E

**Table 3.** Melilli monitoring station, January 2010 NMHC, threshold = 90 μg/Nm**<sup>3</sup>**

**Rule Hour Air temperature Humidity Wind** 

**Table 2.** Melilli monitoring station, January 2010 CH4

**Rule Hour Air temperature Humidity Wind** 

20 ≥ 49.6 E

22 ≤ 3.4 E

**Table 4.** Melilli monitoring station, January 2010 NOx, threshold = 20 μg/Nm**<sup>3</sup>**

17 11–14 ≥ 10.5

18 10–21 ≥ 75.5

**Table 1.** Melilli monitoring station, January 2010 SOx; threshold = 70 μg/Nm<sup>3</sup> . Rough Set Applied to Air Pollution: A New Approach to Manage Pollutions in High Risk Rate… http://dx.doi.org/10.5772/intechopen.75630 9


**Table 2.** Melilli monitoring station, January 2010 CH4 ; threshold = 950 μg/Nm**<sup>3</sup>** .

and the possibility to use this new method to improve air pollution management. As mentioned before, the final results are expressed in the form of 'if…, then…' decision rules, using at any time a particular (relevant) subset of attributes (reducts), according to the season and

In the following sections of this chapter, just some examples of decision rules obtained in our study are presented, useful for understanding and describing concisely pollution effects caused by particular combinations of conditional attribute/criteria values. Such rules, as mentioned before, are very useful in explaining the main reasons of some particular pollution events and can be also used in forecast analysis and for decision support too. The rules were chosen as the most representative among those with the highest degree of confidence, indicating the relative frequency of antecedent ('if' part of the rule) also matching the consequent ('then' part of the same rule) of the considered rule. Apart from the analysis of SOx, CH<sup>4</sup>

and NMHC with respect to the January observations (**Tables 1**–**4**), the considered rules have a confidence equal to one, that means that all the objects match both the antecedent and the

These decision rules are presented in the form of tables which are very easy to read, showing in the first column the number of the rule and in the other columns the values of the conditional attributes/criteria characterizing that rule. These values are expressed as intervals with respect to attributes (corresponding to the partition of their domain) and as real numbers ('vertices' of dominance cones) with respect to criteria. The last columns of **Tables 1**–**3** display the confidence of each rule; in the other tables, the confidence of the rules is one. In particular, **Tables 1**–**4** show results from Melilli Monitoring Station during the month of January, and **Tables 5**–**7** show the results in Melilli Monitoring Station during the month of August. Each

The threshold interval values for the conditional attribute were chosen as following: hour: 0, 1, … 23 and wind direction: N (North), S (South), E (East), W (West), as main direction ±45°. On the contrary, the criteria values were automatically determined by the method applied for

> **Wind direction**

**Wind speed and direction**

.

**Confidence**

**speed**

 ≥11.55 0.54 2 E 0.54 81.9–137.7 0.46 13–16 E 0.58 ≥52.3 E 0.58 ≥52.3 81.9–117.9 0.58 E 81.9–117.9 0.58 ,

the micro-pollutant considered at each time.

8 Emerging Pollutants - Some Strategies for the Quality Preservation of Our Environment

consequent in each rule [37, 41, 43].

table concerns a different micro-pollutant.

**Rule Hour Air temperature Humidity Wind** 

**Table 1.** Melilli monitoring station, January 2010 SOx; threshold = 70 μg/Nm<sup>3</sup>


**Table 3.** Melilli monitoring station, January 2010 NMHC, threshold = 90 μg/Nm**<sup>3</sup>** .


**Table 4.** Melilli monitoring station, January 2010 NOx, threshold = 20 μg/Nm**<sup>3</sup>** , confidence = 1.

them (DRSA). Since the dominance approach is also used for the decisional attribute, pollution is reached 'by definition' depending whether or not the observed value of micro-pollutant is at least equal to the threshold value defined by law and indicated in each table. They are usually some threshold values that it is not allowed to exceed more than three times a year.

In each table, the conditional attributes/criteria are the following: Attribute 1: hour of observation; Criterion 1: air temperature (°C); Criterion 2: air relative humidity index (%); Criterion 3: wind speed (m/s); Attribute 2: wind direction; Attribute 6: wind direction (degrees) with respect to wind speed (measured by SODAR).


greater than the threshold value. We observe that the selected rules involve in the conditional

Rough Set Applied to Air Pollution: A New Approach to Manage Pollutions in High Risk Rate…

In the following lines, some examples of how reading the decisional rules are presented from **Tables 1**–**7**. Rule 18 (**Table 4**): between hours 10.00 and 21.00, if the air relative humidity index

if the air temperature is at least 25.9°C and air relative humidity index lies in the interval

low confidence level; this means that the considered attributes are not sufficient to explain the phenomenon. Perhaps some attributes are missing and therefore, in order to improve this result, it would be useful to consider further attributes. This is another important methodological feature of the rough set approach, underlining that sometimes more information is needed to better describe some object in order to be able to arrive at well-founded conclusions, that is with a high degree of confidence. On the other hand, the same analysis regarding the observations of August gives very interesting results; we can observe the particular

direction and speed in NOx analysis (**Table 7**). We can also observe that sometimes (e.g. rules 12, 15, 23) it is possible to explain a result using only one attribute, that is with very short and simple decision rules. It should be remembered that a general property of the rough set approach is one that uses all conditional attributes; instead of only attributes from a reduct, we can obtain more concise rules, that is with a greater variety a fewer number of attributes

With respect to SOx, we used a greater value for the threshold in January than in August both in order to present the relative pollution level more clearly and to obtain an acceptable confidence degree for same decision rules. Both the analyses of NOx (**Tables 4** and **7**) give excellent results in terms of confidence with respect to all the decision rules obtained, where we can observe a greater relevance of the attributes hour of observation, air temperature, and humidity degree in the analysis of the January data, while a crucial role in the August results

Actually, a first idea about the relevance of the conditional attributes can be directly revealed by the presence frequency of each conditional attribute in the decisional rules, as shown in the **Tables 1**–**7** (see, e.g. how important the conditional attribute for air relative humidity is in **Table 5**). Some more sophisticatedly important indices can also be computed, for example, according to the Shapley value in the cooperative games in the framework of game theory; the main idea is to compute the contribution to the quality of results by adding another attribute/criterion in the conditional part of the rules, in other words, a degree of the involvement of each attribute in all coalitions of attributes, measuring therefore also the interaction (synergy or redundancy) between the considered attributes [20] (Greco, S. et al., 2001 b). It should be observed that this

level is at least 845 μg/Nm<sup>3</sup>

, with a confidence of 1. Rule 33 (**Table 6**):

http://dx.doi.org/10.5772/intechopen.75630

11

with a confidence of 1.

and NMHC of January 2010 (**Tables 2** and **3**) have a very

level (**Table 6**) and the crucial role of the wind

part only few attributes/criteria each time.

37.6–42.9%, then the CH<sup>4</sup>

The decision rules concerning CH4

in the conditional part of the rules.

is played by winds.

relevance of the degree of humidity in the CH4

**5. Discussions**

is at least 75.5%, then the NOx is at least 20 μg/Nm<sup>3</sup>

**Table 5.** Melilli monitoring station, august 2010 SOx, confidence = 1.


**Table 6.** Melilli monitoring station, August 2010 CH4 threshold =845 μg/Nm<sup>3</sup> , confidence = 1.


**Table 7.** Melilli monitoring station, August 2010 NOx, threshold = 20 μg/Nm<sup>3</sup> , confidence = 1.

With respect to the decision, in **Table 5**, we consider three decisional classes, coded as following according to the law: A (Emergency), B (Alarm), C (Alert). The corresponding decision rules are expressed in terms of 'at least (≥)' or 'at most (≤)'; therefore, for example, B–C means 'at most Alarm' and A means '(at least) Emergency'. In all the other tables, the decision rules indicate if the considered threshold values are overtaken or not.

The rules in all the above tables represent only a few of several rules obtained by applying the RSA and they are presented here just as examples of easily understandable samples of the results of this analysis. All these rules are of the type 'At least' with respect to the decision, in the sense that if the antecedence is verified, the level of the corresponding micro-pollution is greater than the threshold value. We observe that the selected rules involve in the conditional part only few attributes/criteria each time.

In the following lines, some examples of how reading the decisional rules are presented from **Tables 1**–**7**. Rule 18 (**Table 4**): between hours 10.00 and 21.00, if the air relative humidity index is at least 75.5%, then the NOx is at least 20 μg/Nm<sup>3</sup> , with a confidence of 1. Rule 33 (**Table 6**): if the air temperature is at least 25.9°C and air relative humidity index lies in the interval 37.6–42.9%, then the CH<sup>4</sup> level is at least 845 μg/Nm<sup>3</sup> with a confidence of 1.
