A new approach in Zadeh's classification: Fuzzy implication through statistic implication

In relationship to the classification of the various approaches to the fuzzy logic of Zadeh (possibilistic, probabilistic, veristic) [14] the implication according to Gras is introduced as a new approach with its own characteristics. The notion of statistical implication is based on the statistical comparison between the inclusion of sets observed in a population and one that would have comparable sets, but chosen casually in the same population. Such an approach has to do with, in particular, variables-intervals. Therefore, it is suitable for representing fuzzy implication. The experimental comparison with classic fuzzy implications (Reichenbach and Lukasievicz) confirms a better semantic adequacy. The implicative methods are implemented in the statistic software (CHIC 3.1). The new epistemological perspective opens interesting application perspectives. The implication of variables of interval of Gras is neither completely descriptive nor completely inferential. We are in the presence of a new epistemological approach to fuzzy implication. The implication of Gras keeps in mind richer semantics when it is experimentally compared with other classical implications such as that of Reichenbach and Lukasiewicz. This type of implication can perhaps have some more interesting results in the applications of the Artificial Intelligence.