Generalized fuzzy rough sets based on new fuzzy similarity relation

Abstract

Fuzzy similarity relations are equivalence class constructs involving a method of handling uncertainty in the feature space. Fuzzy influence value is an expression for quantification of an equivalence class, which describes similarity/dissimilarity between a pair of patterns pertaining to a single class/different classes. Formation of fuzzy similarity relations with the fuzzy influence value to describe the method of handling uncertainty in real life data is primary task. A new fuzzy similarity relation based on a fuzzy influence value is initially defined. A fuzzy rough set involving the lower and upper approximation of a set, based on the fuzzy similarity relation, is then modernized. Moreover, entropy for evaluating uncertainty is defined on basis of the generalized fuzzy rough sets. Several properties of rough set theory which involve in fuzzy rough set are discussed. Computation of fuzzy lower and fuzzy upper approximations of a set (fuzzy rough set) is illustrated using a typical data, as an example. Entropy values for the data comparing with an existing fuzzy rough entropy are provided. These values demonstrate that the proposed entropy is more effective for handling uncertainty arising in overlapping regions.