**5. Discussions**

**Rule Hour Air temperature Humidity Wind** 

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

30 14–20 ≥37.2

32 ≥26.3 ≥37.1 33 ≥25.9 ≥37.6, ≤42.9

**Table 6.** Melilli monitoring station, August 2010 CH4

34 E

36 ≥3.7 E

**speed**

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

 ≥72.8 B–C 24 ≤4.8 E A ≥31.3 ≥54 ≤3.9 A ≥37.2 ≥3.3 B–C ≥33 ≥3.7 B–C 28 ≥37 N C ≥31.9 N C

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

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

35 88.9–103.8

37 E 90.5–103

threshold =845 μg/Nm<sup>3</sup>

, confidence = 1.

, confidence = 1.

31 6–14 132.5–269.1

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

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

indicate if the considered threshold values are overtaken or not.

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

**Wind direction Wind speed and direction**

**Risk Class**

The decision rules concerning CH4 and NMHC of January 2010 (**Tables 2** and **3**) have a very 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 relevance of the degree of humidity in the CH4 level (**Table 6**) and the crucial role of the wind 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 in the conditional part of the rules.

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 is played by winds.

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 kind of importance is therefore an output of the analysis within the rough set approach, and not an input information, as usually happens when we use other approaches, as, for example, weighted sum or outranking methods for the comparative evaluation of some objects.

that if this value is smaller than 31.9, the SOx will never be at a level higher than the threshold

More generally, we can say that using this approach we are able to detect some threshold values of one or more condition criteria that can be considered as boundary values to be reached or to be avoided and the combination of two or more attributes/criteria that can be really dangerous for the air pollution. Of course, the meteorological variables cannot be changed by decision-makers. But the rules inferred using the rough set approach can be actually used as guidelines for forecasting in some areas particular cases of pollution events (e.g. emergency, alarm, alert), consequently giving people useful information and suggestions concerning the

The aim of this chapter is to give a first idea of the possibilities offered by rough sets data analysis in the field of air pollution management. In the following, we summarize its main

From the methodological point of view, the RSA allows us to take into consideration quantita-

The relevance of each subset of attributes/criteria is an output of the analysis, and not an

It is possible to underline the role of each attribute/criterion in terms of reducts and core; the attributes belonging to the core are indispensable, while the attributes belonging to the reducts are exchangeable with one another; the others are actually superfluous or redundant.

The significance of the results can be measured by peculiar indicators (quality, strength, sup-

The results are presented in the form of 'if… then…' logical statements, decision rules

It is not necessary to remove a priori some inconsistency in the data to be analyzed, but—on the contrary—also these inconsistencies are an important piece of information about the degree of uncertainty of the decision rules inferred (certain or approximate rules, degree of confidence, etc.).

From the operational point of view, the decision rules inferred can be used immediately for managerial purposes as guidelines for preventing or warning people about the risk of air pollution (emergency, alarm, or alert situations), when the weather conditions match or are

The decision rules are also able to explain the reasons of particular pollution occurrences, describing the consequences of different meteorological scenarios and their giving a trace-

methodological and operational contributions of this exemplary application.

input, and therefore does not require elicitation of a priori subjective weights.

expressed in simple language and very understandable for the decision-makers.

similar to those shown on the tables and to other rules not included in this chapter.

tive and qualitative data, without being in need of their arbitrary transformations.

ues' of the conditional criterion air of relative humidity.

. These rules, therefore, are able to give us useful information about 'critical val-

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

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

13

of 10/gr/Nm<sup>3</sup>

probable danger of air pollution.

**6. Conclusions**

port, confidence, etc.).

ability of possible decisions.

Moreover, the results also show interesting interpretations in terms of a particular kind of trade-off. From the analysis of the couples of decision rules (26,27) (32,33) we can easily observe some cases of trade-off between the values of the couple of attributes in the classical meaning of 'compensation'. From rules (32,33), there is a relationship between air temperature and degree of humidity, in the sense that the different values of air temperature can be compensated by the different degrees of humidity obtaining the same results in terms of pollution. A similar relationship can be observed in the pair of decision rules (26,27) with respect to the degree of humidity and wind speed. This means that a certain capacity of compensation is allowed (trade-off) between the performances of a couple of attributes: a better value on one attribute is able to compensate the worst value on the other and vice-versa.

By observing the following couples of rules (5,6) (9,10) (20,21), we can see that it is possible to obtain the same results in terms of level of pollution considering the combination of one (fixed) attribute/criterion and step by step another one associated with it (example of exchangeable attributes/criteria). In other words, the same decision could be described and explained by different rules, where at each time are present different combinations (in this case, couple) of attributes/criteria that, therefore, are able to describe the same phenomenon independently one another. So, for example, from the couple of rules (5,6), it can be observed that the same result in terms of level of pollution, with the same degree of confidence, is the consequence of the degree of humidity ≥52.3 and wind direction E (rule 5) or the consequence of the same degree of humidity associated with the wind speed and wind direction between 81.9 and 117.9 (rule 6).

Another similar observation can be made comparing rules 6 and 7, where again the phenomenon of exchangeable attributes can be observed that in this case are the air humidity and the wind direction. This means that using the RSA the same effect in the pollution class assignment can be obtained as a result of a combination of an attribute/criterion value each time with other different attributes/criteria, as a particular very interesting 'qualitative substitution effect' between different attributes/criteria. The exchangeable role played independently by some conditional attributes/criteria in combination with a given level of another conditional attribute/criterion (in the previous example, the degree of humidity or the wind direction and speed) results therefore in the assignment of an object to the same decision class of pollution.

With respect to the operational aspect of this approach, it is important to emphasize how obtained results can be used to capably support the decision-maker to manage the pollution risk. Actually, the information given by decision rules can help to understand the main reasons of a pollution event, giving us the explanation of this (its 'traceability') but also for preventing or forecasting dangerous situations, very probable when meteorological conditions similar to those described by the obtained decision rules are approaching (air temperature, humidity degree, wind direction, …).

Another very interesting result using this approach concerns the information we can receive by so-called non-activated rules in improving or in deteriorating the results of a decision. See, for example, rules from **Table 5** and at levels of air relative humidity index. It can be observed that if this value is smaller than 31.9, the SOx will never be at a level higher than the threshold of 10/gr/Nm<sup>3</sup> . These rules, therefore, are able to give us useful information about 'critical values' of the conditional criterion air of relative humidity.

More generally, we can say that using this approach we are able to detect some threshold values of one or more condition criteria that can be considered as boundary values to be reached or to be avoided and the combination of two or more attributes/criteria that can be really dangerous for the air pollution. Of course, the meteorological variables cannot be changed by decision-makers. But the rules inferred using the rough set approach can be actually used as guidelines for forecasting in some areas particular cases of pollution events (e.g. emergency, alarm, alert), consequently giving people useful information and suggestions concerning the probable danger of air pollution.
