Fuzzy set-based formalization of gradual patterns

In this paper, we attempt at providing a new formalization of gradual patterns based on fuzzy sets. In fact, in the last few years and over the last decade, the extraction of gradual patterns grasped the interest of the data mining community and several approaches were proposed to deal with such patterns. Gradual patterns of the form 'The more/less A, the more/less B' express the co-variation between the attributes A and B. All the proposed approaches differ depending on the way they count the frequency (i.e.; the support) of a pattern, or depending on the way the attributes are treated, i.e.; if they are considered as monotonically growing within the range of values or if they are considered as a fuzzy partition. For instance, the pattern 'The older the age, the higher the salary' is called to be a fuzzy gradual pattern. In this paper, we propose a novel formalization of such patterns.