Mining Association Rules under Imprecision and Vagueness: towards a Possibilistic Approach

Fuzzy sets have already been used for association rules mining problem especially when data is quantitative and precise. Indeed, mining quantitative association rules among relational databases needs to partition the finite domain of quantitative attributes. However crisp partitions generate dilemma between support and confidence measures and produce undesirable threshold effects. Considering fuzzy partitions instead of crisp partitions have usually been proposed as a means to deal with these mentioned problems. Authors using fuzzy partitions have highlighted their interest and proposed the corresponding measures of support and confidence. However these approaches consider only precise and certain attribute values. Also, we propose in this paper to enlarge this framework and consider imprecise and uncertain quantitative data. The state of knowledge about such data is usually represented using a possibility distribution. For this purpose, a generalized possibilistic relational model is first proposed in this paper. Considering possibility distributions upon fuzzy intervals will leads us to introduce "gradual uncertainty rules". Measures of such rules are obtained by mapping fuzzy sets to crisp sets through alpha-cuts decomposition.