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Multigranulation Set-valued Rough Set Model

Set-valued data set (which is short for SvDS in the following parts) is a generalized model of classical data base. Different from objects in single-valued data sets, some objects in an SvDS could get over one value under an attribute. In some existing works, researcher studied SvDSs based on tolerance relation and which has some drawbacks. For example, the tolerance relation cannot reflect the common degree of two object. So in this paper, we try to define similarity relation (which is short for SR in the following parts) and use similarity class (which is short for SC in the following parts) to classify the universe of discourse. And then, based on SCs, we further define lower and upper approximations (which are short for LA and UA respectively in the following parts) of an object set so that we can study SvDSs systematically. Moreover, we can then discuss the properties of these approximations under single-granulation and multi-granulation, respectively.