Properties evaluation of an approach based on probability-possibility transformation

Abstract

The recent research on classification problems, in fields where vague concepts have to be considered, agree on the utility of fuzzy logic. An important step of inference engines preparation is the definition of fuzzy sets. When probability distributions of concerned variables are known, they can be used to define fuzzy sets, and different methods allow to perform this transformation. A method recently proposed by authors is compared here with other existing methods, in terms of assumptions and properties about the obtained fuzzy set, also considered with respect to the probability distribution it was calculated from. The best existing transformation in terms of compromise between consistency and specificity results to be a particular case of the proposed transformation, which can therefore be considered a more general method. Moreover, it enables, with a small loss of consistency, to find more interpretable fuzzy sets, while the case of less specific fuzzy sets is comprised and justified. © 2013 Springer Science+Business Media.