Abstract
The present paper defines four new kinds of measures of roughness of covering rough sets induced by locally finite covering approximation (LFC-, for brevity) spaces which are generalizations of finite covering approximation spaces. More precisely, consider an LFC-space (U,C) and a nonempty set X(⊆U). Using a reduction of a given LFC-space (U,C), the present paper firstly establishes two types of rough membership functions of the set X with respect to LFC-spaces (U,C), where each of the cardinalities of the sets U, C, and X need not be finite. Next, it also develops another two kinds of notions of roughness of digital topological rough sets. Indeed, these notions are based on the concepts of accuracy of rough sets derived from LFC-spaces. Furthermore, we use them to the estimation of roughness of a covering rough set of X(⊆U). Besides, we estimate roughness of a digital topological rough set, such as measures of roughness of the Khalimsky and Marcus–Wyse topological rough sets. Moreover, we compare between the measures of the Khalimsky topological and the Marcus–Wyse topological roughness.
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