A new methodology for fuzzification of rough sets based on α-indiscernibility

This paper presents a new framework for fuzzification of rough sets when the objects are α-indiscernible, that is, indiscernible up to a certain degree α. To this end, a fuzzy proximity relation has been used. Basic properties of the so-called α-fuzzified rough sets are examined. Following Radzikowska and Kerre [28] approach, the technique is further generalized using t-norms and implication operators. Two algorithms followed by an example have also been presented for practical applications of the new technique.