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Quantitative rough sets based on subsethood measures. (English) Zbl 1339.68249
Summary: Subsethood measures, also known as set-inclusion measures, inclusion degrees, rough inclusions, and rough-inclusion functions, are generalizations of the set-inclusion relation for representing graded inclusion. This paper proposes a framework of quantitative rough sets based on subsethood measures. A specific quantitative rough set model is defined by a particular class of subsethood measures satisfying a set of axioms. Consequently, the framework enables us to classify and unify existing generalized rough set models (e.g., decision-theoretic rough sets, probabilistic rough sets, and variable precision rough sets), to investigate limitations of existing models, and to develop new models. Various models of quantitative rough sets are constructed from different classes of subsethood measures. Since subsethood measures play a fundamental role in the proposed framework, we review existing methods and introduce new methods for constructing and interpreting subsethood measures.

##### MSC:
 68T37 Reasoning under uncertainty in the context of artificial intelligence 03E72 Theory of fuzzy sets, etc.
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