\section{Conclusions}

The basic assumption we made in this paper is that the
choice to use small (or simple) associative classifiers can lead 
to more interpretable predictive models with no significant impact on classification effectiveness.
We considered a state-of-the-art associative classification algorithm, LAC~\cite{lac}, and following the Occam's Razor principle we show 
that this algorithm learns classifiers that are unnecessarily complex. Therefore, we propose an alternate classification algorithm, PE-LAC, 
which learns simpler classifiers, that are highly readable. The proposed PE-LAC algorithm evaluates each rule by taking into account multiple
 criteria simultaneously, such as: confidence, support, added-value, and Yules'Q. These criteria correspond to the dimensions of a rule-utility space.
 Then, we employ a central concept in Economics, known as Pareto Efficiency, in order to filter rules that excel in at least one dimension in the 
rule-utility space. We showed, using benchmark data as well as data obtained from recent application scenarios, that both LAC and PE-LAC are similar 
in terms of classification effectiveness, but PE-LAC learns classifiers that are orders of magnitude smaller/simpler than the classifiers built by LAC. This conclusion is supported by a number of paired and group-based significance tests. 
Also, we compared PE-LAC against CL-LAC, a filtering strategy which relies on closed rules, and the results show that: (i) PE-LAC builds smaller classifiers than the ones produced by CL-LAC, but in this case classification performance is similar, and (ii) CL-LAC builds smaller classifiers than the ones produced by PE-LAC, but in this case the classifiers produced by PE-LAC are more accurate than the ones produced by CL-LAC. An alternate strategy, which we call CL-PE-LAC, filters closed rules and showed to be competitive with PE-LAC, but in some cases the number of rules becomes excessively small compromising classification performance.
%For future work we intend to incorporate the rule filtering process into rule extraction. That is, instead of being filtered after being extracted from the training-set, we intend to avoid the extraction of rules that are not Pareto Efficient.
