Defining rough sets as core-support pairs of three-valued functions

11/06/2020

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by   Jouni Järvinen, et al.

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We answer to the question what properties a collection ℱ of three-valued functions on a set U must fulfill so that there exists a quasiorder ≤ on U such that the rough sets determined by ≤ coincide with the core–support pairs of the functions in ℱ. Applying this characterization, we give a new representation of rough sets determined by equivalences in terms of three-valued Lukasiewicz algebras of three-valued functions.