A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators

Parametric Rough Sets with Application to Granular Association Rule Mining

Granular association rules reveal patterns hidden in many-to-many relationships which are common in relational databases. In recommender systems, these rules are appropriate for cold-start recommendation, where a customer or a product has just entered the system. An example of such rules might be “40% men like at least 30% kinds of alcohol; 45% customers are men and 6% products are alcohol.” Mining such rules is a challenging problem due to pattern explosion. In this paper, we build a new type of parametric rough sets on two universes and propose an efficient rule mining algorithm based on the new model. Specifically, the model is deliberately defined such that the parameter corresponds to one threshold of rules. The algorithm benefits from the lower approximation operator in the new model. Experiments on two real-world data sets show that the new algorithm is significantly faster than an existing algorithm, and the performance of recommender systems is stable