Regression analysis based on linguistic associations and perception-based logical deduction

We propose a new generalized model of linguistic variables based on fuzzy partition and its subpartitions. We use this new model for mining relationships between linguistic variables (linguistic associations) from a data set. These relationships can be interpreted as fuzzy IF-THEN rules in the implicative fuzzy inference engine, which is an extended version of the implicative inference called Perception-based Logical Deduction. We show that our extension leads to statistically significant improvements with respect to the previous model used with the help of original and successful Perception-based Logical Deduction. We perform the comparison with different measures of rule quality and five datasets. We can obtain improvements in prediction precision while retaining the interpretability of the models. We also compare our method with the classical machine learning methods and obtain a similar quality of precision, which is very encouraging because interpretability usually leads to worse precision.