**6. Conclusions**

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,

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

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,

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

weighted sum or outranking methods for the comparative evaluation of some objects.

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

attribute is able to compensate the worst value on the other and vice-versa.

humidity degree, wind direction, …).

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 methodological and operational contributions of this exemplary application.

From the methodological point of view, the RSA allows us to take into consideration quantitative and qualitative data, without being in need of their arbitrary transformations.

The relevance of each subset of attributes/criteria is an output of the analysis, and not an input, and therefore does not require elicitation of a priori subjective weights.

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, support, confidence, etc.).

The results are presented in the form of 'if… then…' logical statements, decision rules expressed in simple language and very understandable for the decision-makers.

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

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 traceability of possible decisions.

Moreover, the results obtained point out other relevant profiles of the phenomenon considered. They clearly show, for example, the more or less important role played by each meteorological variable in the assignment of the actions to different pollution classes, the fundamental relationships between the antecedent (attributes and conditional criteria), and the consequent (ordered decision class). Furthermore, they provide interesting information about the semantic importance of quantitative and qualitative trade-offs between attribute/criteria, that is the role of combination of different levels and/or different pollutants considered together, showing therefore also the main interaction among some meteorological factors. Finally, using the RSA it is also possible to detect some particularly interesting threshold values, of one or more condition criteria, that can be considered as boundary values to be reached or to be avoided.

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The decision rules, in fact, could be the basis for the development of air-quality management strategies under the impacts of climate change, that is fundamentally a risk valuation and risk management process involving priority assessment of the impacts of climate change and associated uncertainties, including determination of air-quality targets, the selection of potential management options, and identification of effective air-quality management strategies through decision-support models.

The simple application of the method presented in this chapter shows how it can effectively help decision-makers in making appropriate responses to climate change, since it provides an integrated approach for climate risk assessment and management when developing air-quality management strategies. The risk-based decision-making framework can also be applied to develop climate-responsive management strategies for the other environmental dimensions and appraise costs and benefits of future environmental management policies.

Like any study, this could be improved and a more in-depth study can be carried out. For example, the original database could be enlarged, both in time limits and with reference to the variables considered. If we take into consideration data concerning different years or places, and analyze them by using the same methodology, we can, for instance, eliminate the peculiar effects related occasionally to atypical weather conditions. Moreover, if we extend the analysis to other meteorological variables we could obtain decisional rules which are sometimes easier, more intuitive, and more precise than those obtained by using a smaller number of descriptors.
