An Experimental Study on the Behaviour of Fuzzy Quantification Models

In this paper we evaluate empirically whether there exist significant differences in the numerical results produced by six well-known fuzzy quantification models when applied to the evaluation of unary and binary fuzzy quantified statements on numerical data sets. The models we analyzed are: Zadeh's scalar and fuzzy cardinality, Yager's OWA, Delgado's GD, Sugeno integral and Vila's VQ. These models were tested by evaluating the degree of fulfillment they produced on fifteen numerical data sets from the UCI Machine Learning repository for all the possible fuzzy quantified statements generated by partitions of up to seven quantifiers and linguistic terms of the variables involved. We conducted tests of statistical significance for these evaluation results under a pair-wise comparison. Results indicate that no significant differences were found among the models for unary quantifiers involving a single imprecise property, with a single exception of very limited outreach. For binary quantified statements involving two imprecise properties, significant differences were observed in general among all the pairs of fuzzy quantification models under study. Therefore, in spite of unary models fulfill different theoretical properties, the models under study exhibit very similar empirical behaviour. For binary models, results point out that the selection of a particular model should be guided by other criteria (e.g. the properties they fulfill) different than their experimental behaviour, which is empirically proved to be different.